Блог Анкара

■ n this Appendix you can photocopy these blank forms and fill them in,

Using the instructions provided here and within specific chapters. You can also print out the forms from www. wi ley. com/go/cbt.

The ‘Old Meaninq-Nert Meaning’ Sheet

The sheet has the three headings. Fill them in as follows:

1. In the first column, ‘Event’, record what actually happened.

2. Under ‘Old Meaning’ in the second column, record what you believe the event means about you.

This is your unhealthy core belief.

3. In the ‘New Meaning’ third column, record a healthier and more accurate meaning for the event.

This is the new belief that you can work on strengthening.

Head to Chapter 14 for a worked example of the sheet, and for more about reviewing past events.

Event

Old Meaning

New Meaning

The Cost-Benefit Analysis Form

Carry out a Cost-benefit analysis (CBA) to examine the pros and cons of something can help galvanise your commitment to change. You can use a CBA to examine the advantages and disadvantages of a number of things, such as:

Behaviours: How helpful is this action to you? Does it bring short-term or long-term benefits?

Emotions: How helpful is this feeling? For example, does feeling guilty or angry really help you?

Thoughts, attitudes, or beliefs: Where does thinking this way get you? How does this belief help you?

Options for solving a practical problem: How can this solution work out? Is this really the best possible answer to the problem?

Evaluate the pros and cons:

In the short-term In the long-term For yourself For other people

Try to write CBA statements in pairs, particularly when you’re considering changing the way you feel, act, or think. What are the Advantages Of feeling anxiety? And the Disadvantages! Write down pairs of statements for what you feel, do, or think Currently, And for other, healthier alternatives. Head to Chapter 8 for worked examples of the form.

The ‘Tic-Toe’ Sheet

TICs Are Task interfering cognitions, The thoughts, attitudes, and beliefs that get in the way of your progress. You need to respond with TOCs – task orienting cognitions, Which are constructive alternatives to TICs. The list of unhelpful attitudes (sand traps) in the nearby sidebar is helpful for getting some ideas about task interfering cognitions.

Fill out the Tic-Toe sheet by following these steps:

1. Identify the goal or task you want to focus on.

2. In the left column (TICs), list your thoughts, attitudes, and beliefs that get in the way of you achieving your aim.

3. In the right column (TOCs) put responses to each of your TICs that will help you achieve your goal or task.

Head to Chapter 17 for more on the Tic-Toe sheet.

Goal or task:

Task Interfering Cognitions (TICs)

Task Orienting Cognitions (TOCs)

The Zigzag Form

1. Write down in the top left-hand box of the zigzag form a belief that you want to strengthen.

2. In the next box down, write your doubts, reservations, or challenges about the healthy belief.

3. In the next box, dispute your attack and redefend the healthy belief.

4. Repeat Steps 2 and 3 until you exhaust all your attacks on the healthy belief.

5. Re-rate, from 0 To 100 Per cent, how strongly you endorse the healthy belief after going through all your doubts.

Refer to Chapter 15 for more information about the zigzag form.

HEALTHY BELIEF

THE

ZIG-ZAG

FORM

Rate conviction in Healthy Belief_%

ATTACK

DEFENCE

DEFENCE

ATTACK

Re-rate conviction in Healthy Belief_%

The Vicious Ftotfer

1. In the Trigger box, write down the trigger that makes you feel anxious or upset.

2. In the central circle, write down the key thoughts and meanings you attach to the trigger.

3. In the flower petals, write down the emotions, behaviours, and sensations you experience when your uncomfortable feeling is triggered. In the top petal, write down what you tend to focus on.

Chapter 7 has loads more about the vicious flower exercise, and a filled-in example.

Trigger:

The Task Concentration Sheet

Head to Chapter 5 for more about the task-concentration exercise, and a filled-in example.

The ABC Form 1

1. In the ‘Consequences’ box, point 1, Write down the emotion you’re feeling.

2. In the ‘Consequences’ box, point 2, write down how you acted.

3. In the ‘Activating Event’ box, write down what triggered your feelings.

4. In the ‘Beliefs’ box, write down your thoughts, attitudes, and beliefs.

5. In the ‘Thinking Error’ box, consider what your thinking errors may be.

Refer to Chapter 3 for more detailed instructions on filling out the first ABC form.

Date

The’ABC Form #11

Disputing (Questioning and Examining) and Generating Alternative Thoughts, Attitudes, and Beliefs: 1. Identify your thinking errors’ at B (e. g. Mind Reading, Catastrophising, Labelling, Demands etc.). Write them next to the appropriate ‘B’. 2. Examine whether the evidence at hand supports that your thought at B is 100% true. Consider whether someone whose opinions you respect would totally agree with your conclusions. 3. Evaluate the helpfulness of each B. Write down whatyou think might be a more helpful, balanced and flexible way of looking at A. Consider what you would advise a friend to think, what a role model of yours might think, or howyou might look at A if you were feeling OK. 4. Add evidence and arguments that support your alternative thoughts, attitudes and beliefs. Write as if you were trying to persuade someone you cared about.

•••••••••••••••••••••••••••••••••••••••••••••••.ft*

Assage, like any new field you’re just getting into, can be a little confusing at first. There are so many resources you could use, so many directions you could search in. This appendix lists just a few of the many tools that could help you, but youTl find more than enough here to keep you busy for a long time.

Massage Books

There are lots of informative books on massage specialties. So, if you really feel the need to own another book besides this one, don’t worry, you won’t hurt my feelings. In fact, here are some suggestions:

Capellini, Steve, The Royal Treatment: How You Can Take Home the Pleasures of the Great Luxury Spas. New York, New York, Dell, 1997.

Claire, Thomas, Bodywork: What Type of Massage to Get — and How To Make the Most of It, William Morrow, New York, 1995.

Ford, Clyde, Compassionate Touch. NY: Simon and Schuster, 1993.

Knaster, Mirka, Discovering the Body’s Wisdom, Bantam, New York, 1996.

Krieger, Dolores, Accepting Your Power to Heal: The Personal Practice of Therapeutic Touch, Santa Fe, Bear & Co., 1993.

Miller, Erica, Day Spa Operations. Albany, Milady, 1995.

Montagu, Ashley, Touching: The Human Significance of the Skin, Harper & Row, New York, 1971…..

Nelson, Dawn, Compassionate Touch: Hands-On Caregiving for the Elderly the III and the Dying, New York, Talman Company, 1993.

Pierpont, Margaret, The Spa Life at Home, Longstreet Press, Atlanta, 1997.

Thomas, Zach, Healing Touch: The Church’s Forgotten Language. Louisville, KY, Westminster/John Knox Press, 1994.

Massage Magazines

In the U. S., there are three main magazines read by massage therapists. All of them include tons of information to help you get "plugged into" the massage world.

Massage Magazine: 1315 West Mallon, Dept. 50, Spokane, WA 99201-2038, 800-533-4263, ext. 50.

Massage Therapy Journal: 820 Davis Street, Suite 100, Evanston, IL 60201-4444, 847-864-0123.

Massage & Bodywork Quarterly: 28677 Buffalo Park Road, Evergreen, CO 80439-7347, 303-674-8478.

Massage on the Web

Given the velocity of change on the Internet, I can’t absolutely guarantee that all of the following links will be completely current. However, you can rest assured that they will provide you with mega-amounts of information, more than you could possibly digest in one lifetime. So log on, start surfing, and prepare to launch into the World Wide Web of massage.

General sites

Www. dharmanet. org/TBI/webring. html: This massage "Web ring" is a good place to start because it links together many sites all focused on massage therapy, and you can travel from place to place, always remaining within the ring. Note: Especially helpful if you have a Web site on the subject of massage that you want to promote.

Www. qwl . com/mtwc/guide/techni ques. html: This site is known as "Massage Therapy Web Central," and you’ll be able to find tons of links here for massage.

Www.Carpaltunnelmassage. com: Check here for insight into massage moves that can help with repetitive stress pain in the wrist.

Www. babymassage. com: This is a site with a video available for instruction in (surprise!) baby massage.

Www.Childbirth. org: Here you’ll find everything you could possibly want to learn about childbirth, including baby massage and massage for pregnant people.

Www. day break-mas sage. com: This is thee site for people interested in offering massage to seniors (also called geriatric massage). They offer training and certification.

Www. i nnerpeacemusi c. com: This is thee site for Stephen Halpern, a musician who has devoted his career to providing healing through sound. Many massage pros choose his music to accompany their massage.

Www. hometown. aol. com/ESMSatHome/school s. html: Check here for links to many horse massage schools.

Www. NCBTMB. com: The site for National Certification Board for Therapeutic Massage & Bodywork (NCBTMB). This organization offers certification for massage pros in every state of the U. S..

Massage therapist locator sites

Massagetherapynetwork. com: This site links therapists with customers and vice versa.

Www.Althealthsearch. com: This is a good place to find a practitioner in your area. It covers a lot of territory with over 180,000 listings.

Www. massagenetwork. com: Look here for tons of info from around the world, locating therapists, etc.

Www.Massageresource. com: Travel to this Web site first if you’re seeking therapists, schools, info, etc.

Www. massagetherapyhomepage. com/di rectory. html: This page will help you find a school or therapist anywhere in the world.

Massage products

Www. pressureposi ti ve. com: This site has several massage products for sale, such as the "Backknobber" and others.

Www. bodybal anci ng. com: This is the home site for the Body Balancer tool.

Www. mtswa rehouse. com: Here’s a site for discounted massage tables of many makes and models.

Www. monmouth. com/~bestof nature: This company bills themselves as a "massage supply superstore." The site definitely has a large number of products.

Www. rel axtheback. com: These are the ergonomic experts with a large chain of retail stores featuring back-friendly furniture, tools, and some massage items.

Www. wi 1 dsyde. com/ kamamai n. htm: This page on the Wild Syde Web site lists a sizable selection of edible massage oils, including the infamous "cappuccino" flavor.

Www.Massagetools. com: This is the Web site for the manufacturer of the Thumper vibrating massage device.

Www. mass agema tte rs. com: A massage entrepreneur in the Atlanta area offers this special site featuring just a few well-chosen, high quality massage items.

Heating retreat and spa resources

Www. spas. about. com: This may be the most comprehensive source of information about spas on the Web. Your experience here will be lead by a spa guide, Julie Register, who has spent many hours researching and cataloguing information as well as forging useful connections with many professionals in the spa industry.

Http://209.41.63.136/spa/spa. htm: Check here for travel and related information about the original town of Spa in Belgium.

Www.Spawish. com: This is the 1-800-FLOWERS of the spa world. Get in touch with Spa Wish to order a gift certificate good at hundreds of day spas across the U. S.. Also, check out the coupon in the back of this book.

Www.Spadiscoveries. com: This is the International Spa of the Month Club Web site. This outfit will send you new spa products from top resorts every month.

Www. spamagazi ne. com: This is the Web site for Spa Magazine.

Www. spaf i nders. com: This is the place to go when you’re searching for spa vacations.

Equipment and Supplies

The following is a list of companies that make equipment for use by massage pros or the public, as well as some retail outlets where you can go to purchase massage items.

Living Earth Crafts: 600 East Todd Road, Santa Rosa, CA 95407, 800-358-8292, Www.1i v ingearthcrafts. com

Living Earth Crafts offers portable, stationary, and spa tables, plus oils, books, T shirts, videos, massage tools, and more.

Golden Ratio Woodworks: 2896 Hwy. 89 South, Emigrant, Montana 59027, 800-345-1129 or 406-333-4578, Www. goldenratio. com

Golden Ratio offers a full line of tables, chairs, and allied products. They also made the extremely cool Massage For Dummies Massage chair featured in some of the photos in this book!

The Body Balancer: Body Balancing Ltd., P. O. Box 51977, Palo Alto, CA 94303, 800437-7004

This is where you can order the Body Balancer, featured in Chapter 10.

Natura Essentials: 2845 Harriet Ave South, Minneapolis 55408, 888-606-0055,

Www. naturaessenti al s. com

This company features an incredible collection of some of the finest aromatherapy products you can find anywhere, including candles, essential oils, diffusers, and more.

Trigger Point Co.: P. O. Box 391171, Anza, CA 92539, 800-763-2430.

This company manufactures the popular Thera Cane self-massage tool.

Educating Hands Bookstore: 120 SW 8th Street, Miami, FL 33130 305-285-0651 or 800-999-6991, Www. educatinghands. com

This store-in-a-school near downtown Miami offers a great selection of books, videos, tables, chairs, massage muscle-builders, and accessories.

Downeast School of Massage Bookstore: 99 Moose Meadow Lane, Waldoboro, ME 04572, 207-832-553, Www. midcoast. com/~dsm

This stores offers lots of books, study aids, charts, videos, models, music, lotions, oils, and accessories including the Thermophore moist heat pack.

Best of Nature: 176 Broadway, Long Branch, NJ 07740, 800-228-6457 or 732-728-0004, www. bes tof n a t u r e. c om

Billing themselves as "the largest massage supply superstore," Best of Nature offers tables, chairs, sheets, oils, accessories, creams, and more.

Inner Peace Linens: P. O. Box 940, Walpole, NH 03608-0940, 800-949 7650,

Www. innerpeace. com

What’s the use of lying on an expensive padded massage table if it’s covered with a cheap sheet? Contact Inner Peace for 100-percent cotton flannel massage table linens.

Massage Oils and Creams

Take it from me: if you’re going to apply long firm massage strokes to the hairy leg of an Italian man, you’d better use some kind of lubricant, or you’re going to have one angry Italian on your hands. You can find massage oils and creams at many health food stores and specialty shops, but in this section I’ve listed a few top-of-the-line products that the pros use.

Biotone: 4757 Old Cliffs Rd., San Diego, CA 92120, 800-445-6457 or 619-582-0027, www. bi otone. com

This is a popular massage cream and oil manufacturer.

Heritage Products: Box 444, Virginia Beach, VA 23458, 800-TO-CAYCE,

Www. caycecures. com

Heritage produces the Edgar Cayce Aura Glow oil, the formula for which was inspired by the renowned healer.

Pure Pro Massage Oils: 955 Massachusetts Avenue, Suite 232, Cambridge, MA 02139, 781-933-8638, 877-373-5298, Www.rel axu. com

These nice folks will send you a free catalogue if you ask for one nicely.

Tara Spa Therapy: P. O. Box 222639, Carmel, CA 93922, 800-552-0779 or 831-648-1932

Tara Spa Therapy carries Bindi Body Oil (my favorite). They also have a line of ayurvedic products, and much more.

Catalogues

These catalogues specialize in all kinds of products that are good for you and your body. Some also offer unique items like meditation pillows, prayer bells and such.

Harmony: 800-869-3446

This catalogue offers "products in harmony with the earth," and all the models look clean cut and happy.

Basic Massage Lines: 1207 W. Kingshighway, Paragould, AR 72450, 800-643-4751,Www. bmlmassage. com

Like the name says, this company carries basic massage lines for pros and amateurs alike, offering one-stop shopping.

Inner Balance: 800-482-3608

This catalogue offers "natural solutions for health," and it has a number of massage related items.

Best of Nature: 176 Broadway, Long Branch, NJ 07740, 800-228-6457 or 732-728-0004, www. bestof nature. com

This is a no-frills massage, spa, aromatherapy, and body care product catalogue, mostly for the pros.

Self-Care: 2000 Powell Street, Suite 1350, Emeryville, CA 94608-1858, 800-345-3371, Www. selfcare. com

Called "America’s foremost specialty catalog of products for healthy living," this company carries large selection of health and wellness related products.

Explorations: 800-720-2114

A little bit on the "mystical" side, this catalogue offers great stuff for energy awakening, spirituality, relaxation, etc.

Organizations and Associations

Check out the organizations and associations listed here if you would like some information or you just want to chat with someone who knows what they’re talking about.

American Massage Therapy Association (AMTA): 820 Davis Street, Suite 100, Evanston, IL 60201-4444, 847-864-0123, www. amt amass age. org

American Oriental Bodywork Therapy Association (AOBA): Laurel Oak Corporate Center, Ste 408, 1010 Haddonfield-Berlin Rd., Voorhees, NJ 08043, 609-782-1616, Www. healthy. net/aobta

Associated Bodywork & Massage Professionals (ABMP): 28677 Buffalo Park Road, Evergreen, CO 80439-7347, 800-458-2267 or 303-674-8478, www. abmp. com

International Massage Association (IMA): 3000 Connecticut Ave. NW, #308, Washington, DC 20008, 202-387-6555, Internationalmassage. com

International Institute of Reflexology: 5650 First Avenue North, Saint Petersburg, FL 33733-2642, 727-343-4811, www. ref 1 exol ogy-usa. net

International Spa Association (ISPA): International Spa & Fitness Association (ISPA), 546 East Main Street, Lexington, KY, 40508, 888-651-4772, 606-2264326,

Www. globalspaguide. com

International Sports Massage Federation: P. O. Box 25983, Santa Ana, CA 92799-9610,949-642-0735

National Certification Board for Therapeutic Massage & Bodywork: 8201 Greensboro Drive, Suite 300, McLean, VA 22102-3810, 703-610-9015,

Www. NCBTMB. com

National Association of Bodywork in Religious Services (NABRS): 337

Tranquil Avenue, Charlotte, NC 28209

Touch Research Institute: Department of Pediatrics, University of Miami School of Medicine, P. O. Box 016820 (Dept. – 820), 1601 NW 12th Avenue, Miami, FL33101, 305-243-6781, Www. mi ami. edu/touch-research

Get in touch with these organizations if you’re searching for information, schools, and therapists in the U. K., France, Italy, and Australia.

Australia: Massage Australia, P. O. Box 38, Wentworth Falls NSW 2782 Australia, teL 02 4757 3050 or 61 2 4757 3050, Www. massageaus .com. au

The U. K.: The Institute for Complementary Medicine, P. O. Box 194, London SE16 1QZ, tel. 00 44 171 237-5165

Italy: Federazione Nazionale dei Collegi dei Massofisioterapisti (F. N.C. M.), Via Aosta 16, Trento, 38100 Rome, Italy, tel. 03 94 61 915 499 Www. geoci ties. com/CapeCanaveral / Lab/2521

France: French Federation of Masseurs Kinesitherapeutes (FFMKR), 24 rue des Petits Hotels, 75010, Paris, France, tel. 01 44 83 46 00

Massage Specialties and Trainings

There are so many massage specialties and trainings out there that an entire book could be written just trying to explain all the different kinds. And in fact several books on that very topic have been written. This appendix is not here to confuse you about the subject, but rather to help if you’re seriously interested in massage and bodywork as either a practitioner or a recipient and you’d like to start looking into some of the specialties that are available.

With each listing, you’ll find contact numbers for trainings offered. These are by no means the only trainings available, but they represent some of the best. Also, if you’re looking for a practitioner in a particular specialty, many of the training centers have lists of qualified people.

Note that some of the Web sites listed are not directly affiliated with the training centers but contain much relevant information.

Ayurveda

Many practitioners in the West are now offering massage and other treatments based upon this 5,000 year old system of natural healing from India.

Ayurvedic Institute: 11311 Menaul NE, Suite A, Albuquerque, NM 87112, 505)291-9698, Www. ayurveda. com

Baby Massage

You don’t have to be a massage pro in order to massage your own baby. Different types of classes are offered for therapists and novices.

Association of Labor Assistants & Childbirth Educators: P. O. Box 382724, Cambridge, MA 02238, 888-222-5223 or (617)441-2500, www. al ace. org

Cinnabar School: P. O. Box 34326, Westbrook, Calgary, AB, Canada T3C 3W0, 403-246-6720, www. baby mas sage. com

Kate Jordan Seminars: 8950 Villa La Jolla Drive, Suite 2162, La Jolla, CA 92037, 760-436-0418, Pregmassage@aol .com

Nurturing the Mother: 8703 Rollingwood Road, Chapel Hill, NC 27516, 919-929-4253

Chair massage

To learn how to give effective massage using the specially built massage chairs available today, contact these providers.

TouchPro Chair Massage Workshops: 800-999-5026

Seated Massage Experience: Touch 4 Productions, P. O. Box 260395, Tampa, FL33685-0395, 800-868-2448 or 813-249-2911, www. seatedmassage. com

Connective tissue massage

These therapies usually "dig in deep" to re-pattern the way your body is held together by its basic glue, or connective tissues. They’re great for changing poor postural habits, increasing energy, and improving physical function.

The Anatomy Trains by Tom Myers: 20 Roundabout Way, Scarboro, ME, 888-546-3747

The Rolf Institute of Structural Integration (RoMng): P. O. Box 1868, Boulder, CO 80302, 800-530-8875 or 303-449-5903, Www. rolf. org

Guild for Structural Integration (Rolfing): P. O. Box 1559, Boulder, CO 80306, 800-447-0150, www. rol fgui 1 d. org

Aston-Patterning: P. O. Box 3568, Incline Village, NV 89450, 702-831-8228,

Www. astonpatterni ng. com

Hellerwork: 406 Berry Street, Mt. Shasta, CA 96067, 800-392-3900,

Www. hel1erwork. com

Energy ufork

Energy work Is massage and bodywork that focuses on treating the invisible pathways of energy running in the human body. This energy has different names in different cultures. In Asia, it’s known as Chi, ki And other names. The following types of massage and bodywork deal primarily with this energy, affecting the entire body through that process.

Jin Shin Jyutsu: 8719 E. San Alberto, Scottsdale, AZ 85258, 602-998-9331,

Www. JinShinJyutsu. com

American Polarity Therapy Association: 2888 Bluff Street, #149, Boulder, CO 80301, 303-545-2080, Www. PolarityTherapy. org

The Reiki Alliance: P. O. Box 41, Cataldo, ID 83810, 208-682-3535, www.

Rei kicentrum. nl/reiki4a11

Shiatsu: Ohashi Institute, 12 W. 27th Street, New York, NY 10001-6903, 800-810-4190, Www. ohashi .com

Healing Tao: 1205 O’Neill Hwy, Dunmore, PA 18512, 717-3484310, www.

Healing-tao. com

Therapeutic Touch: Nurse Healers & Professional Associates, 175 Fifth Ave, Suite 3399, New York, NY 10010, www. therapeuti ctouch. com

Freedom of movement massage

These techniques have been developed by people in the performing arts, sports, the medical professions, and other backgrounds. All of them open the body/mind to higher levels of freedom and expression, creating improved wellbeing at the same time.

The Alexander Technique: North America Society of Teachers of the Alexander Technique, P. O. Box 517, Urbana, IL 61801, 800473-0620, Www. alexandertechni que. com

Feldenkrais: The Feldenkrais Guild, P. O. Box 489, Albany, OR 97321-0143, 800-775-2118, www. Fel denkrai s. com

Pilates: Physical Mind Institute, 1807 Second Street #28129, Santa Fe, NM 87505, 800-505-1990 or (505)988-1990, www. themethod. com

Pilates Institute: Sydney City Lvl 2, George Street, Sydney NSW Australia 2000, tel 02 9267 8223, www. pi 1 ates. net

Trager: The Trager Institute, 21 Locust, Mill Valley, CA 94941-2806, 415-388-2688, Www. trager. com

Geriatric massage

If you would like to help senior citizens in a profoundly important and simple way/reaching out to them through massage is an excellent choice, and taking the training offered here is a good way to begin.

Daybreak Geriatric Massage Project: 216 Pleasant Hill Ave. N., Sebastopol, CA 95472, 707-829-2798, www. d ay b re a k – ma s s a ge. c om

Horse massage

I know it may be hard for you to believe, but it’s true: There are courses for people who want to learn how to massage horses, which is actually quite a big business these days.

Equissage: P. O. Box 447, Round Hill, VA 20142, 540-338-1917, www.

Equissage. com

Don Doran’s Equine Sports Massage: 14735 SW 71 Avenue Road, Ocala, FL 34473-5102, 352-347-3747

Jack Meagher Institute of Sports Therapy: Equine Sports Massage, P. O. Box 1244, Concord, MA 01742, 413-772-1815

Mind/body/emotion massage

These methods work in a very profound way to help people uncover and deal with emotions and memories that might cause painful conditions.

The Rosen Method: The Rosen Method Center, 825 Bancroft Way, Berkley, CA 94710, 510-845-6606, www. men. org/b/ rosen/def aul t. html

Rosen Method Center Southwest: P. O. Box 344, Santa Fe, NM 87504,

505-982-7149, Www. men. org/b/rosen/swrc. html

The Rubenfeld Synergy Center: 115 Waverly Place, New York, NY 10011,

212-254-5100, Www. hometown. aol. comXrubenfeld\synergy\index. html

Pain relief massage

Although every style of massage can potentially help reduce pain, there are certain styles that specialize in pain reduction and reversal of trauma. The following a just a few of them.

The Bodywork Research Institute: 123 E. 8th Street, Suite 121, Frederick, MD 21701, 301-698-0932, trains people in massage techniques to relieve the painful symptoms of fibromyalgia.

Craniosacral Therapy: Upledger Institute, 11211 Prosperity Farms Road, Palm Beach Gardens, FL 33410-3487, 800-233-5880, www. upl edger. com

Hoshino Therapy Clinic: Center for Biotherapeutics, 430 South Dixie Hwy, Miami, FL 33146, 305-666-2243

Neuromuscular Therapy Seminars: 1121 Prosperity Farms Road, #D-325, Palm Beach Gardens, FL 33410-3487, 800-311-9204 or 561-622-4334,

Www. iahe. com

Reflexology

International Institute of Reflexology: P. O. Box 12642, St. Petersburg, FL, 33733-2642, 727-343-4811, www. ref 1 exology-usa. net

Spa therapy training

This category is for those people who would like to specialize in giving massage, hydrotherapy, and other treatments in the spa setting, as well as spa owners and managers.

The Bramham Institute & Spa: 1014 N. Olive Ave, West Palm Beach, FL 33401, 800-575-0518, Www. spamastery. com

Thai massage

Many people make the pilgrimage to Thailand every year to learn the techniques of this traditional system, which includes a lot of stretching and moves similar to Shiatsu.

Institute of Thai Massage: 17/7 Morakot Road, Hah Yaek Santitham, Chiang Mai 50300 Thailand, tel. (66-53) 218632, www. i nf othai. com/i tm

Water massage

Some very interesting types of massage can be done in the water. The buoyancy helps to free people of chronic pain and ease certain fears.

Watsu: Massage School at Harbin Hot Springs P. O. Box 570, Middletown, CA 95461, 707-987-3801, www. w a b a. e d u

Aquassage: 800-957-4808, Www. massagetherapynetwork. com

A college degree in massage

If you want a college degree and a massage license, how about going to school where you can get both at the same time? At the New Center College, you’ll earn an Associate of Occupational Studies (A. O.S.) degree with a major in Massage Therapy, the first of its kind in the United States.

The New Center College for Wholistic Health Education and Research: 6801 Jericho Tpk., Syosset, New York 11791-4413, 516-364-0808, ext.126, www.

Newcenter. edu

In This Chapter

^ Identifying a president famous for a mathematical proof ^ Naming a world conqueror who did a proof while in exile ^ Pointing out some contemporary figures

Athematics has inspired so many people over the centuries. Picture a future U. S. president sitting through a wonderfully exciting meeting of Congress. Was he paying attention? No, he was discovering a proof of the Pythagorean theorem, of course! Other mathematicians came from wealthy families or monasteries. Mathematicians are found in all walks of life. Anyone can be a mathematician with just a bit of curiosity, respect for the basic mathematical rules, and willingness to stick her neck out a bit.

Pythagoras

How can Pythagoras be an Unlikely Mathematician when practically everyone knows his name? His contributions to the world of music and mathematics are legendary, although he would have preferred to keep his discoveries a secret. Pythagoras was a prophet and mystic. He established a secret society that had a strict code of conduct. Members of the society were vegetarians who were forbidden from eating beans (lentils). The Pythagoreans, as the society members were called, believed that odd numbers had male attributes and even numbers had female attributes. They based their worship on numerology and let it influence their way of life. The Pythagoreans believed that all numbers were Rational (could be written as a fraction), even though the Pythagorean theorem belies this with its need for numbers under Radicals (irrational numbers).

Napoleon Bonaparte

Emperor Napoleon Bonaparte is known for many things, but not many people know how much he contributed to mathematics. Napoleon was always a great supporter of mathematical inquiry and promoted mathematical study whenever he could. One of his better-known contributions is his discovery that, if you construct an equilateral triangle on each side of any other triangle, the centers of those equilateral triangles are the vertices of another equilateral triangle.

Figure 22-1 shows you three different triangles — one scalene, one isosceles, and one right. According to Napoleon, you construct an equilateral triangle (one with all the sides the same measure) on each side of any kind of triangle — the equilateral triangle has its sides measuring the same as that particular side of the base triangle. When the centers of the equilateral triangles are connected by segments, you see that Napoleon’s discovered another equilateral triangle formed in the middle.

Figure 22-1:

Napoleon kept himself busy while in exile.

Rene Descartes

Descartes was born into a wealthy family and received a thorough, general education at a Jesuit college. He studied law for a while but wasn’t really all that interested in it. For some years he traveled around with various military campaigns. Descartes wasn’t really a professional soldier. He took time off from his accompaniment of military campaigns for some interesting travel and study. He is known as the father of modern philosophy. His most serious interest in mathematics may have coincided with wanting to stay warm. He was traveling with the Bavarian army during a cold, winter campaign, and chose to stay in bed until 10 a. m. thinking about mathematical problems. Doesn’t sound like any army I know. In any case, Descartes made huge contributions to mathematics.

President James A. Garfield

President Garfield was the first ambidextrous U. S. president and the second president to be assassinated. He earned money to attend college by driving canal boat teams. He was a classics professor, then college president. He tired of the academic life, so he studied law and became a politician. While a member of the House of Representatives, in 1876, he discovered a novel proof of the Pythagorean theorem. Figure 22-2 shows his construction of a trapezoid, starting with a right triangle. His proof involves the areas of the triangles and trapezoid.

Figure 22-2:

President Garfield’s proof.

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President Garfield was shot in 1881 and died two months later of an infection. Alexander Graham Bell tried to find the bullet with a metal detector that he had invented, but failed — probably due to the metal in the president’s bed frame.

Charles Dodgson (Lewis Carroll)

More famous for his Alice in Wonderland And Alice through the Looking-Glass, Charles Dodgson is also well-known in mathematics circles for his work in probability, theory of elections, and algebra. Charles Dodgson studied at and later taught at Christ Church College, Oxford. He spent most of his time teaching and tutoring in algebra and developed study materials for students who were struggling with the material. His two Alice Books have many references to mathematics and logic. Dodgson liked working with children and amused them with his stories and word games — including an early version of Scrabble.

M. C. Escher

M. C. Escher was a Dutch graphic artist. His works are easily recognizable because of the many impossible-looking constructions and titillating tessellations. Figure 22-3 shows an example of the type of tessellation that Escher might have produced. (A Tessellation Is a tiling or filling of the plane with figures that leave no gaps between them.)

Escher was born in 1903 in the Netherlands and lived in and traveled to many other countries as world and political events affected his life. Although he didn’t have any formal mathematical training, his work has strong mathematical components including order and symmetry. His journey to the Alhambra in Spain resulted in his trying to improve upon those artworks using geometric grids as a basis for his own work. His art took many forms from his earliest work in 1937 until his death in 1972.

Sir Isaac Newton

Isaac Newton is probably best known for his discovery of the Law of Gravity, supposedly due to an apple falling on his head. Whether the apple story is true or not, his mathematical discoveries are even more remarkable, because most of his work was done during a two-year period when he had retired to the countryside to think and wait out the bubonic plague that was sweeping Europe. Even more startling is the fact that this two-year period ended with his 25th birthday.

Newton is recognized as the co-inventor of calculus. Both Newton and Gottfried Leibniz discovered calculus at the same time, and independently,

But Newton waited about 20 years to publish his findings, while Leibniz published almost immediately. Newton also discovered three laws of motion, the Corpuscular Theory of Light, and the Law of Cooling. He built telescopes and used them to calculate orbits of planets, but Newton’s main interest was really alchemy. After his early discoveries in mathematics and physics, he really did little more to add to the knowledge in these fields.

Marilyn Vos SaVant

Marilyn vos Savant’s column Ask Marilyn Is found weekly in Parade Magazine. She started writing this column after being featured in a Parade Article for her high IQ and then responding to a selection of questions in a follow-up article. Marilyn solves mathematical and logical problems in her column and also answers questions on physics, philosophy, and human nature.

Perhaps you remember her response to what has been dubbed the "Monty Hall problem" (see the nearby sidebar). In a 1990 column, she responded that you’d have a better chance of winning if you switched doors. This lead to all sorts of responses from academics and other readers — much of it criticism of her answer. She was, of course, found to be correct.

Marilyn, in addition to writing her column, is Chief Financial Officer of Jarvik Heart and assists her husband, Robert Jarvik, with cardiovascular disease research.

The Monty Hall problem

Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, and behind the other two doors are goats. You pick a door, say door #1, and the host, who knows what’s behind the doors, opens another door, say door #3, which has a goat. He says to you: "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors?

Marilyn’s answer was that you should switch, giving you a two-thirds chance of winning rather than one-third, if you stayed with door #1.

Why was Marilyn correct? Consider the situation where the car is behind door #1 and goats are

Behind doors #2 and #3. The game show host is always going to show you one of the goats.

If you pick door #1, the host will show one of the goats behind door #2 or door #3, and if you switch, you lose.

If you pick door #2, the host will show you door #3, so if you switch to door #1, you win.

If you pick door #3, the host will show you door #2, so if you switch to door #1, you win.

You win two-thirds of the time if you switch. This same chance will appear, no matter where you put the car and where you put the goats.

Leonardo da Vinci

When you think of Leonardo da Vinci, you probably think first of the artist. As an artist, Leonardo turned to science as a means of improving his artwork. His study of anatomy and nature led to his remarkably realistic paintings. He was recognized as an inventor, scientist, engineer, musician, mathematician, astronomer, and painter.

His interest in the mathematics of art and nature led him to show how the different parts of the human body are related by the golden rectangle. Leonardo believed that artists should know the laws of nature as well as the rules of perspective.

Martin Gardner

Martin Gardner first came to my attention with his Mathematical Games Column in Scientific American, Which he wrote for about 25 years. In addition to this column, he has published over 60 books.

Martin Gardner grew up in Oklahoma, served in the U. S. Navy during World War II, and later earned his bachelor’s degree in philosophy from the University of Chicago. He decided to try for a life as a freelance writer after selling a humorous short story to Esquire. His second sale was a story based on mathematical topology — a story in science fiction. He is considered to be almost single-handedly responsible for creating the interest in recreational mathematics in the later part of the 20th century. Some subjects that he has popularized are

Flexagon: A Flexagon Is a hexagon made up from a long strip of equilateral triangles (most easily constructed from adding-machine tape). Folding and refolding reveals the three different faces of a Trihexa-flexagon, The six faces of a Hexahexaflexagon, And so on.

Uu Polyomino: A Polyomino Is a grouping of squares — three, four, five, and so on — such that no grouping is the same shape as any other, even when the grouping is flipped or rotated.

IU Soma cubes: Soma cubes Are the three-dimensional versions of polyomi-noes. Cubes are stacked or otherwise connected, producing different shapes that can’t be duplicated by any rotations or flips of the grouping.

IU Hex: The game of Hex Is played on a game board consisting of hexagons. Players take turns choosing hexagons (usually with different-colored game pieces) trying to form a path from one side of the board to the other.

LU Tangram: A seven-piece Tangram Starts out as a square. The different pieces — triangles, squares, parallelogram, and so on — are rearranged to form other shapes and pictures.

I Penrose tiling: A Penrose tiling Consists of Rhombi (a rhombus has all four sides the same measure) that appear to have no pattern or symmetry but that, in fact, have repeated patterns within the tiling.

I Fractal: A Fractal Is a geometric shape that can be continuously broken down into parts that are reduced copies of the original shape. The book Jurassic Park Introduced the dragon fractal and referred to chaos theory. (I’ll leave you with those two topics to search out on your own!)

Affinity diagram: An organization of individual pieces of information into groups or broader categories.

ANOVA (analysis of variance): A statistical test for identifying significant differences between process or system treatments or conditions, performed by comparing the variances around the means of the conditions being compared.

Attribute data: Data that has a set of discrete values such as pass or fail, yes or no.

Average: Also called the mean, it is the arithmetic average of all of the sample values. It is calculated by adding all of the sample values together and dividing by the number of elements (n) In the sample.

Bar chart: A graphical method depicting data grouped by category.

Black Belt: An individual who receives approximately four weeks of training in the Six Sigma DMAIC methodology, analytical problem solving, and change management methods. A Black Belt is a full time Six Sigma team leader solving problems under the direction of a Six Sigma Champion.

Breakthrough improvement: A rate of improvement at or near 70 percent

Over baseline performance of the as-is process characteristic.

Capability: A comparison of the required operation width of a process or system to its actual performance width. Expressed as a percentage (yield), a defect rate (DPM, DPMO), An index (Cp, Cpk, Pp, Ppk), Or as a sigma score (Z).

Cause-and-effect diagram: See Fishbone diagram.

Central tendency: A measure of the point about which a group of values is clustered; two measures of central tendency are the mean and the median.

Champion: A Six Sigma leader, who recognizes, defines, assigns, and supports the successful completion of Six Sigma projects; a Six Sigma Champion

Is accountable for the results of projects and the business roadmap to achieve

Six Sigma results within their span of control.

Characteristic: A process input or output that can be measured and monitored.

Common causes of variation: Those sources of variability in a process that are truly random; that is, inherent in the process itself.

Complexity: The level of difficulty to build, solve, or understand something based on the number of inputs, interactions, and uncertainties involved.

Control chart: The most powerful tool of statistical process control. It consists of a run chart, statistically determined upper and lower control limits, and a centerline.

Control limits: Upper and lower bounds in a control chart that are determined by the process itself. They can be used to detect special or common

Causes of variation. They are usually set at ±3 standard deviations from the

Central tendency.

Correlation coefficient: A measure of the linear relationship between two

Variables.

Cost of poor quality (COPQ): The costs associated with any activity that is not done right the first time. It is the financial qualification of any waste that is not integral to the product or service that your company provides.

CP: A capability measure defined as the ratio of the specification width to

Short-term process performance width.

CPk: An adjusted short-term capability index that reduces the capability score in proportion to the offset of the process center from the specification target.

Critical-to-quality (CTQ): Any characteristic that is critical to the perceived quality of the product, process, or system. See also Significant Y.

Critical X: An input to a process or system that exerts a significant influence on any one or all of the key outputs of a process.

Customer: Anyone who uses or consumes the output of a process, whether internal or external to the providing organization or provider.

Cycle time: The total amount of elapsed time from the time a task, product, or service is started until it is completed.

Defect: An output of a process that fails to meet a defined specification or

Requirement, such as time, length, color, finish, quantity, temperature, and

Soon.

Defective: A unit of product or service that contains At least one defect.

Deployment: The planning, launch, training, implementation, and management of a Six Sigma initiative within a company.

Design for Six Sigma (DFSS): The use of Six Sigma thinking, tools, and methods applied to the design of products and services to improve initial release performance, ongoing reliability, and life-cycle cost.

Design of Experiments (DOE): An efficient, structured, and proven approach to

Investigating a process or system to understand and optimize its performance.

DMAIC: The acronym for the five core phases of the Six Sigma methodology:

Define, Measure, Analyze, Improve, and Control; used to solve process and business problems through data and analytical methods.

DPMO (defects per million opportunities): The total number of defects observed divided by the total number of opportunities, expressed in events per million. Sometimes called Defects per Million (DPM)

DPU (defects per unit): The total number of defects detected in some number of units divided by the total number of those units.

Entitlement: The best demonstrated performance for an existing configuration of a process or system. It is an empirical demonstration of the level of improvement that can potentially be reached.

Epsilon (f): Greek symbol used to represent uncertainty or residual error.

Experimental design: See Design of Experiments (DOE).

Failure mode effects analysis (FMEA): A procedure used to identify, assess, and mitigate risks associated with potential failure modes in a product, system, or process.

Finance representative: An individual who provides an independent evaluation of a Six Sigma project in terms of hard and/or soft savings. They are a

Project support resource to both Champions and project leaders.

Fishbone diagram: A pictorial diagram in the shape of a fishbone showing all

Possible variables that could affect a given process output measure.

Flowchart: A graphic model of the flow of activities, material, and/or information that occurs during a process.

Gauge R&R: The quantitative assessment of how much variation (repeatability

And reproducibility) is in a measurement system compared to the total variation of the process or system.

Green Belt: An individual who receives approximately two weeks of training in the Six Sigma DMAIC methodology, analytical problem solving, and change management methods. A Green Belt is a part time Six Sigma practitioner who applies Six Sigma techniques to their local area, performing smaller-scoped

Projects and providing support to Black Belt projects.

Hidden factory or operation: Corrective and non-value-added work applied

To produce a unit of output generally not properly recognized as unnecessary

And a form of waste of time, resources, materials, and cost.

Histogram: A bar chart that depicts the frequency of occurrence (by the

Height of the plotted bars) of numerical or measurement categories of data.

Implementation team: A cross-functional executive or management team representing multidisciplinary areas of the company, whose charter is to drive the implementation of Six Sigma by defining, documenting, and leading

Practices, methods, and operating policies.

Input: A resource consumed, utilized, or added to a process or system. Synonymous with the terms X, Characteristic, and input variable.

Lshikawa diagram: See Fishbone diagram.

Least squares: A method of curve-fitting that defines the best fit as the one that minimizes the sum of the squared deviations of the data points from the

Fitted curve.

Long-term variation: The observed variation of an input or output characteristic that has had the opportunity to experience the majority of the variation

Effects that influence it.

Lower control limit (LCL): For control charts: the limit above which the subgroup statistics must remain for the process to be in control; typically three standard deviations below the central tendency.

Lower specification limit (LSL): The lowest value of a characteristic that is

Acceptable.

Master Black Belt (MBB): An individual who has received additional training

Beyond Black Belt. The MBB is a technical, go-to expert for technical and project issues in Six Sigma. Master Black Belts are qualified to teach and mentor other Six Sigma Belts and support Champions.

Mean: See Average.

Measurement: The act of obtaining knowledge about an event or characteristic through measured quantification or assignment to categories.

Measurement accuracy: For a repeated measurement, it is a comparison of the average of the measurements compared to some known standard.

Measurement precision: For a repeated measurement, it is the amount of

Variation that exists in the measured values.

Measurement Systems Analysis (MSA): The assessment of the accuracy and precision of a method for obtaining measurements. See also Gauge R&R.

Median: The middle value of a data set when the values are arranged in either ascending or descending order.

Metric: A measure that is considered to be a key indicator of performance. It should be linked to goals or objectives and carefully monitored.

Natural tolerances of a process: See Control limits.

Nominal group technique: A structured method used by a team to generate and rank a list of ideas or items.

Non-value-added (NVA): Any activity performed in producing a product or

Delivering a service that does not add value, where value is defined as changing the form, fit, or function of the product or service and is something for which the customer is willing to pay.

Normal distribution: The distribution characterized by the smooth, bell -

Shaped curve; synonymous with Gaussian distribution.

Objective statement: A succinct statement of the goals, timing, and expectations of a Six Sigma improvement project.

Opportunities: The number of characteristics, parameters, or features of a product or service that can be classified as acceptable or unacceptable.

Out of control: A process is out of control if it exhibits variations larger than its control limits or shows a pattern of variation.

Output: A resource, item, or characteristic that is the product of a process or system. See alsoY And CTQ.

Pareto chart: A bar chart for attribute (or categorical) data where the categories are presented in descending order of frequency.

Pareto Principle: The general principle originally proposed by Vilfredo Pareto (1848-1923) that the majority of influence on an outcome is exerted by a minority of input factors.

Poka-Yoke: A transliteration of a Japanese term meaning "to mistake-proof."

Probability: The likelihood of an event or circumstance occurring. Problem statement: A succinct statement of a business situation used to

Bound and describe the problem that a Six Sigma project is destined to solve.

Process: A set of activities, material, and/or information flow that transformsa set of inputs into outputs for the purpose of producing a product, providing a

Service, or performing a task.

Process certification: The act of establishing documented evidence that a

Process will consistently produce its required outcome or meet its required

Specifications.

Process characterization: The act of quantitatively understanding a process,

Including the specific relationship(s) between its outputs and the inputs, and its performance and capability.

Process flow diagram: See Flowchart.

Process member: An individual who performs activities within a process to

Deliver an output, product, or service to a customer.

Process owner: The individual who has responsibility for process performance

And resources, and who provides support, resources, and functional expertise

To Six Sigma projects. The process owner is accountable for implementing Six Sigma solutions in processes.

Quality function deployment (QFD): A systematic process for integrating customer requirements into every aspect of the design and delivery of products and services.

Range: A measure of the variability in a data set; the difference between the

Largest and smallest values in a data set.

Regression analysis: A statistical technique for determining the mathematical relation between a measured quantity and the variables upon which it

Depends; includes simple and multiple linear regression.

Repeatability: The extent to which repeated measurements of a particular object with a particular instrument produce the same value. See also Gauge

R&R.

Reproducibility: The extent to which repeated measurements of a particular object with a particular individual produce the same value. See also Gauge R&R.

Rework: Activities required to correct defects produced by a process.

Risk priority number (RPN): In failure mode effects analysis, the aggregate score of a failure mode including its severity, frequency of occurrence, and ability to be detected.

Rolled throughput yield (RTY): The probability of a unit going through all

Process steps or system characteristics with zero defects.

RUMBA: An acronym for Reasonable, Understandable, Measurable, Believable,

And Achievable, used to describe a method for determining the validity of customer requirements.

Run chart: A graphical tool for charting the performance of a characteristic

Over time.

Scatter plot: A chart in which one variable is plotted against another to

Observe or determine the relationship, if any, between the two.

Screening experiment: A type of experiment used to identify the subset of

Significant factors from among a large group of potential factors.

Short-term variation: The amount of variation observed in a characteristic

That has not had the opportunity to experience all the sources of variation from the inputs acting on it.

Sigma score: A commonly used measure of process capability that represents the number of short-term standard deviations between the center of a process and the closest specification limit. Sometimes referred to as sigma level, or simply Sigma. Also called the Z Score.

Significant Y: The output of a process that exerts a significant influence on

The success of the process or customer satisfaction.

SIPOC (Suppliers-Inputs-Process-Outputs-Customers): A visual representation of a process or system where inputs are represented by input arrows to a box

(representing the process or system) and outputs are shown using arrows emanating out of the box.

Six Sigma: A proven and proscriptive set of analytical tools, project con -

Troltechniques, reporting methods, and management techniques that combine to form breakthrough improvements in problem solving and business performance.

Six Sigma leader: An individual who leads the implementation of Six Sigma, coordinating all of the necessary activities, and who assures optimal results are obtained and keeps everyone informed of progress.

Six Sigma project: A specifically-defined effort that states a business problem

In quantifiable terms and with known improvement expectations. Special cause variation: Those non-random causes of variation that can be

Detected by the use of control charts and good process documentation.

Specification limits: The bounds of acceptable performance for a characteristic.

Stability: A process with no recognizable pattern of change and no special

Causes of variation.

Standard deviation: One of the most common measures of variability in a data set or in a population; the square root of the variance.

Statistical problem: A problem that is addressed with facts and data

Analysis methods.

Statistical process control (SPC): The use of basic graphical and statistical methods for measuring, analyzing, and controlling the variation of a process

For the purpose of continuously improving the process. A process is said to be in a state of statistical control when it exhibits only random variation.

Statistical solution: A data-driven solution with known confidence/risk levels; as opposed to a qualitative, or "I think," solution.

Supplier: An individual or entity that provides an input to a process in the

Form of resources or information.

Trend: A gradual, systematic change over time (or some other variable). TSSW (thinking the Six Sigma way): A mental model for improvement that

Perceives outcomes through a cause-and-effect relationship combined with

Six Sigma concepts to solve everyday and business problems.

Two-level design: An experiment where all factors are set at one of two levels, denoted as low and high (-1 and +1).

Upper control limit (UCL): The upper limit below which a process statistic

Must remain to be in control. Typically, this value is 3 standard deviations above the central tendency.

Upper specification limit (USL): The highest value of a characteristic that is

Acceptable.

Variability: The property of a characteristic, process, or system to take on

Different values when it is repeated.

Variable data: Data where values are continuous, and can be meaningfully measured and subdivided; that is, can have decimal subdivisions.

Variables: Quantities that are subject to change or variability.

Variance: A specifically defined mathematical measure of variability in a data

Set or population. It is the square of the standard deviation. Variation: See Variability.

VOB (voice of the business): The representation of the needs of the business and the key stakeholders of the business; usually including profitability, revenue, growth, market share, employee satisfaction, and so on.

VOC (voice of the customer): The representation of the expressed and non -

Expressed needs, wants, and desires of the recipient of a process output, a

Product, or a service; usually expressed as specifications, requirements, or

Expectations.

VOP (voice of the process): The performance and capability of a process to achieve both business and customer needs; usually expressed in some form of an efficiency and/or effectiveness metric.

Waste: Material, effort, and time that does not add value in the eyes of key stakeholders (customers, employees, investors).

X: An input characteristic to a process or system. In Six Sigma, it is usually used in the expression of Y = F(X), Where the output (Y) is a function of the inputs (X).

Y: An output characteristic of a process. In Six Sigma, it is usually used in the expression of Y= F(X), Where the output (Y) is a function of the inputs (X).

Yellow Belt: An individual who receives approximately one week of training in Six Sigma problem solving and process optimization methods. Yellow Belts

Participate in Process Management activities, participate in Green and Black

Belt projects and apply concepts to their work area and their job. Z Score: See Sigma score.

Fj Ou hold in your hands The Six Sigma book for everyone! Perhaps you’re a

Business owner, a manager, or even an executive. Or you may be an engineer or administrator. Maybe you’re an employee in a Six Sigma company, or you’re considering employment with one. Perhaps you’re a student, and you

Want to improve your employment opportunities. Or maybe you’re pondering

A Six Sigma deployment in your company. Whether compelled or just curious,

There is something in this book for everyone, just as there is something in Six Sigma for everyone.

Six Sigma is now found across the world and throughout all of business. It’s

Not just for manufacturing anymore; in service and transactional businesses,

Not-for-profits, religious organizations, and governments, Six Sigma has improved thousands of organizations. Six Sigma is everywhere.

As the leader of the Six Sigma industry’s professional society, I’ve seen businesses of all sizes and types use Six Sigma as a means to effect robust change and create extraordinary value. I’ve also seen professionals apply these tools

To change their thinking, fuel significant contributions to their organizations, and gain personal opportunities beyond their dreams.

Written with a hands-on focus, Six Sigma For Dummies Is a unique book in the world of Six Sigma. Unlike the story-telling, parable books or the advanced

Statistics tomes, in this book, you find clear explanations as well as practical insights. The authors still give you the statistical understanding, but with a unique emphasis on the how and the why.

Two dramatic things happen to people who read this book. First, they see their world very differently. They see cause-and-effect connections; recognize

Inputs, process flow, and outputs; and understand variation. Second, with this

Newfound understanding and great problem-solving knowledge, readers make improvements in their personal lives and work environments. This change

Inmindset alone eliminates countless frustrating problems and adds value worth thousands or even millions of dollars.

The power to make change for the better is now available to everyone. With the stakes higher than ever, Six Sigma For Dummies Gives you the tools to

Improve and to prosper. Roxanne O’Brasky

President, International Society of Six Sigma Professionals

In This Chapter

^ Dispelling common Six Sigma myths ^ Knowing what to watch for ^ Avoiding common mistakes

Tions t

Avigating through Six Sigma can be treacherous. There are storms and hidden reefs. This chapter gives you ten common mistakes and perceptions that can hinder your success.

Not Atto©ing Enough Time

An organization breaking through to a new level of performance requires an engine of project activity. That’s why a small portion of an organization — the Black Belts — are asked to dedicate all their time and efforts toward completing Six Sigma projects. They set aside their usual job duties and concentrate

Full time on completing assigned project(s).

A common mistake is to assume that an organization can get the same magnitude and speed of change by having Black Belts work on projects on the side,

As a part-time assignment, between the tasks and duties of their regular work.

This approach simply doesn’t generate the force necessary to sustain organizational change. Project completion drags out and resulting savings languish. Ultimately, momentum and interest wane.

Who’s the Leader?

Some organizations have tried to deploy Six Sigma without a designated, empowered deployment leader. They train Belts, they assign projects, they infuse tools, they track results. They believe breakthrough change will occur

By the sum of the individual, independent efforts. But a Six Sigma deployment without a leader is like a ship without a captain — individual crew members may know what to do in their own areas, but there is no direction or overall progress.

Taking Too Big a Bite

Almost invariably, the failure of any Six Sigma project can be traced to a scope

That was too broad. Trying to minimize variation in an entire product, for

Example, is so defocused that little improvement can happen on any part of the product. Concentrating on minimizing the variation in a single critical

Characteristic of a product, however, allows you to dig deep enough to discover the real source of improvement.

Always err on the side of scoping your projects too small.

Focusing On lsotated Areas

A mistake companies can make with Six Sigma is to implement it in isolated pockets, rather than as a uniform and pervasive campaign. Sometimes, an organization will allow a couple of Black Belts or Green Belts to be trained

And to work a few projects. The problem with this approach is that the Belts

Don’t get the needed support from management, and they run into political

And organizational roadblocks that impede their success.

Organizations are living, connected organisms. When you make an improvement in one area or in one process, you have to make other improvements in other areas to receive the full benefits. What sense does it make, for example,

To improve the design of a product but not improve your ability to manufacture that product?

"But We’re Different"

It’s natural to consider yourself or your organization to be unique — so unique that you may even think that what’s worked for others couldn’t possibly work for you. This is one of the most common myths people have about Six Sigma.

Six Sigma is a general methodology. It has proven itself in every arena where it’s been applied — manufacturing, operations, logistics, design, supply chains,

Services, transactions, processing, legal, human resources, software, sales, marketing, management, healthcare, the public sector, defense contracting —

The list literally goes on and on! Don’t fall into the trap of thinking you’re the

Lone exception to the rule.

Overtraining

Not every officer of the peace needs to be trained as an elite Special Forces commando. Likewise, not everyone doing Six Sigma needs to know the details of every advanced statistical tool and method.

The amount of information in Six Sigma courses has ratcheted up, as consultants and trainers have competed against each other in their marketing efforts. But the use of the tools tells the real story. Only a handful of the taught Six Sigma tools are used regularly. The majority are brought out only occasionally for rare Sunday drives.

Don’t get fooled into thinking that more and more knowledge is always better.

And don’t think you have to use every tool on every project. Expediency in

Learning and in application is the key! The best system gets the right knowledge to the right person at the right time.

Btindty Bettering \lour Measurement System

Data and measurements are the foundation of Six Sigma. All too often, however, Six Sigma practitioners neglect to check the validity of their measurements. Unknowingly relying on a faulty measurement system is like building a house with a crooked ruler — you won’t get what you thought you were going to

Get, and you won’t know why.

Always take the time to perform a measurement systems analysis at the

Beginning of your project. Taking this step saves you from many potential

Headaches.

"RemindMe Again, Is It CLs or SLs>"

Control limits (CLs) are a critical part of every control chart. They capture and represent the true voice of the process. The problem is that they are often confused with specification limits — which represent only the voice of the customer. It’s critically important to know when to use which limit in which situation — control limits for the voice of the process and specification limits for the voice of the customer. See Chapter 10 for details.

Exaggerated Opportunity Counts

The definition of Six Sigma performance is no more than 3.4 defects per million opportunities for defects — counting every single opportunity for defects in a given system. But one way to achieve a high capability is to offset the discovered number of defects with a falsely inflated assessment of the number of opportunities. Some practitioners erroneously inflate the number of opportunities in a system to make their performance look better than it really is. What you want is performance that looks and Is Great.

Leveraging Technology

Technology and software are inseparable from Six Sigma. Yet many people try to segment technology into its own, isolated corner. Others dismiss its contribution outright, because they don’t understand how to leverage its potential.

The right technology can help any person in Six Sigma do his or her work better and faster — and that’s a goal everyone desires.

Chapter 15

In This Chapter

► Setting ambitious goals and achieving quantifiable results ^ Living by some important principles

Selecting the right projects and people

► Changing the culture through exposure and training

Uccessful Six Sigma efforts have several practices and characteristics in

Common. This chapter lists ten of the best. As you launch into your own

Six Sigma journey, use these as landmarks to set your course and bearing. Even after you’ve been doing Six Sigma for a while, it’s a good idea to periodically compare what you do with what others have found to be most effective,

So revisit this chapter from time to time.

Six Sigma isn’t for the mildly ambitious manager or the person who wants to incrementally improve the output of a process. Instead, Six Sigma is for people who want to improve by leaps and bounds.

Six Sigma has repeatedly proven that it produces breakthrough improvement. But to achieve this, you have to combine the power of the Six Sigma method and tools with Stretch goals, Goals that almost seem too aggressive, too

Optimistic.

Specifically, a stretch goal represents a 70 percent improvement over current performance. For example, if your company’s profit margin is seven percent, you want to aim for 11.9 percent (a 70 percent increase). Or if a certain process or product is producing ten defects per 100 units, you want to reduce that number to three defects per 100 units (a 70 percent improvement).

Set Stretch Goats

Another common way to set the right stretch target is to benchmark yourself against your competition. A Benchmark Is the level of performance achieved by the best companies, organizations, functions, or processes in your industry. If someone else is doing it, you should be able to do it, too, right? Toyota, for example, is a company that is benchmarked for the time it takes them to introduce a brand-new vehicle design. Most companies take 36 to 48 months to bring a new vehicle to market; Toyota did it in about 24 for its hybrid car, the Prius, which also presented a technical challenge far beyond those of traditional gasoline-only cars.

Target Tangible Results

Typically, Six Sigma leads organizations to reduce their costs by as much as

20 to 30 percent of revenue. At the same time, these organizations increase

Their revenues by 10 percent or more.

To realize these returns, however, each Six Sigma project must be tied to a tangible financial measure of return — dollars saved, new revenue gained,

Specific costs avoided, and so on (see Chapter 4 for details). These measured

Financial returns must be formally measured, tracked, and rolled up if you want to achieve the startling financial return that is a hallmark of Six Sigma.

Without tying projects to tangible financial measures and tracking their financial impact, Six Sigma efforts naturally drift away from their financial potential.

In isolated cases, a Six Sigma project is not directly focused on cost reduction or revenue enhancement. Instead, it is targeted on a strategic objective of the organization. If you complete a project with an object of increasing brand awareness, for example, you’ll have difficulty quantifying how much that project improves the company’s bottom line. But if it enables the company’s key business strategies, the project is still worth the effort.

Determine Outcomes

Every output or result is determined by a set of inputs. This is the idea of

Determinism discussed in Chapter 2. The natural outgrowth of this principle

Is that you actively go out and adjust and control the inputs in a way that enables you to reach your desired outcomes with certainty and consistency.

Think Before \lou Act

Too often, people jump into action and do something — anything — to solve a problem. They confuse action with effectiveness. Undoubtedly, this approach showcases activity, but it usually ends in a continuation of the problem or, at

Best, a suboptimal solution.

Six sigma’s DMAIC methodology (see Chapter 3 for details) forces you to shift the bulk of the activity of solving a problem into defining, measuring, and

Planning a solution. Each project starts with a detailed, in-depth definition

Of what the problem really is and what the objectives of the solution are. Next, extensive measurements are taken to verify the current performance of the process or system. This is followed by in-depth analysis of inputs, outputs, conditions, and causes-and-effects. Only after completion of all of these steps

Is an improvement solution attempted. The result of this upfront rigor is,

Almost always, an optimal solution that can be quickly and efficiently put in

Place. In the long-run, the front-loaded DMAIC approach solves the problem

More quickly and with better, more consistent results than other approaches.

Businesses and organizations have a vested interest in getting optimal results

Quickly and consistently. This is the emancipating power of Six Sigma.

Put \lour Faith in Data

There is an admonition among Six Sigma practitioners: "In God we trust; all others bring data." Without data, decisions are based on supposition, estimation, opinion, and sometimes wishful thinking. Data allows you to objectively identify and select the truly best ideas and solutions from among the many

Alternatives.

Making decisions based on data, however, is not easy. Data require you to suspend judgment and personal bias, to confront sometimes brutal and

Undesirable facts. You have to believe that, in the long-run, trusting data will consistently lead you to better and more rapid solutions.

If you listen to it, the data will tell you what you need to do to improve by

Leaps and bounds. Common sense, opinion, and "trying harder" are not guaranteed to get you there.

Minimize Variation

Most people think of excellence in terms of averages or single numbers — the average yield on a production line, the monthly cost to run a department, the rate of return on an investment. But the reality is that variation around these averages or single numbers — even when they are at acceptable levels — can

Often cause more damage than their level itself.

For example, having a high average number of orders is great. But if the day-today number of orders varies widely, it requires the company to have excess

Equipment and staff always on hand, just in case. When the number of orders

Varies to the low side, equipment and staff sit idle. The company would

Actually come out ahead if its average number of orders were lower but

Its day-to-day variation were smaller. That way equipment and staff needs would be steady and costs would be reduced.

Variation will always be present in the plans you design, the products you

Make, the transactions you conduct, the services you deliver. Even in the environment outside your control, events and circumstances change and

Vary in ways beyond your control.

Six Sigma does two important things. One, it narrows the range of variation in any process, product, service, or transaction. Two, it enables you to configure your work so that you can meet your performance targets in spite of the variation you can’t control.

Align Projects ©ith Key Goals

One of the most important Six Sigma success factors is selecting projects that are aligned with the key goals and objectives of your organization (see Chapter 4 for details). Six Sigma efforts that are successful and lasting are always made up of projects that are each specifically focused on moving

An organization towards its stated objectives.

Celebrate Success!

A Six Sigma initiative may start small with a single pilot project, or a deployment within a lone department. Others grow to include an entire global organization or accumulate staggering financial returns. Regardless,

Celebrate success.

Success is contagious. When the first, small victories are showcased and

Lauded — with recognition, rewards, praise, and publicity — people develop real interest. They build confidence and trust. They begin to believe in the power and potential of the method. Each successive victory becomes that

Much easier.

Involve the O©ner

Six Sigma projects require change. Black Belts and Green Belts develop improvements to systems and processes for which they are not accountable. And when these participants are done with their project, they ask the real

System or process owner to implement and sustain their solution.

Put yourself in the owner’s shoes. Does the idea of tinkering with the process you own without knowing the future results sound exciting?

Successful Six Sigma practitioners communicate with and involve the owner of the process or system they are working in. They solicit their input and

Provide feedback through all the stages of DMAIC. Then, when the time for change arrives, the owner jumps at the chance to implement the awaited improvements.

Unleash Everyone’s Potential

The best Six Sigma efforts extend beyond full-time Black Belts. When an organization broadens its Six Sigma knowledge and participation to Green Belts

And Yellow Belts, it unleashes the vast potential of a greater number of its

Employees. What an advantage! Instead of relying on a handful of isolated,

Specialized experts to drive organization-wide improvement, an entire army is enlisted to contribute to the effort.

Chapter 14

In This Chapter

Using a Web portal Perusing publications ^ Joining associations and societies

Using the services of trainers and consultants

Hether it’s the statistics, the projects, the deployment planning,

WW Applications, leadership, management, or support — Six Sigma is

Hard. No doubt about it. It’s big and it’s complicated, and you need lots of

Smarts (or, at the very least, this book) to pull it off. But while you may be blazing new trails through your own life and organization, thousands of people have forged similar trails before you. You can trod merrily on the

Bleached bones of those who have gone before.

There are many, many places to go for all kinds of help on every subject.

Academics, corporations, societies, associations, practitioners, consultants,

And authors — they’re all out there and available to assist you, with knowledge, education, training, consulting, tools, technologies, and publications.

We’ve organized them into ten groups.

Colleagues

Chances are, you know someone who has been involved in Six Sigma, perhaps even a specialist of some type. If you’re working in a company that’s deployed Six Sigma, you have Champions, Master Black Belts, and Black Belts all around

You. You then also have reference material at your fingertips.

Even if you don’t know of anyone personally, you may be surprised by just how few degrees of separation lie between your interest and a Six Sigma

Expert. Ask your friends and associates, at your church or at the ballgame.

Try shouting "Six Sigma" in a crowded movie theater! You know people who know Six Sigma; you just have to ask around.

Six Sigma Corporations

Hundreds of corporations have deployed Six Sigma, including corporations in every industry and every corner of the world. Many of them will openly meet

With you to discuss their experiences and offer advice. Several, like pioneer Motorola, have consulting groups that offer this advice as a service. Don’t

Hesitate to consider calling on a company that’s been through the process

And ask them about it.

Associations and Professional Societies

Several associations and professional societies cater to the Six Sigma industry and audience. These associations offer a variety of services to members,

Including access to knowledge and information, such as white papers and case studies, special events, contacts, and discounts on materials and services. If you’re entering the Six Sigma world, membership to one of these is highly recommended.

The International Society of Six Sigma Professionals (ISSSP): ISSSP is the premier industry organization that caters to the professional.

F American Society for Quality (ASQ): ASQ is the largest quality association in the United State, with over 100,000 members.

Six Sigma Benchmarking Association: This association conducts

Benchmarking studies, shares best practices, and facilitates process

Improvement and total quality.

F American Statistical Association (ASA): ASA is a scientific and educational society that promotes statistical practice, applications, and research;

Publishes statistical journals; and improves statistical education.

The Royal Statistical Society (RSS): RSS, based in the U. K., is the world’s oldest quality association. RSS publishes a journal, organizes meetings, sets and maintains professional standards, accredits university courses,

And administers examinations.

Conferences and Symposia

Numerous organizations regularly sponsor conferences and symposia around the United States and the world on topics in Six Sigma, quality, and Business

Process Improvement. These conferences are outstanding forums for meeting

With peers, surveying product and service providers, and attending seminars on current topics of interest.

Major Six Sigma conferences include the following:

F ISSSP Conferences: ISSSP holds several conferences annually.

F The International Quality and Productivity Center (IQPC): IQPC provides tailored conferences and hosts numerous Six Sigma conferences

Worldwide.

American Society for Quality (ASQ): ASQ hosts a large annual

Conference.

F Worldwide Conventions and Business Forums (WCBF): A conference organization that hosts topical Six Sigma conferences.

Ixperion: This group hosts focused conferences, primarily in Europe.

Check the Internet for more information about these groups.

In addition to these major industry events, many minor events of topical interest occur regularly. These events are hosted by associations, consultancies,

And tool vendors. You wouldn’t want to miss the International Conference on Axiomatic Design, for example!

Publications

At last count, we place the number of books on Six Sigma at over 200 titles. You can find them easily through iSixSigma or directly on Amazon. The authors of these tomes are usually consultants and practitioners who have published works based directly on industry experience. The works in general are grouped by topic; choose the ones that best suit your needs:

F Guide books: How to implement Six Sigma in your company

F Pocket guides: Handy little reference books that you can literally stick in

Your pocket

F Management books: Stories and advice on how to manage Six Sigma

Initiatives

F Handbooks to be used as tools: Detailed, mathematically rich volumes on every statistical tool and topic

Technology books: Books about the technical and management tools

Web Portals

The fastest access information is right at your fingertips. Web portals aggregate vast sums of information and whisk you directly to the source with the

Click of your computer mouse. We recommend the Web as the starting point for outside help.

Google: There’s no bigger access point to the world’s information. We

Mentioned in Chapter 1 that the term "Six Sigma" returns over 2 million hits on Google. But that’s only the starting point. Try entering ANOVA, And Google returns 2 million hits on that! How about something more esoteric? Six Sigma Black Belt Yields 9,000 places to go. How about Run charts? 1,200 responses. Or Six Sigma online training: 700 hits.

Google is a portal of awesome power.

V ISixSigma: The Six Sigma industry has its own commercial portal, www. i s ixsi gma. com. iSixSigma provides extensive free information on almost any Six Sigma topic. Content on the site focuses on three primary areas: information, community, and supplemental services. You

Can find products, tools, hire a Black Belt, and even find a job. The site also includes chat rooms, forums, and libraries.

Periodicals

Several publications support the Six Sigma industry. The larger and more significant journals include the following:

ISixSigma Magazine: The publishing end of the Web portal

Six Sigma Forum – The magazine of the American Society for Quality (ASQ); directed at the Six Sigma audience

International Journal of Six Sigma and Competitive Advantage: A

Practical and research-oriented journal that addresses new Six Sigma

Developments, thinking, tools, techniques, and methodologies that improve business and organizational performance

V Quality Progress: The quality publication of the ASQ

F Quality Digest: An independent magazine about the business of quality

Technology Vendors

An increasing number of software and technology products related to Six Sigma (see Chapters 11 and 12) are on the market. These tools are powerful

And enable your initiatives. These vendors sell the software, provide product training, and assist with implementation and integration in your environment.

Technology vendor products and services come in several categories:

Process modeling and simulation Statistical analysis Process management and execution Program portfolio and project management

Consultants

Help is on the way. Numerous consultancies cater to supporting Six Sigma initiatives. These consultancies can help you with every aspect of your interest — everything from "Should I consider a Six Sigma initiative?" to "How do I run a process simulation?" and everything in between.

The consultancies fall primarily into three categories:

Large scale consultancies from Big-6-type firms: These firms have Six

Sigma expertise but also tend to provide enterprise-class coverage of

Topics in business process management and information technology systems integration.

Six Sigma consultancies: The industry boasts several dozen firms who cater specifically to Six Sigma implementation and support.

Boutiques: Numerous highly focused one-person firms dot the landscape; these consultants provide specialized assistance in specific

Topics and areas.

Six Sigma consulting is expensive. Don’t be surprised to pay $3,000 or more per day for experienced senior consulting. It’s worth it — if you can afford it.

Six Sigma Trainers

Training in the principles and practices of Six Sigma is a commodity industry with numerous providers. Training is available on every conceivable topic

And through multiple modes, including traditional classroom, computer-based training, and asynchronous learning networks. Several firms license training materials and train a company’s trainers.

Training providers come in three flavors:

F Academics: More and more colleges and universities offer Six Sigma training. This is usually offered through the College of Engineering or

TheBusiness School, and is either part of the regular undergraduate or graduate curriculum or offered as an outreach through a professional

Development center. Contact your local college or university for more

Information.

F Training consultancies: Most of the Six Sigma consulting firms also offer training. Unlike many academic sources, consultancies train on both technical and non-technical topics. In addition, they often tailor

Thetraining curriculum to the needs of a particular business.

V Online training: Growing in popularity, online training is increasingly available on topics in Six Sigma. Online courses are available through

Universities and several of the training consultancies, and is also offered

By firms that specialize in online curriculum.

In This Chapter

^ Putting all the annoying exceptions into one corral ^ Handling exceptions more easily with tips and tricks

•Exceptions seem like nature’s way of hedging its bets. As such, they’re annoying — why

Can’t nature just go ahead and Commit? But nature knows nothing of our rules, so it certainly isn’t going out of its way to annoy you. Nor is it going out of its way to make things easier for you. Either way, seeing as you have to deal with exceptions, we thought we’d corral many of them into this chapter so you can confront them more conveniently.

However, one big caveat! This chapter is at the end for a reason. Don’t get so hung up on the exceptions that you don’t master the basics properly. Many AP students lose points on the exam because they omit describing the basic principles that underlie the exceptions. It is not enough to only understand the exceptions without quoting the "normal" rules or trends.

In the field of psychology, Maslow’s hierarchy of needs declares that people need a sense of belonging. It’s a good thing hydrogen isn’t a person because it belongs nowhere on the periodic table (which we describe in Chapter 3). Although hydrogen is usually listed atop Group IA along with the alkali metals, it doesn’t really fit. Sure, hydrogen can lose an electron to form a +1 cation, just like the alkali metals, but hydrogen can also gain an electron to form hydride, H-, especially when bonding to metals. Furthermore, hydrogen doesn’t have metallic properties under normal conditions, but typically exists as the diatomic gas, H2.

These differences arise largely from the fact that hydrogen has only a single 1s orbital and lacks other, more interior orbitals that could shield the valence electrons from the positive charge of the nucleus. (See Chapter 7 for an introduction to S And other types of orbitals.) Another factor is that H+ is a bare proton with extremely compact charge density.

Hydrogen Isn’t an Alkali Metal

The Octet Rule Isn’t Always an Option

An Octet, As we explain in Chapter 5, is a full shell of eight valence electrons. The octet rule states that atoms bond with one another so as to acquire completely filled valence shells that contain eight electrons. It’s a pretty good rule. Like most pretty good rules, it has exceptions:

Atoms containing only 1s electrons simply don’t have eight slots to fill. So, hydrogen and helium obey the "duet" rule.

Certain molecules (like NO, for example) contain an odd number of valence electrons. In these cases, full octets aren’t an option. Like people born with an odd number of toes, these molecules may not be entirely happy with the situation, but they deal with it.

Atoms often attempt to fill their valence shells by covalent bonding (see Chapter 5). Each covalent bond adds a shared electron to the shell. But covalent bonding usually requires an atom to donate an electron of its own for sharing within the bond. Some atoms run out of electrons to donate, and therefore can’t engage in enough covalent bonds to fill their shell octets. Boron trifluoride, BF3, is a typical example. The central boron atom of this molecule can only engage in three B-F bonds, and ends up with only six valence electrons. This boron is said to be electron deficient. You might speculate that the fluorine atoms could pitch in a bit and donate some more electrons to boron. But fluorine is highly electronegative and greedily holds fast to its own octets. C’est la vie.

Some atoms take on more than a full octet’s worth of electrons. This is known as an Expanded octet. These atoms are said to be Hypervalent Or Hypercoordinated. The phosphorous of phosphorous pentachloride, PCl5, is an example. These kinds of situations require an atom from period (row) 3 or higher within the periodic table. The exact reasons for this restriction are still debated. Certainly, the larger atomic size of period 3 and higher atoms allows more room to accommodate the bulk of all the binding partners that distribute around the central atom’s valence shell.

Some Electron Configurations Ignore the Orbital Rules

Electrons fill orbitals from lowest energy to highest energy. This fact is true.

The progression of orbitals from lowest to highest energy is predicted by an Aufbau diagram. This isn’t always true. Some atoms possess electron configurations that deviate from the standard rules for filling orbitals from the ground up. For Aufbau’s sake, why?

Two conditions typically lead to exceptional electron configurations:

First, successive orbital energies must lie close together, as is the case with 3d and 4s orbitals, for example.

Second, shifting electrons between these energetically similar orbitals must result in a half-filled or fully filled set of identical orbitals, an energetically happy state of affairs.

Want a couple of examples? Strictly by the Aufbau, but not by the "energy" rules, chromium should have the following electron configuration:

[Ar]3d*4s2

Because shifting a single electron from 4S To the energetically similar 3D Level half-fills the 3D Set and lowers the energy, the actual configuration of chromium is

[Ar]3D54S1

For similar reasons, the configuration of copper is not the expected [Ar]3d°4s2, but instead is [Ar]3d104s’. Shifting a single electron from 4s to 3d fills the 3d set of orbitals.

Strictly speaking, the above arguments only apply to isolated atoms. Once the atom is involved in bond formation in a compound, the whole energy level scheme has to be re-examined, and apparent filling order may change again.

Flip to Chapter 5 for full details on electron configurations and Aufbau diagrams.

One Partner in Coordinate Covalent Bonds Giveth Electrons; the Other Taketh

To form a covalent bond (as we explain in Chapter 5), each bonding partner contributes one electron to a two-electron bond, right? Not always. Coordinate covalent bonds Are particularly common between transition metals and partners that possess lone pairs of electrons.

Here’s the basic idea: Transition metals have empty valence orbitals. Lone pairs Are pairs of nonbonding electrons within a single orbital. So, transition metals and lone-pair bearing molecules can engage in Lewis acid-base interactions (see Chapter 17). The lone-pair containing molecule acts as an electron donor (a Lewis base), giving both electrons to a bond with the metal, which acts as an electron acceptor (a Lewis acid). When this occurs, the resulting molecule is called a Coordination complex.

The partners that bind to the metal are called Ligands. Coordination complexes are often intensely colored and can have properties that are quite different than those of the free metal.

All Hybridized Electron Orbitals Are Created Equal

Different electron orbital types have grossly different shapes. Spherical S Orbitals look nothing like lobed P Orbitals, for example. So, if the valence shell of an atom contains both S – And P-orbital electrons, you might expect those electrons to behave differently when it comes to things like bonding, right? Wrong. If you attempt to assume such a thing, valence bond

Theory politely taps you an the shoulder to remind you that valence shell electrons occupy hybridized orbitals. These hybridized orbitals (as in sp3, sp2, and Sp Orbitals) reflect a mixture of the properties of the orbitals that make them up, and each of the orbitals is equivalent to the others in the valence shell.

Although this phenomenon represents an exception to the rules, it’s somewhat less annoying than other exceptions because hybridization allows for the nicely symmetrical orbital geometries of actual atoms within actual molecules. VSEPR theory presently clears its throat to point out that the negative charge of the electrons within the hybridized orbitals causes those equivalent orbitals to spread as far apart as possible from one another. As a result, the geometry of Sp3-hybridized methane (CH4), for example, is beautifully tetrahedral. However, this is messed up easily once total symmetry is upset. CH3I is no longer a perfect tetrahedron. Sigh.

Check out Chapter 7 for the details on VSEPR theory and hybridization.

Use Caution When Naming Compounds with Transition Metals

The thing about transition metals is that the same transition metal can form cations with different charges. Differently charged metal cations need different names, so chemists don’t get any more confused than they already are. These days, you indicate these differences by using Roman numerals within parentheses to denote the positive charge of the metal ion. An older method adds the suffixes -ous Or -ic To indicate the cation with the smaller or larger charge, respectively. For example

Cu+ = copper (I) ion or cuprous ion Cu2+ = copper (II) ion or cupric ion

Metal cations team up with nonmetal anions to form ionic compounds. What’s more, the ratio of cations to anions within each formula unit depends on the charge assumed by the fickle transition metal. The formula unit as a whole must be electrically neutral. The rules you follow to name an ionic compound must accommodate the whims of transition metals. The system of Roman numerals or suffixes applies in such situations:

CuCl = copper (I) chloride or cuprous chloride CuCl2 = copper (II) chloride or cupric chloride

Chapter 7 has the full scoop on naming ionic and other types of compounds.

You Must Memorize Polyatomic Ions

Sorry, it’s true. Not only are polyatomic ions annoying because they must be memorized, but they pop up everywhere. If you don’t memorize the polyatomic ions, you’ll waste time trying to figure out weird (and incorrect) covalent bonding arrangements when what you’re really dealing with is a straightforward ionic compound. Here they are in Table 33-1.

Liquid Water Is Denser than Ice

Kinetic molecular theory, which we discuss in Chapters 9 and 11, predicts that adding heat to a collection of particles increases the volume occupied by those particles. Heat-induced changes in volume are particularly evident at phase changes, so liquids tend to be less dense than their solid counterparts. Weird water throws a wet monkey wrench into the works. Because of H2O’s ideal hydrogen-bonding geometry, the lattice geometry of solid water (ice) is very "open" with large empty spaces at the center of a hexagonal ring of water molecules. These empty spaces lead to a lower density of solid water relative to liquid water. So, ice floats in water. Although annoying, this watery exception is quite important for biology.

No Gas Is Truly Ideal

No matter what your misty-eyed grandparents tell you, there were never halcyon Days of Old when all the gases were ideal. To be perfectly frank, not a single gas is really, truly ideal. Some gases just approach the ideal more closely than others. At very high pressures, even gases that normally behave close to the ideal cease to follow the Ideal Gas Laws that we discuss in Chapter 9.

When gases deviate from the ideal, we call them Real gases. Real gases have properties that are significantly shaped by the volumes of the gas particles and/or by interparticle forces.

Common Names for Organic Compounds Hearken Back to the Old Days

Serious study of chemistry predates modern systematic methods for naming compounds. As a result, chemists persistently address a large number of common compounds, especially organic compounds, by older, "trivial" names. This practice won’t change anytime soon. A cynical take on the situation is to observe that progress occurs one funeral at a time. A less cynical approach involves serenely accepting that which you cannot change and getting familiar with these old-fashioned names. Table 33-2 lists some important ones; head to Chapter 25 for details on organic compounds.

In This Chapter

^ Concentrating on the most important concepts ^ Listing key math skills

^ Using tips and tricks to manipulate equations

/f you think that you’re going to get away with doing chemistry and chemistry alone on the AP exam, you’re sorely mistaken. Chemistry is a very mathematically oriented science, and you will be asked to do a great number of calculations as well as applying chemistry concepts. Listed in this chapter are the ten most essential AP chemistry math skills and some tips and tricks on avoiding errors. In particular, this chapter points out the skills necessary to build a natural intuition for the correctness of your answers.

Dimensional Analysis/Conversion Factors

You’re guaranteed to use conversion factors, perhaps the most essential of all math skills for the purposes of AP chemistry, several times on every AP chemistry exam. The purpose of a conversion factor is just as its name implies — to change (convert) one unit to another. All conversion factors have the same essential property — their numerator and denominator are two different representations of the exact same quantity. For example, at STP 22.4L and 1mol of a gas are the exact same thing, so both the conversion factor 22.4L/1 mol and its companion 1mol/22.4L are equivalent to each other and both equal to 1 because their numerators and denominators are exactly equal quantities. So what’s the purpose of multiplying something by 1? It allows you to manipulate units, getting rid of unwanted ones and bring in the ones that the problem asks for. In general, you will place the unit you wish to get rid of in the denominator and the one that you wish to change it to in the numerator of the conversion factor.

PH and Logs

PH calculations are notoriously difficult even for a seasoned Chemistry student such as yourself because they apply the difficult algebraic concept of the logarithm. It is essential that you realize that pH utilizes a base ten logarithm, which is the reverse operation of raising ten to a number. In other words, you can "undo" a logarithm by raising ten to both sides of a pH equation. This step leads you to the very useful formula 10-pH = [H+], which allows you to backsolve from pH to [H+]. The other essential thing to realize about pH is that if the coefficient on the H+

Concentration is 1, then the negative power of ten to which it is raised is equivalent to the pH and no actual calculation is necessary. Also, any coefficient greater than 1 will have a pH between its power of ten and one less than its power of ten. For example, a solution with [H+] = 4.55 x 10-12 has a pH between 11 and 12. This knowledge can save you lots of time on multiple-choice questions or on free-response questions with which you cannot use a calculator.

Isolating a Variable

Another essential algebra skill to bring with you to the exam is the ability to isolate a variable in an equation. The AP exam provides you with a plethora of equations. However, it will be up to you to isolate each variable that you need to solve for (i. e. get it "by itself" on one side of the equation). We are not attempting to undermine your intelligence by pointing out this seemingly trivial concept. There is a subtlety to this skill that many AP chemistry exam-takers neglect — you are much more likely to get the correct answer if you isolate the variable that you need to solve for Before You plug any numbers in. This minimizes algebraic and rounding errors, which can lose you points.

Significant Figures

After you get an answer on the AP exam, make sure that you provide the correct number of significant figures in your answer. Here is a summary of the rules for assigning significant figures:

U Any nonzero digit is significant. Thus, 6.42 seconds (s) contains three significant figures.

U Zeros sandwiched between nonzero digits are significant. Thus, 3.07 s contains three significant figures.

U Zeros on the left side of the first nonzero digit are Not Significant. Thus, 0.0642 s and 0.00307 s each contain three significant figures.

U When a number is greater than 1, all digits to the right of the decimal point are understood to be significant. Thus, 1.76 s has three significant figures, while 1.760 s has four significant figures. We understand that the 6 Is uncertain in the first measurement, but is certain in the second measurement.

U When a number has no decimal point, any zeros after the last nonzero digit May or may not Be significant. Thus, in a measurement reported as 1370 s, we cannot be certain if the "0" is a certain value, or if it is merely a placeholder. Be a good chemist. Report your measurements in scientific notation to avoid such annoying ambiguities.

U Numbers resulting from Counting (e. g., one kangaroo, two kangaroos, three kangaroos. . .) or from Defined quantities (e. g., 60 seconds per 1 minute) are considered completely certain. These values are understood to have an unlimited number of significant figures, consistent with their complete certainty.

U When taking the log of a number, as when calculating pH or pOH from [H+] or [OH-], only the decimal portion of the answer applies toward the significant figure count (not the preceding integer). For example, if [H+] = 0.0100Mand pH = – log[H+], then pH = 2.000. Why? 0.0100 contains three significant figures. Therefore, the decimal portion of the log answer (the mantissa) contains three significant figures. The preceding integer (the characteristic "2" in this case) does not count toward the significant figure total.

The final thing to burn into your brain about significant figures is that your final answer should always be rounded to the same number of significant figures as the least-precise number you were given in the problem. However, do not round any of the numbers you are given until the very end after you have plugged them into your equations in their full, precise glory.

Scientific Notation

You must be comfortable with scientific notation before taking the AP chemistry exam. Remember that the coefficient for a number in scientific notation must be greater than one and less than ten, that positive exponents mean very large numbers, and that negative exponents mean very small numbers. Also, you must be able to properly add, subtract, multiply, and divide numbers in scientific notation. Adding and subtracting is easily accomplished by adding or subtracting the coefficients As long as the exponents of the two are the same. So, you must adjust the values to have the same exponents Before Adding or subtracting. To multiply two numbers in scientific notation together, you must multiply their coefficients but Add Their exponents. To divide, you must divide their coefficients but Subtract The exponent of the denominator from that of the numerator.

Percent Error, Percent Yield, and Percent Composition

The key percentage measurements in chemistry all have the exact same underlying concept: Remember, "percentage" is just asking how many would you have if you had a hundred of the total. Keep that in mind and you won’t get lost. Divide the portion under consideration by the whole and you have the percentage you’re looking for. For percent errors, subtract your result from the accepted value of the quantity (this value is the error in your measurement) and then divide that by the accepted value. Percent yield is calculated in an equivalent way: by subtracting the actual yield from the theoretical yield and then dividing by the theoretical yield. Unsurprisingly, percent composition is also quite similar, though even simpler. Divide the number of grams of each particular atom in one mole of a substance by its molar mass and you have its percent composition. For all three of these quantities, remember that your answer will be in decimal form so you will need to multiply by 100 to change it into percentage form.

The Si System of Units

Make sure that you’re familiar with the SI system of units and, more importantly, have a sense of the relative size of each one. This familiarity can go a long way toward honing your intuition as to whether an answer seems to be about the right size based on what you know about the problem. The five SI base units that you will need to do chemistry problems, as well as their non-SI equivalents, are given in Table 31-1.

Metric System Prefixes

Nobody, not even a chemist, likes dealing with scientific notation if she doesn’t have to. Metric system prefixes often appear in problems in lieu of scientific notation. For example, the size of the nucleus of an atom is roughly 10 femtometers across, which is a nicer way of saying 10 x 10-15 meters. The most useful of these prefixes are given in Table 31-2 below for you to memorize.

Deducing Qualitative Trends from an Equation

It is important not only that you be adept at manipulating chemical equations, but that you also understand their underlying meaning if you wish to do well on the AP chemistry exam. In other words, when you look at an equation, you should always be thinking first and foremost about the relationship between variables. Are they inversely or directly proportional (in other words, does one increase as the other decreases, or do they increase or decrease

Together)? Recognizing trends like this can help you eliminate wrong answers in the multiple-choice section more quickly and can help to hone your intuition for correct and incorrect responses. A typical example is in solving for changes in ideal gas

If P1V1 = NRT1, Then changing to new conditions gives you P2V2 = nRT2.

The Greek Letter Delta

The delta symbol (A) appears quite often in chemistry and always signifies that a quantity has changed from an initial to a final state. It can be interpreted to mean "change in" the variable that follows it. For example AT Is the change in temperature from the initial to the final state and can be written as TF – TI.