The Pythagorean Theorem: A 4,000-Year History Hardcover – 10 Jun 2007
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Honorable Mention for the 2007 Best Professional/Scholarly Book in Mathematics, Association of American Publishers
"This excellent biography of the theorem is like a history of thought written in lines and circles, moving from ancient clay tablets to Einstein's blackboards. . . . There is something intoxicating about seeing one truth revealed in so many ways. It all makes for hours of glorious mathematical distraction."--Ben Longstaff, New Scientist
"[The Pythagorean Theorem] is aimed at the reader with an interest in the history of mathematics. It should also appeal to most well-educated people...It is a story based on a theme and guided by a timeline...As a popular account of important ideas and their development, the book should be read by anyone with a good education. It deserves to succeed."--Peter M. Neumann, Times Higher Education Supplement
"Based on this recent book, Maor just keeps getting better. Already recognized for his excellent books on infinity, the number e, and trigonometry, Maor offers this new work as a comprehensive overview of the Pythagorean Theorem...If one has never read a book by Eli Maor, this book is a great place to start."--J. Johnson, Choice
"Maor's book is a concise history of the Pythagorean theorem, including the mathematicians, cultures, and people influenced by it. The work is well written and supported by several proofs and exampled from Chinese, Arabic, and European sources the document how these unique cultures came to understand and apply the Pythagorean theorem. [The book] provides thoughtful commentary on the historical connections this fascinating theorem has to many cultures and people."--Michael C. Fish, Mathematics Teacher
"This book will make for good supplementary reading for high school students, high school teachers, and those with a general interest in mathematics. . . . The author's enthusiasm for his subject is evident throughout the book."--James J. Tattersull, Mathematical Reviews
"This book goes beyond the theorem and its proofs to set it beautifully in the context of its time and subsequent history."--Eric S. Rosenthal, Mathematics Magazine
"This is an excellent book on the history of the Pythagorean Theorem. . . . This book is suitable to any student who has basic knowledge of calculus but the layperson will also find it interesting. . . . Maor has an exceptional method of writing very technical mathematics in a seamlessly way."--Kuldeep, Mathematics and My Diary
From the Back Cover
"At last, a popular book that isn't afraid to print a mathematical formula in all its symbolic glory! Thanks to Eli Maor for proving--in his delightful, playful way--the eternal importance of a three-sided idea as old as humankind."--Dava Sobel, author of Longitude
"Eli Maor has brought four thousand years of history back to life, all based on the Pythagorean theorem but still giving the times a distinctly human look. This book is designed for readers who are inspired, or who want to be inspired, by the numbers that Eli uses to tell his story. Readers will learn about the mathematics of the time, but more important, they will understand the people and the ideas of that period. A monumental effort."--David H. Levy, National Sharing the Sky Foundation
"There's a lot more to the Pythagorean theorem than a² + b² = c², and you'll find it all in Eli Maor's new book. Destined to become a classic, this book is written with Maor's usual high level of skill, scholarship, and attention to detail. He's also got a sense of humor that will please a range of readers. As we used to say in the 1950s, 'Miss it and be square!'"--Paul J. Nahin, author of Chases and Escapes and Dr. Euler's Fabulous Formula
"Eli Maor states that the Pythagorean theorem 'is arguably the most frequently used theorem in all of mathematics.' He then supports this claim by taking his reader on a journey from the earliest evidence of knowledge of the theorem to Einstein's theory of relativity and Wiles's proof of Fermat's last theorem, from the Babylonians around 1800 BCE to the end of the twentieth century. I think that the reader who makes the journey with Maor will be convinced beyond a reasonable doubt. He is the first author who has sifted through all the mathematics, history of mathematics, and physics books and collected for us just the material directly related to the Pythagorean theorem."--Robert W. Langer, Professor Emeritus, University of Wisconsin, Eau Claire
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Top Customer Reviews
The book starts with the assertion that the Babylonians knew Pythagoras's Theorem 1000 years before Pythagoras but it was the Greeks who proved the result.
There are a number of gems in the book which are not that well known in the mathematics community:
Hypotenuse is derived from the Greek words hypo meaning under or down and teinen meaning to stretch. Maor points out the reason for this is that the hypotenuse of a right triangle in Euclid's Elements was always on the bottom. (I did not know this).
There are over 400 proofs of Pythagoras's Theorem.
It was the French lawyer Ferancois Viete who first converted verbal algebra into symbolic algebra.
Many more of these gems crop up throughout the book.
Maor does give a number of different proofs of Pythagorasfs Theorem.
More importantly the author does not shy away from producing mathematical expressions and symbols in a popular book like this. Here are a few examples:
1. Every even perfect number is of the form 2^(n-1)*(2^n-1).
2. Viete's Identity product which expresses 2/Î in terms of ã2.
3. Shows how the area of one arch of the cycloid is 3 times the area of the circle generating it.
4. Gives an excellent brief description of Hilbert Spaces and non Euclidean geometry.
5. Explains why Pythagoras's Theorem is not valid in non-Euclidean geometry.
There are many more fantastic mathematical examples. The more serious mathematics is left for the appendices.Read more ›
Many proofs of the theorem are given, but what disappoints is the long-windedness and repetition, some proofs being trivial variations of others. Despite there being a chapter on calculus, nowhere do we see that wonderful proof by solving a differential equation (set up by considering similar triangles). One wonders if Maor is even aware of such a proof.
You would imagine that alongside the obvious generalisations (eg extending to three dimensions) there would be some explanation of the analogue of Pythagoras' Theorem on the surface of a sphere (the utterly astonishing and unforgettable formula cos(c)=cos(a)cos(b)). But no, it's all dull and predictable. What a missed opportunity to brighten the mathematical literature!
Misprints are pretty obvious and cause no real problem.
Most Helpful Customer Reviews on Amazon.com (beta)
Since the class I taught most often was geometry, I was very happy to see this book on the Pythagorean theorem. I have to admit, as an avid reader on the subject, I was familiar with much of what's here; particularly, the historical development and the more "Euclidean" applications of the theorem. On the other hand, he developed some proofs and problems I hadn't seen before which I found quite interesting.
Overall, however, I didn't find this book quite as engaging as some of his other work. I got the feeling he started off wanted to write a book that would have more universal appeal than some of his other titles. I mean, after all, nearly everyone knows what the Pythagorean theorem is, or has at least heard of it. But there wasn't nearly enough of the "simple" stuff and the last half of the book really goes quite far afield into mathematics without which someone without a pretty decent background in the subject will have a difficult time; particularly since the development is rather sparse in what feels like an aborted effort to keep things simple. Even some of the earlier demonstrations and proofs are a bit difficult if you don't have the background in Greek mathematics which, unfortunately, is often lacking these days.
Still, as someone who loves geometry and has a pretty good background in it, I found much here to like. Any reader who feels confident in their mathematical ability will probably find much here to like too.
"To this day, the theorem of [Greek mathematician] Pythagoras [which states that the square of a right-angled triangle's longest side or hypotenuse is equal to the sum of the squares of the other two sides, written in the language of mathematics as (c^2 = a^2 + b^2) or, more commonly, (a^2 + b^2 = c^2)] remains the most important single theorem in the whole of mathematics. That seems like a bold and extraordinary thing to say, yet it is not extravagant; because what Pythagoras established is a fundamental characterization of the space in which we move, and it is the first time that it is translated to numbers...In fact, the numbers that compose right-angled triangles [called Pythagorean Triples such as (3,4,5), (28, 45, 53) and (65, 72, 97)] have been proposed as messages which we might send out to planets in other star systems a test for the existence of rational life there."
The above quotation is found in this fascinating book authored by history of mathematics professor and author Eli Maor. (Note that the above quotation was not said by Maor.) It catches the importance of this deceptively simple theorem, a theorem children's writer Lewis Carroll (who was also a mathematician) called "dazzlingly beautiful."
What did I learn from this book? Answer: there's a lot more to the Pythagorean theorem than (a^2 + b^2 = c^2)!! Maor may be the first author who has examined all the mathematics, history of mathematics, and physics books and collected just the material directly and indirectly related to the Pythagorean theorem.
The result is that Maor has brought the long history of the Pythagorean theorem back to life. Sometime around 570 BCE Pythagoras proved (notice I said "proved" and not "discovered") a theorem about right triangles that made his name immortal. He also pondered the workings of the universe and tried to relate its workings to the laws of musical harmony. In the subsequent centuries, this theorem was used and developed by others such that it has become central to almost every branch of science, pure or applied. After twenty-five centuries, this theorem was expanded and thrust into four-dimensional space-time by Albert Einstein to formulate his own picture of the universe.
Yes, there is simple mathematics in this book. To understand it, all you will need is some high school algebra and geometry and a bit of elementary calculus.
Do you have to follow the mathematics found in this book? NO. Personally, I found that you could skim, even skip the mathematical parts and still not lose the essential flow of the main narrative. (Actually, the more difficult mathematics is relegated to the book's appendices.)
Throughout the book are diagrams and even some pictures to enhance its main narrative. As well, there are eight pages of colour photographs found near the book's center.
A feature of this book is that it contains "sidebars." These are brief sections (there are ten) found at the end of some chapters that usually focus on some aspect of the Pythagorean theorem. My two favourites have the following titles: "The Pythagorean Theorem in Art, Poetry, and Prose" and "Four Pythagorean Brainteasers." You don't have to read each sidebar.
Another feature of this book is its chronology. It more or less summarizes the main events in this book in chronological order. This chronology begins in the year 1800 BCE and ends in the year 1996.
Finally, a note on the book's cover picture (displayed above by Amazon). It shows the detail or "zooming in" of a beautiful larger 1649 picture called "Allegory of Geometry" by artist Laurent de la Hyre (displayed on this book's inside back flap). The book's cover picture zooms in on several geometric figures, the one on the top left showing Euclid's proof of the Pythagorean theorem.
In conclusion, this book is essential for anyone that wants to be familiar with the four thousand year history of the Pythagorean theorem. I leave you with some actual lines from Gilbert and Sullivan's "Pirates of Penzance:"
"I'm very well acquainted, too, with matters mathematical,
I understand equations, both simple and quadratic,
About Binomial Theorem I'm teeming with a lot o'news,
With many cheerful facts about the square of the hypotenuse."
(first published 2007; list of colour plates; preface; prologue; 16 chapters; epilogue; main narrative 215 pages; 8 appendixes; chronology; bibliography; illustrations credits; index)
<<Stephen Pletko, London, Ontario, Canada>>
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