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Roger B. Nelsen
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Proofs without Words: Exercises in Visual Thinking (Classroom Resource Materials) First Edition, Later Printing

by Roger B. Nelsen (Author)
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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. While in some proofs without words an equation or two may appear to help guide that process, the emphasis is clearly on providing visual clues to stimulate mathematical thought. The proofs in this collection are arranged by topic into five chapters: Geometry and algebra; Trigonometry, calculus and analytic geometry; Inequalities; Integer sums; and Sequences and series. 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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  1. ISBN-10
    0883857006
  2. ISBN-13
    978-0883857007
  3. Edition
    First Edition, Later Printing
  4. Publisher
    The Mathematical Association of America
  5. Publication date
    August 7, 1997
  6. Language
    English
  7. Dimensions
    7.25 x 0.25 x 9.75 inches
  8. Print length
    157 pages
  9. See all details
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Editorial Reviews

Book Description

Teaches the reader to think visually in mathematics.

Product details

  • Publisher ‏ : ‎ The Mathematical Association of America; First Edition, Later Printing (August 7, 1997)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 157 pages
  • ISBN-10 ‏ : ‎ 0883857006
  • ISBN-13 ‏ : ‎ 978-0883857007
  • Item Weight ‏ : ‎ 10.6 ounces
  • Dimensions ‏ : ‎ 7.25 x 0.25 x 9.75 inches
  • Customer Reviews:

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Roger B. Nelsen

Roger B. Nelsen

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Customer reviews

3.9 out of 5 stars
3.9 out of 5
33 global ratings

Top reviews from the United States

phinary
5.0 out of 5 stars Five Stars
Reviewed in the United States on January 3, 2017
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Waited a while to buy this book because of the price, but it's completely worth it.
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NL
4.0 out of 5 stars Ok
Reviewed in the United States on January 2, 2017
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A lot of it is hard to make sense of.
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The S.
5.0 out of 5 stars Five Stars
Reviewed in the United States on November 27, 2015
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Just flip through and love it.
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tech collector
3.0 out of 5 stars I spent how much for this?
Reviewed in the United States on January 5, 2011
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When I first examined the book I thought "I spent how much for this?" The price should be closer to $10 new for what it is. And what is it? It's a collection of visual proofs, one per page, from a variety of sources. One probably could assemble the collection from the Internet, but thankfully Dr. Nelsen has done the work already. Don't expect written explanations, for that one will need to go the original works, which are nicely cited. I'll learn new proofs from the book, but they feel more like 'tricks', and I'm not sure how useful they'll be in new situations. Most likely, other books by Dr. Nelsen, such as Charming Proofs, will have greater lasting value.
8 people found this helpful
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delta
5.0 out of 5 stars It should be in the hands of all highschool students
Reviewed in the United States on June 19, 2020
This series should be part of high school education, the Proofs without words books should be in the school supply of all kids.
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John
2.0 out of 5 stars I'm not wild about this book.
Reviewed in the United States on June 3, 2010
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I'm a math teacher and this is one of several books that I purchased for reading during my summer vacation. This book would have benefited greatly from short descriptions or annotations to go along with the proofs, most of which I've seen elsewhere. If I had thumbed through this book in a store I would not have bought it.
11 people found this helpful
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Peter Krumins
5.0 out of 5 stars Wow! This book is the real vitamins for the brain!
Reviewed in the United States on May 4, 2016
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.)

.
3 people found this helpful
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David Collins
4.0 out of 5 stars Engaging exercises to train your intuition
Reviewed in the United States on September 12, 2000
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".
33 people found this helpful
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Top reviews from other countries

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ROBERTO
5.0 out of 5 stars Sensacional
Reviewed in Brazil on May 6, 2023
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Instigando e divertido.
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William Rolston
5.0 out of 5 stars must have on bookshelf
Reviewed in Canada on February 28, 2018
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important for everyone who loves mathematics.
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Dr. Ron Knott
5.0 out of 5 stars This is a great resource for many results
Reviewed in the United Kingdom on October 14, 2014
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This is a great resource for many results, equations, formulas and theorems for school. A Proof Without Words gives insight, convinces and is a brilliant aid to the memory. This is a terrific resource collecting many separate articles over many years into one volume. There's a second volume too that is worth getting together with this one.
One person found this helpful
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Willy Van den Driessche
5.0 out of 5 stars Tantalizes the mind
Reviewed in France on October 7, 2010
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This book is a series of one-page proofs of theorems. Most of them have a very appealing beauty. In more than one case, you will need to stare a little at the page before you see the proof. But that's a good thing. I sure wish these visual proofs were used a lot more in the classroom. Kids would probably find math less boring.
2 people found this helpful
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S B
4.0 out of 5 stars A bit pricey but enjoyable
Reviewed in the United Kingdom on August 3, 2016
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A lovely, enjoyable book with some fascinating insights from history but it is somewhat lacking in strategic overview: there are quite a few "obvious" proofs which fill too much space and I can't help but feel a few more would fit in. Also, the size of images and font suggest an A5 booklet blown up to a bigger size which is a shame. The proofs here are nice and interesting (and include a few exciting surprises) but some clearly use "words" (in the sense of particular notation) and I can't help but feel there could have been more for the price.
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