Proofs without Words: Exercises in Visual Thinking (Classroom Resource Materials) by Roger B. Nelsen (PDF)

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. 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.

User’s Reviews

Editorial Reviews: Book Description Teaches the reader to think visually in mathematics.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐Waited a while to buy this book because of the price, but it’s completely worth it.

⭐A lot of it is hard to make sense of.

⭐Just flip through and love it.

⭐Is geometric intution important? You betAre these pictures inspiring? well case by caseIs this picture new and fresh? Not at all. I can tell over 90% in high school textbooks in my country. Probably you can in your own.

⭐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.

⭐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”.

⭐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.). ⭐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. ⭐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. ⭐Very interesting! I use to "study" one proof per day, which is a nice brain gymnastic. ⭐important for everyone who loves mathematics. ⭐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.

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