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■ 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.

■ his appendix contains an A-Z of every complementary medical therapy W That I can fit in these pages!

All the main therapies that feature in this book have chapter references so that you can nip directly to the chapter if you want to find out much, much more. All the jargon words, such as Meridian And Acupoint, Are explained in the relevant chapters, too.

The A-Z also contains lots of other, perhaps lesser known, therapies that I wasn’t able to squeeze in anywhere else in the book. If a single, main contact link for the therapy exists, then I’ve tried to include that, too.

Mention of these less well-known therapies in the A-Z list doesn’t necessarily mean that they’re effective or have been scientifically validated or are even safe. However, neither can you necessarily assume they’re no good. Many of these therapies are relatively new and have not yet been investigated independently. For all we know, some of these therapies may even become mainstream in the future.

If you want to try out any of these therapies, find out as much as you can about the therapy and the practitioner’s level of skill and experience before treatment. Take a look at Chapter 1 and the individual chapters on all the main therapies for guidance on how to select a therapy, how to know if it’s effective, and the type of questions you may want to ask.

If I’ve missed out any therapy in this A-Z through oversight or ignorance, then please let me know about it and I’ll consider including it in future editions of this book.

I hope you find this handy reference guide useful.

Acupressure: The application of finger-tip or thumb pressure to different points on the body in order to balance the meridian (vital energy) system. For more, see Chapter 9 on acupuncture and Chapter 17 on massage.

Acupuncture: The insertion of fine needles into points on the skin, said to balance the flow of Qi (vital energy) that is believed to flow in invisible channels known as Meridians. For more, see Chapter 9 on acupuncture.

Alexander Technique: A technique for realigning posture devised by Australian actor, F. M. Alexander. For more, see Chapter 16 on bodywork therapies.

Allergy testing: A range of diagnostic approaches used to determine which food or inhaled substances may cause body imbalance or illness. For more, see Chapter 12 on nutritional medicine and Chapter 22 on energy medicine.

Amatsu: A modern-day synthesis of Anma Massage with Japanese bodywork techniques. For more, see Chapter 17 on massage.

Anma: An ancient Japanese massage technique using fingers, thumbs, and hands, or sometimes elbows and feet, to apply pressure to acupoints and stimulate flow in the acupuncture meridians. For more, see Chapter 17 on massage.

Anthroposophical medicine: A system of medicine based on creative therapies, herbal medicine, homeopathy, and healthy eating of foods grown bio-dynamically. For more, see Chapter 23 on creative therapies.

Applied kinesiology: See ‘Kinesiology’.

Aqua detox: A therapy involving placing the feet in an electrically operated footbath supposedly designed to remove toxins from the body. Regarded by some as a scam but others swear by it! For more, see Www. aquadetoxuk. com or Www. devicewatch. org/reports/aquadetox. shtml.

Aqua touch: A whole body treatment given in water.

Aromatherapy: The use of essential oils, extracted from plants, in massage, inhalations, and so on. For more, see Chapter 19 on aromatherapy.

Art therapy: The use of art (painting, drawing, collage making, sculpture, clay modelling, and so on) to promote physical, mental, and emotional well-being. For more, see Chapter 23 on creative therapies.

Auricular acupuncture: Acupuncture treatment for the whole body using just the ear! For more, see Chapter 9 on acupuncture.

Auro-soma: See ‘Colour therapy’.

Autogenic training/therapy (AT): A relaxation technique to ease mental and physical stress. For more, see Chapter 21 on psychological therapies.

Ayurveda: Traditional Indian system of medicine with treatments that include diet, yoga, and meditation. Also includes Marma massage, Panchakarma purification techniques, Chavutti Thirumal, and Indian head massage. For more, see Chapter 5 on Ayurveda and Chapter 17 on massage.

Baby massage: Gentle massage strokes and stretches to stimulate the baby’s immune system and aid digestion and relaxation. For more, see Chapter 17 on massage.

Bach flower remedies: Flower remedies developed by Dr Edward Bach for the treatment of emotional conditions. For more, see Chapter 22.

Bates method: Exercises to improve eye health and vision developed by Dr William Bates in the US. For more, see Chapter 16.

Bi-aura therapy: A system of bio-energy healing used to remove blockages in energy flow. See Chapter 22 for more.

Bibliotherapy: The therapeutic use of literature, through books, film, and theatre, to help resolve trauma or emotional problems. For more, see Chapter 23 on creative therapies.

Biodynamic massage: A form of massage therapy to release physical and energetic blockages. For more, see Chapter 17 on massage.

Bio-energetics: A therapy involving holding various physical positions and exploring feelings to release inner blockages. For more, see Chapter 16 on bodywork therapies.

Bio-energy therapy: A system of gentle hand movements to increase the flow of vital energy, or Qi, In the body and remove blockages. See Chapter 22 and

Www. bioenergyhealing. net.

Biofeedback: The use of electronic devices to feed back information on body functions with the purpose of bringing them under voluntary control. For more, see Chapter 21 on psychological therapies.

Biorhythm therapy: Calculating biorhythms, supposed cycles of emotional, physical, and mental ‘highs’ and ‘lows’ calculated mathematically on the basis of your birth date, to determine the best day for activities, operations, and so on. For more, see Chapter 21 on psychological therapies.

Bowen technique: A soft-tissue therapy developed by Tom Bowen involving light finger and thumb movements over the body to relax and release tension. For more, see Chapter 16 on bodywork therapies.

Buteyko breathing technique: A system of breathing exercises devised to promote relaxed breathing and relieve asthma. For more, see Chapter 18.

Chelation therapy: A treatment designed to remove heavy metals from the body that has also been used to help clear blockages in the arteries. For more, see Chapter 12 on nutritional therapy.

Chinese medicine: Also known as Traditional Chinese Medicine (TCM), a system of medicine that for thousands of years has incorporated acupuncture, herbal medicine, massage (Tui na), Therapeutic exercises (Qi Gong), And dietary and lifestyle regimes. For more, see Chapter 4.

Chiropractic: A system of spinal manipulation and therapy for joint and muscular problems. See also McTimoney chiropractic. For more, see Chapter 15 on chiropractic.

Chua Ka: An ancient form of Mongolian massage originally used by warriors preparing themselves for battle. For more, see Chapter 17 on massage.

Clinical ecology: Also known as environmental medicine, this involves assessment with electronic devices to detect sensitivities to foods, chemicals, moulds, pollens, and so on. For more, see Chapter 22 on energy medicine and Chapter 12 on nutrition.

Colonic hydrotherapy: Involves the therapeutic cleansing of the colon using water, or other liquids, which can be done by machine or manually. For more, see Chapter 13 on naturopathy.

Colour therapy: The use of coloured light, with different wavelengths and frequencies, or exposure to coloured materials, liquids (auro-soma), and so on, to affect the body therapeutically. For more, see Chapter 23 on creative therapies.

Cranial osteopathy: A subtle form of osteopathy that focuses on the ebb and flow of cerebro-spinal fluid and slight movements within the cranial bones. For more, see Chapter 14 on osteopathy.

Cranio-sacral therapy: A system of light pressure techniques on the cranium (skull) and sacrum (tailbone) that is designed to release tension and promote free flow of the fluid in the spinal cord. For more, see Chapter 14 on osteopathy.

Crystal healing: Healing via different types of crystals designed to balance energy in the body. For more, see Chapter 20.

Dance therapy: The use of movement and dance to promote mental and physical well-being. For more, see Chapter 23 on creative therapies.

Darkfield microscopy: A form of live blood analysis that uses powerful microscopes to illuminate the blood cells and is claimed to detect internal health problems and disease risk. For more, see Chapter 22 on energy medicine.

Deep-tissue massage: A form of massage that uses slow, deep finger pressure to break down scar tissue and release toxins, tension, and pain. For more, see Chapter 17 on massage.

Do-In: A traditional Japanese system for personal and spiritual development that combines self-massage, acupressure, and shiatsu stretches with a macrobiotic diet, breathing exercises, and meditation. For more, see Chapter 7 on Japanese medicine.

Dolphin therapy: Swimming with dolphins has been found to be therapeutic for various conditions such as depression and autism. For more, see www. Idw. org/html/about_idw. html.

Dowsing: The use of a pendulum, branch, or rod to detect water or diagnose imbalance in the body. For more information, see Chapter 22 on energy medicine.

Dramatherapy: The use of theatrical techniques to increase self-awareness and promote mental and physical health. For more, see Chapter 23 on creative therapies.

Dream therapy: Analysing dreams for insights into current problems. See Chapter 21 on psychological therapies.

Emotional freedom technique (EFT): Involves light tapping with the fingers on 11 acupressure points to release emotional blockages. For more, see Chapter 21 on Psychological Therapies.

Feldenkrais technique: A system of gentle movements devised by Moshe Feldenkrais, an Israeli physicist and Judo expert, to reduce patterns of muscular tension and pain and promote ease of movement and vitality. For more, see Chapter 16 on bodywork therapies.

Feng shui: Various techniques used to rebalance energy flows in order to create harmonious environments and increase health, happiness, and prosperity. For more, see Chapter 23 on creative therapies.

Flotation: Floating in salt water in an enclosed tank to promote deep relaxation. This therapy grew out of American physiologist and psychoanalyst

John C. Lilly’s work on sensory deprivation in the 1950s. For more, see Chapter 18.

Gerson Diet: A form of nutritional therapy based on raw food, devised by German army surgeon Max Gerson in the 1950s, to control his migraines and now used as a therapeutic regime for cancer. For more, see Chapter 12 on nutritional medicine.

Healing: The use of the hands, heart, and mind to transfer healing energy and promote healing in another being. For more, see Chapter 20 on healing.

Hellerwork: A form of deep tissue massage combined with psychotherapy and postural realignment developed by Joseph Heller, a pupil of Dr Ida Rolf (creator of Rolfing). For more, see Chapter 16 on bodywork therapies.

Herbal medicine: The use of the stems, roots, leaves, branches, and fruits of different plants to promote healing and relieve illness. Herbal traditions exist in both Eastern and Western traditions. For more, see Chapter 11 on herbal medicine.

Holographic re-patterning: Now renamed resonance patterning, this therapy synthesises polarity therapy, kinesiology, and acupuncture to ‘re-pattern body frequencies causing dissonance’. For more on polarity therapy and kinesiology see Chapter 16 on bodywork therapies.

Homeopathy: A therapy based on treating ‘like with like’ using infinitesimal doses of diluted plant, mineral, human, and animal substances to enable the body to repair itself. For more, see Chapter 10 on homeopathy.

Hot stone massage: The application of stones, heated or cooled to different temperatures, to different parts of the body to promote circulation and relaxation. For more details, see Www. lastonetherapy. com.

Hydrotherapy: All kinds of therapeutic treatments using water. For more, see Chapters 8 and 13 on Nature Cure and naturopathy.

Hydrotherm massage: A massage performed while you lie on a mattress filled with warm water. For more, see Chapter 17 on massage.

Hypnotherapy: The introduction of therapeutic suggestions to the mind during a receptive and relaxed state to facilitate healing of mental, physical, and emotional problems. For more, see Chapter 21 on psychological therapies.

Indian head massage: See ‘Ayurveda’.

Indonesian massage: A form of deep-tissue massage that uses the thumbs to work deep into the muscles and surrounding tissues. For more, see Chapter 17 on massage.

Iridology: Diagnosis of the iris in the eye, viewed under magnification. For more, see Chapter 13 on naturopathy.

Jin Shin Do: A synthesis of acupressure, Qi gong Exercises, and psychology for releasing physical and emotional tension. For more, see Chapter 17 or

Www. jinshindo. org.

Johrei: A healing approach involving the channelling of ‘universal energy’ or ‘divine light’ through the giver to the receiver. For more, see Chapter 20 on healing therapies.

Kahuna: A Hawaiian form of deep-tissue massage for the whole body, sometimes called Lomi Lomi. For more about massage, see Chapter 17.

Kinesiology: A system of muscle testing to detect and regulate body imbalances. For more, see Chapter 16 on bodywork therapies.

Kum nye: Poses and breathing exercises designed to increase awareness and still the mind, a part of Tibetan medicine. For more, see Chapter 16 on bodywork therapies.

LaStone therapy: See ‘Hot stone massage’.

Laughter therapy: Using humour and laughter to boost mental and physical well-being. For more, see Chapter 21 on psychological therapies.

Light therapy: Therapy that involves exposure to sunlight, full-spectrum light, or coloured light. For more, see Chapter 23 on creative therapies.

Magnet therapy: The use of fixed magnets or pulsed magnetic field devices to stimulate tissue healing, improve circulation, and aid muscle relaxation. For more, see Chapter 22 on energy medicine.

Manual lymphatic drainage: A gentle massage approach designed to stimulate the flow of lymph in the tissues. For more, see Chapter 17 on massage.

Massage: Gentle pressure applied with the fingers and hands and sometimes other body parts (such as knuckles, elbows, or feet) to relax and heal, performed with or without oil. For info on all types of massage, see Chapter 17.

McTimoney chiropractic: A gentle form of manipulation therapy devised by British engineer and chiropractor John McTimoney. For more, see Chapter 15 on chiropractic.

Metamorphic technique: A gentle touch technique designed to release emotional, mental, and physical blocks created while in the womb. For more, see Chapter 16 on bodywork therapies.

MORA therapy: A type of ‘bio-resonance’ therapy using an electro-acupuncture device to test for allergies and imbalances. For more, see Chapter 22 on energy medicine.

Music therapy: The use of musical sounds and sound frequencies to stimulate healing. For more, see Chapter 23 on creative therapies.

Myofascial massage: A type of massage that stretches the tissues to release tension and pain. For more, see Chapter 17 on massage.

Naturopathy: A system of natural medicine incorporating nutritional and herbal medicine, homeopathy, acupuncture, and Nature Cure and designed to stimulate the body’s innate healing ability. For more, see Chapter 13 on naturopathy.

Neuro-linguistic programming: A set of techniques for modifying language, behaviour, and experience. For more, see Chapter 21 on psychological therapies.

Neuromuscular therapy: Also known as trigger-point therapy or myotherapy, this involves direct thumb or finger pressure on tender points, known as trigger points, to improve circulation and release pain. For more, see Chapter 17 on massage.

Nutritional therapy: Also called nutritional medicine, this therapy uses foods and sometimes nutritional supplements to improve digestion and ease common ailments. For more, see Chapter 12 on nutritional medicine.

On-site massage therapy: Mobile massage therapists take a portable chair into workplaces and perform 15- to 30-minute massages on the head, neck, upper back, and arms. For more about the different types of massage, see Chapter 17.

Orthomolecular therapy: The treatment of disease using concentrated doses of vitamins and minerals. For more, see Chapter 12 on nutritional therapy.

Osteopathy: A type of manipulation therapy that uses mobilisation and massage techniques to improve mobility and restore structural balance. For more, see Chapter 14.

Oxygen therapy: The use of oxygen, either inhaled or introduced into extracted blood as in ozone therapy, which is believed to oxygenate the tissues and help limit the spread of bacteria and cancer cells.

Photodynamic therapy (PDT): The application of light-sensitive substances to increase oxygenation at cancer sites, which is believed to help trigger cancer cell death. For more information, see Chapter 22 on energy medicine

Or Www. doveclinic. com.

Pilates: A system of exercises for increasing body awareness, improving posture and alignment, and increasing flexibility. For more, see Chapter 16 on bodywork therapies.

Play therapy: The use of sand play, art, story telling, drama, puppetry, music, movement, and so on to help children with emotional, behavioural, and mental health problems. For more, see Chapter 23 on creative therapies.

Polarity therapy: A system using massage techniques, touch, and healing to rebalance the body’s ‘energy field’. For more, see Chapter 16 on bodywork therapies.

Pranayama: See ‘Yoga’.

Pregnancy massage: Massage technique specially designed for use with pregnant women to ease discomfort and facilitate blood flow to the unborn child. For more, see Chapter 17 on massage.

Psionics: A form of dowsing similar to radionics. For more, see the discussion on radionics in Chapter 22.

Psychic healing: Healing given by someone while in a trance-like or meditative state, involving the transfer of energy and sometimes even ‘surgery’, where the body is apparently entered by hand or cut open without anaesthetic or surgical instruments. For more, see Chapter 20 on healing therapies.

Psychosynthesis: A form of psychological therapy that emphasises self-awareness and Soul Knowledge. For more, see Chapter 21 on psychological therapies.

Qi gong: Part of Traditional Chinese Medicine (TCM), this form of movement therapy is designed to free the flow of Qi (vital energy) and promote flexibility and healing. For more, see Chapter 4 on TCM and Chapter 16 on bodywork therapies.

Quantum touch: A form of energy healing using such elements as hand healing and breathing techniques. For more, see Www. quantumtouch. com.

Radionics: A form of dowsing, using a hand-held pendulum or a radionic device to detect energetic imbalances in the body and ‘broadcast’ healing at a distance. For more, see Chapter 22 on energy medicine.

Rebirthing: The use of breathing and other physical techniques to ‘re-enact’ your birth and resolve birth traumas that can impact on later life. For more, see Chapter 21 on psychological therapies.

Reflexology: A form of foot massage using finger-tip and thumb pressure to nerve reflex points on the feet. For more, see Chapter 17 on massage.

Regression therapy: Sometimes called past-life therapy or past-life regression therapy, this therapy involves deep relaxation and then being taken back supposedly to specific times in your early life or even past lives. For more, see Chapter 21 on psychological therapies.

Reiki: A Japanese healing approach involving the transfer of healing energy. For more, see Chapter 20 on healing.

Remedial massage: A form of soft tissue massage often used for healing joint pain and sports and other injuries. For more, see Chapter 17 on massage.

Rolfing: Also called structural integration, a bodywork system for correcting misalignment developed by Ida Rolf in the 1950s. For more, see Chapter 16 on bodywork therapies.

Self-massage: Simple do-it-yourself massage techniques, using finger-tip and hand pressure and kneading to release tension and promote circulation. For more, see Chapter 17 on massage.

Shamanic healing: The use of rituals, singing, dancing, drumming, fasting, consciousness-altering plants, and trance-like states for self-development and healing. For more, see Chapter 20 on healing therapies.

Shiatsu: A Japanese massage system, often performed through clothing, involving pressure from fingers, elbows, feet, and knees to rebalance the body. For more, see Chapter 17 on massage.

Sonodynamic therapy: This therapy uses low-level ultrasound in an attempt to destroy tumour cells. For more, see Chapter 22 and Www. doveclinic. com.

Spiritual healing: The channelling of universal healing energy or ‘life force’ via a trained healer intended to promote mental, physical, and spiritual well-being. For more, see Chapter 20 on healing therapies.

Sports massage: A combination of massage techniques designed to enhance sports performance and promote healing of injuries. For more, see Chapter 17 on massage.

Swedish massage: A popular form of massage developed in Sweden and sometimes called therapeutic massage, Swedish massage is based on kneading, stroking, and pummelling movements designed to stimulate circulation and promote relaxation. For more, see Chapter 17 on massage.

Ta’i chi: Part of Traditional Chinese Medicine, this movement therapy involves slow, flowing sequences of movements and breathing techniques to stimulate and regulate the flow of Qi Energy. For more, see Chapter 16 on bodywork therapies.

Thai massage: A thorough form of deep-tissue massage with muscle stretching and pressure techniques designed to ease tension and pain and promote relaxation. For more, see Chapter 17 on massage.

Therapeutic touch: A type of laying-on-of-hands therapy. For more, see Chapter 20 on healing.

Thought field therapy (TFT): A form of psychological treatment designed to ease emotional problems, stress, and anxiety rapidly. For more, see Chapter 21 on psychological therapies.

Tibetan massage: An ancient Tibetan medical technique involving oil massage and pressure to particular points on the body to ease pain and obstructions and promote healing. For more, see Chapter 6 on Tibetan medicine.

Touch for Health: Developed out of applied kinesiology by US chiropractor John Thie, who believed simple techniques for body balancing could be learnt and used by anyone. See also ‘Kinesiology’.

Traditional Chinese Medicine (TCM): See ‘Chinese medicine’.

Tragerwork: A system of gentle, rhythmical movements, devised by one-time chronic back-sufferer Milton Trager, to ease tension and pain and improve mobility. For more, see Chapter 16 on bodywork therapies.

Trigger-point therapy: See ‘Neuromuscular therapy’.

Tsubo therapy: Therapy involving stimulation of Tsubo, Acupoints, using massage, heat treatment, or electrical stimulus. For more, see Chapter 17 on massage.

Tui na: A Traditional Chinese Medicine (TCM) form of massage that uses fingers, hands, arms, elbows, and knees to rub, knead, and roll the skin. Tui na Is designed to release blockages in the acupuncture meridians and to release muscular tension. For more, see Chapter 17 on massage.

Visualisation: Sometimes also called mental imagery, guided imagery, or creative visualisation, this therapy involves creating positive images, while in a relaxed state, to help resolve mental or physical problems. For more, see Chapter 21 on psychological therapies.

Watsu: Shiatsu performed in the water! The idea is that the body is relaxed and weightless to aid stretches. See also ‘Shiatsu’.

Yoga: A system of therapeutic exercises and breathing (pranayama) And meditation techniques that are a part of Ayurveda. For more, see Chapter 5 on Ayurveda and Chapter 16 on bodywork therapies.

Zero balancing: A light manipulation therapy designed to rebalance the ‘energetic body’. For more, see Chapter 16 on bodywork therapies.

Zone therapy: See ‘Reflexology’.

•••••••••••••••••••••••••••••••••••••••••••••••.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.

B

A

B

A

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!)

■ n Chapter 16, I mention the possibility of buying prescription drugs from

Abroad by mail order as a way to lower expenses in Part D’s doughnut hole (formally called the coverage gap). You need to weigh the pros and cons, but if you decide to go this route, your chief concern is to make sure you order from a legitimate, licensed pharmacy that sends you the drugs your doctor prescribed.

Importing prescription drugs from abroad is still illegal in the United States. (Congress has passed legislation to legalize the practice, but it has never been put into effect, for reasons explained in Chapter 21.) However, no American has ever been prosecuted for importing drugs for his own personal use, and it’s extremely unlikely that anybody would be. For the millions of otherwise law-abiding citizens who’ve ordered prescription drugs from abroad — mostly senior citizens before Medicare drug coverage began in 2006 — it’s a no-brainer. The same meds that cost a fortune without insurance in the U. S. can often be bought from Canada and other countries, where drug prices are nationally regulated, for much less.

Certainly, getting drugs from abroad can be risky — unless you’re careful. Unscrupulous sellers who lurk behind anonymous Web sites peddle counterfeit and other harmful drugs. Scammers will take your money without sending you any meds. The U. S. Food and Drug Administration regularly cites these reasons in warning Americans against buying drugs from abroad.

But many reputable online pharmacies sell bona fide prescription drugs to Americans safely and ethically. This appendix shows you how to find those that offer quality services and how to avoid the ones that are dubious. It also suggests ways of locating pharmacies that have been prescreened for safety and service by state governments or organizations that give seals of approval to online pharmacies that meet certain standards.

In these pages, I focus on ordering drugs from licensed Canadian pharmacies. The Canadian federal and provincial governments regulate pharmacy practices and drug safety as rigorously as American health authorities do, and after nearly a decade of experience in the cross-border trade, these pharmacies have an established track record. They operate mail-order services because that’s the only way most Americans can buy drugs from Canada, although many people living in the northern-most states physically cross the border to fill prescriptions in regular drugstores. The mail-order pharmacies maintain Web sites that state their drug prices and policies and allow you to order online.

What if you don’t have Internet access? You can order meds by phone from a mail-order pharmacy, but first you’ll usually need someone to go online to look for a reputable one (by using the suggestions in this chapter) and find its phone number. Or you can call one of the state-operated services that provide links to prescreened Canadian pharmacies, as described later in this chapter.

Distinguishing the Good Guys from the Bad

Just because an online pharmacy Says It’s based in Canada doesn’t mean it is. And just because it has a Canadian address doesn’t mean it necessarily provides good service. Here are ways to evaluate legitimate pharmacies and avoid dubious sellers so you can be more confident that the medications you’ll receive are the ones your doctor prescribed.

Assessing safe and ethical service

American and Canadian pharmacy experts recommend that you choose an online pharmacy that uses the following best practices of

U Displaying on its Web site its license number and the name of the Canadian regulatory agency that granted it. This means you can check that it’s an authentic pharmacy. As an American, you have the same right to complain about a pharmacy to its licensing agency as a Canadian does.

U Displaying on its Web site the approval seals of organizations that set standards for safety and service and accredit pharmacies that meet the standards. See the next section for details of these organizations and how to ensure that the seals posted on pharmacy Web sites are genuine.

U Requiring a prescription from your doctor. This isn’t a hassle — it’s your best safety protection. Some reputable pharmacies may allow you to fax in the prescription, but will then phone your doctor to confirm the prescription or wait until they receive the original one in the mail before filling your order.

U Requiring you to have taken the drug for at least one month before you order by mail so you and your doctor know it’s working well for you.

U Requiring you to submit details of your medical history, usually through an online questionnaire.

U Stating its policy for ensuring your medical and personal privacy in clear language on its Web site.

U Sending drugs in the manufacturer’s original container with seals intact. This is normal practice among reputable Canadian pharmacies. In some cases, though, they may send drugs in regular pharmacy bottles if the manufacturer’s own containers hold different quantities than you order.

U Sending drugs with labeling written in English that includes strength, dosing directions, expiration date, appropriate warnings, and a Drug Identification Number (DIN) that shows the drug has been approved by the Canadian government health authorities.

U Explaining differences between American and Canadian drug names and labeling. The same drugs sometimes have different names in other countries.

U Explaining why it can’t provide certain drugs. Reputable pharmacies don’t sell drugs that are regarded as controlled substances under American law (like narcotics), or drugs that can’t be sent safely through the mail (such as some that require careful handling or refrigeration).

U Providing a full mailing address and a toll-free phone number on its Web site so you can call the pharmacist with questions, check on the status of an order, or order by phone instead of online if you prefer.

U Displaying on its Web site full information about shipping fees, payment policies, and refunds. Reputable pharmacies offer encrypted (that is, secure) online payment for credit cards, alternative payment options (such as electronic fund transfers and regular checks), and don’t charge any separate fees except for shipping.

U Charging the cost of drugs to your credit card only when they’ve been shipped to you — and not when the order is first placed.

U Refunding your money or shipping replacement drugs immediately if your order doesn’t arrive. Reputable pharmacies will do this even if your shipment is intercepted and confiscated by U. S. Customs, a practice that has happened in the past but has become much rarer in recent years since Congress condemned it.

Avoiding scams and dubious sellers

The snake oil salesmen are still out there and thriving — though these days they’re usually peddling fake Viagra and other drugs that folks feel too shy to ask their doctors about. These are basic guidelines for avoiding unscrupulous sellers and counterfeit drugs:

W Never use an online pharmacy that offers to sell you a prescription drug without a doctor’s prescription. This is the number-one no-no — a clear sign of unethical and potentially dangerous practices.

W Never use an online pharmacy that sends you an uninvited e-mail.

Those unwanted e-mails that pop up so frequently in your in-box should always be seen as outright attempts to scam you. Delete them!

W Don’t trust an online pharmacy that doesn’t display a customer service number on its Web site. If there’s no phone number, you can’t contact the pharmacy — so how can you know it actually exists?

Finding a Pharmacy You Can Trust

The best way to find reputable licensed pharmacies that give quality service is to use some kind of filter — that is, a system that has already identified pharmacies that operate according to the best practices listed in the "Assessing safe and ethical service" section. In the following sections, I suggest two types of filters:

W Programs set up by state governments to link consumers to prescreened Canadian pharmacies

W Organizations that give seals of approval to online pharmacies that meet their standards

Using state links to Canadian pharmacies

In 2003-04, two state governors lost patience waiting for the federal government to legally allow people access to low-cost prescription drugs from Canada. Both governors created Web sites offering links to Canadian pharmacies that state health officials have prescreened and regularly inspect to ensure safety and quality service.

W Minnesota RxConnect: This program, set up by Minnesota Governor Tim Pawlenty in 2003, offers links to four prescreened Canadian pharmacies. Some other states (and the District of Columbia) direct their residents to this program, but residents of any state can use it. Go to rxconnect. dhs. state. mn. us and click "Order Your Medicine from Canada." Or call 800-333-2433.

W Illinois I-SaveRx: This program, created by Illinois Governor Rod

Blagojevich in 2004, offers a link to one prescreened Canadian pharmacy. The program is open to residents of Illinois, Kansas, Missouri, Vermont, and Wisconsin. Call 866-472-8333 or go online to Www. i-saverx. net.

Looking online for seals of approval

Iijj|kB£W Hundreds of advertisements for low-cost prescription drugs litter the Internet, aimed at Americans who are trying to save money on their prescriptions. Every time you go online to search for any medical topic, these ads pop up onscreen in profusion. Some are legitimate, and some are total rip-offs. How can you tell which are which? You can’t. However, you can play it safe. Ignore the ads. Instead, look for licensed pharmacies that display, on their Web sites, the seals of approval awarded by organizations that have screened them to meet certain safety and service standards.

Here’s where those seals of approval come from:

W Internet and Mail-Order Pharmacy Accreditation Commission (IMPAC):

IMPAC was founded in 2003 in Vermont by an independent group of doctors and pharmacists to promote consumer safety and quality service among licensed mail-order pharmacies in the U. S. and other countries. A pharmacy must meet rigorous standards during a two-day on-site inspection every two years to receive and retain IMPAC accreditation. To see a list of the currently accredited pharmacies, go to Www. impac Survey. org or call 800-677-7019.

W Canadian International Pharmacy Association (CIPA): CIPA was formed in 2002 to represent licensed Canadian pharmacies that sell prescription drugs to Americans by mail order and that meet its safety, service, and ethical standards. The group has testified before Congress and state legislatures to address safety issues and to promote U. S. legalization of the cross-border trade for consumers buying prescription drugs from Canada for their personal use. To verify that a pharmacy is currently accredited by CIPA, go to Www. ciparx. ca.

W Better Business Bureau (BBB): The BBB awards its BBBOnline seal of approval to Web sites that meet its standards for ethical service, trustworthy business practices, and truth in advertising. You can check out BBB records for an online pharmacy, including whether the BBB has received consumer complaints about it, at Www. bbbonline. org. If you go to a pharmacy Web site that displays the BBB seal, clicking the seal will take you straight to the BBB report on that pharmacy.

W PharmacyChecker. com: This Web site, run by an independent American consumer research group, provides ratings and drug price comparisons for about 30 online pharmacies in the US. and abroad (mainly Canada). It gives its "verification" seal to those that meet five service standards — it’s licensed, requires a doctor’s prescription, displays its address and phone number, offers secure online financial transactions, and promises privacy for medical information. The site also posts names of "rogue" pharmacies that it considers unethical or unsafe. It compares prices for more than 1,000 drugs at verified pharmacies and posts customers’ comments on quality of service. Check it out at Www. pharmacychecker. com.

JttNG/ Approval seals awarded by these organizations provide a useful guide for

Consumers looking for a legitimate online pharmacy. However — wouldn’t you know? — some scam artists use these seals too to cheat customers by posting copies of them on their own rogue Web sites. The copies are good — you wouldn’t know the difference just by looking at them. However, you can verify whether the displayed seals are genuine or fraudulent. Clicking the image of a seal on a pharmacy Web site should take you straight to the Web site of the organization that awarded it, whether IMPAC, CIPA, BBB, or PharmacyChecker. If nothing happens, you can be sure that the seal isn’t genuine. Or you can go directly to the organization’s Web site and enter the name of the pharmacy. This will tell you whether the pharmacy is entitled to display the seal.