Proofs without Words
by Roger B. Nelsen · first published 1993
67% recommend33% neutral
Why HN recommends it
Collection of visual proofs where diagrams alone demonstrate equations and inequalities across many fields; recommended for anyone who enjoys intuitive, picture-based problem solving and mathematical reasoning.
Summarised by Claude from recommending comments
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
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If you like this, you'll love the book Proofs without Words: Exercises in Visual Thinking: http://www.amazon.com/Proofs-without-Words-Exercises-Classro...
on “Six Visual Proofs” ↗If you really like visual mathematics, then there is a book called "Proofs without words": http://www.amazon.com/Proofs-without-Words-Exercises-Classro...
on “Visual mathematics” ↗If you like this sort of thing, definitely check out this book: http://www.amazon.com/Proofs-without-Words-Exercises-Classro...
on “a² + b² = c²” ↗The 3 wonderful Roger Nelsen books Proofs Without Words entirely consist of equations & inequalities from various mathematical fields 'proved' in intuitive pictorial form. http://gen.lib.rus.ec/search.php?req=proofs+without+words
on “Ask HN: Best resources to gain math intuition?” ↗…https://artofproblemsolving.com/store/list/aops-curriculum I've got a PhD in bioengineering but I'm currently going through Introduction to Counting and Probability and I'm really enjoying it. Some others (not AOPS series): Nelsen - Proofs Without Words Polya - How to Solve it Strogatz - Nonlinear Dynamics and Chaos
on “Ask HN: Recommend a maths book for a teenager?” ↗Great introductory books along with videos: - Mathematics and Its History (John Stillwell) - Journey through Genius: The Great Theorems of Mathematics (William Dunham) - Proofs Without Words: Exercises in Visual Thinking (Roger B. Nelsen) - The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems, and Personalities (William Dunham) - Odds & Ends: Introducing…
on “Ask HN: Serious mathematics books that can replace a good teacher?” ↗Proofs Without Words, https://www.amazon.com/dp/1470451867, is a very fun exploration of this general topic.
on “Visual Sum of Cubes” ↗If you like this kind of intuitive problem solving you might like "Proofs without Words". It was one of my favorite "math" books in highschool.
on “I cheated on my Microsoft interview (2019)” ↗A fun book I have is Proofs Without Words (https://www.amazon.com/gp/aw/d/1470451867). Tons of neat diagrams like this.
on “A visual proof that a^2 – b^2 = (a + b)(a – b)” ↗There are full books on these called "Proofs Without Words". On my wishlist. :) https://amazon.com/dp/0883857006
on “Proof without words: Cubes and Squares” ↗…PhD advisor and another colleague [3]. We planned to print them as posters and hang them for a Pi day event that unfortunately never happened because the pandemic broke out. [1] https://www.amazon.com/Proofs-without-Words-Exercises-Classr... [2] https://en.m.wikipedia.org/wiki/Proof_without_words [3] https://www.antonellaperucca.net/didactics/proof-without-wor...
on “A visual proof that a^2 – b^2 = (a + b)(a – b)” ↗…1) Math Made Visual: Creating Images for Understanding Mathematics by Claudi Alsina and Roger Nelsen - https://bookstore.ams.org/CLRM/28 2) Roger Nelsen has also written other similar works like the Proofs without Words(3-vols), Nuggets of Number Theory: A Visual Approach, Cameos For Calculus: Visualization In The First-year Course, etc. - https://bookstore.ams.org/browse?Author=%22Roger%20B.%20Nels...
on “Math's pedagogical curse – Grant Sanderson [video] (2023)” ↗Some shorter proofs are available in the book "Proofs without Words." But then again, that book begins with a description that visual arguments aren't truly proofs.
on “The shortest paper ever published in a serious math journal explained” ↗…allows the viewer to appreciate the fractal nature of the numerical order. Educational and fun, it's a creative success. Just yesterday on HN there was a thread concerning favored books, mentioning "Proofs Without Words", which this site reminds me of. Where it works it is a wonderful concept, and here it works well.
on “Prime Number Patterns” ↗