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Proofs without Words: Exercises in Visual Thinking (Classroom Resource Materials) (v. 1) First Edition, Later Printing Edition

4.0 out of 5 stars 10 customer reviews
ISBN-13: 978-0883857007
ISBN-10: 0883857006
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Editorial Reviews

Book Description

Proofs without words are generally pictures or diagrams that help the reader see why a particular mathematical statement may be true, and how one could begin to go about proving it. Teachers will find that many of the proofs in this collection are well suited for classroom discussion and for helping students to think visually in mathematics.
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Product Details

  • Series: Classroom Resource Materials (Book 1)
  • Paperback: 160 pages
  • Publisher: The Mathematical Association of America; First Edition, Later Printing edition (October 1993)
  • Language: English
  • ISBN-10: 0883857006
  • ISBN-13: 978-0883857007
  • Product Dimensions: 6 x 0.6 x 9 inches
  • Shipping Weight: 10.6 ounces (View shipping rates and policies)
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon Best Sellers Rank: #436,691 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

By David Collins on September 12, 2000
Format: Paperback
Famous mathematicians have often emphasized the role of visual intuition; e.g., Hilbert: "Who does not always use along with the double inequality a > b > c the picture of three points following one another on a straight line as the geometrical picture of the idea "between"? Who does not make use of drawings of segments and rectangles enclosed in one another, when it is required to prove with perfect rigor a difficult theorem on the continuity of functions or the existence of points of condensation?" (from his famous address at the 1900 International Congress). This book is a collection of well over 100 one-page proofs, collected from various sources. The topics range from number theory to calculus, and most of them require no advanced mathematics. Typically there is a statement of a result, with a labelled diagram showing how it is "proved"; in some cases there are a few auxiliary equations along with the picture. These are not simple, often requiring quite a bit of thought before the "Aha!" moment. Working through them is a valuable exercise for the student of mathematics--having seen, e.g., six different visual proofs of the Pythagorean theorem, one comes to really *understand* the result, not just "follow the logic". I have not encountered any better way than this book to "see" how mathematical truth is discovered and proved. It can be valuable as a supplement to courses through precalculus and elementary calculus. Perhaps one of its best uses is to inspire teachers to present results in a more lively way then "definition-theorem-proof" or "just memorize it".
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Format: Paperback
How many of you remember doing geometry proofs in High School? How many of you enjoyed writing them? I don't know about you but I've always preferred pictures to words when it comes to understanding how something works.

This is a wonderful book that provides visual insights into how one might go about proving mathematical theorems. The Pythagorean Theorem has always been a mystery to me. How are the squares of the sides of a right triangle related to its hypotenuse? "Proof Without Words" has five clever illustrations that guide readers in writing their own proofs.

If you ever doubted that algebra and geometry were related, the diagrams demonstrating how to compute sums of series will produce aha! experiences.

Writing proofs when one is guided by visual cues is a much more fulfilling endeavor than stringing together dry facts from memory. This book delivers much fulfillment in exploring theorems in geometry, algebra, trigonometry, sequences, and other aspects of Math.
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Format: Paperback
Wow! When I found these books I immediately fell in love. I'm a visual thinker and I love visual proofs. These books have no words but have hundreds of proofs. One proof per page. I wish I had more time to work through all these proofs. Some of the proofs take a few seconds to understand but many others take hours. These books are the real vitamins for the brain.

I've placed this book #20 in my Top 100 Programming, Computer and Science books list:

[...]
(If this link gets removed google for >>catonmat top 100 programming computer science books<< to find my article.)

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Format: Paperback
I think I started to like "thinking" when I looked at this book. Visual aids are the way to education, at least its entry. Thanks Dr. Roger B Nelsen for presenting such a wonderful piece of knowledge.

Nasser
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Format: Paperback
Proof without words really opened my insights into how some of the proofs of formula came about. Sometimes we just take for granted the formula and do not discover how they came about. Through graphics and pictures we are able to visualize better.
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