by Eli Maor
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Product Description
By any measure, the Pythagorean theorem is the most famous statement in all of mathematics, one remembered from high school geometry class by even the most math-phobic students. Well over four hundred proofs are known to exist, including ones by a twelve-year-old Einstein, a young blind girl, Leonardo da Vinci, and a future president of the United States. Here--perhaps for the first time in English--is the full story of this famous theorem. Although attributed to Pythagoras, the theorem was known to the Babylonians more than a thousand years before him. He may have been the first to prove it, but his proof--if indeed he had one--is lost to us. Euclid immortalized it as Proposition 47 in his Elements, and it is from there that it has passed down to generations of students. The theorem is central to almost every branch of science, pure or applied. It has even been proposed as a means to communicate with extraterrestrial beings, if and when we discover them. And, expanded to four-dimensional space-time, it plays a pivotal role in Einstein's theory of relativity. In this book, Eli Maor brings to life many of the characters that played a role in the development of the Pythagorean theorem, providing a fascinating backdrop to perhaps our oldest enduring mathematical legacy.
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Average Customer Review:
3 of 3 people found the following review helpful:
 Finally!! A book that deals exclusively with the history of one of the most beautiful and most recognized math equations!!, 2008-10-11
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"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)
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13 of 15 people found the following review helpful:
 Not as exciting as e: the story of a number, 2007-11-11
I loved e: the story of a number, both the story and the mathematics in it. But for some reason this book does not catch the same spirit. It doesn't have the exciting thread of a story that makes you want to turn to the next page, and the many different proofs make it feel like it's a patchwork of items forcing itself to support the topic rather than a natural inspiring thread that helps you see the growth in the mathematics. I found it disappointing.
15 of 16 people found the following review helpful:
Probably the World's Best-Known Theorem, 2007-09-24
Eli Maor is a fine mathematician who has produced some wonderful books on math topics for a general--well, let me say, educated--readership. His book, Trigonometric Delights, is my favorite. It is very interesting and engaging. I want to say "for an educated reader" again, though it seems rather redundant. Why would anyone who didn't know anything about trig and have an interest in the subject even bother to pick up the book? Still, as someone who spent more than ten years in high school math classrooms, I also found his work useful to interest and inspire my students (and myself).
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.
19 of 30 people found the following review helpful:
Behold the Book!, 2007-06-23
The Pythagorean Theorem could rightfully be called the 'Crown Jewel of Mathematics'. For from its truths and intellectual spawn come all the wonders of our modern word--high rises, automobiles, cell phones, interplanetary probes, you name it! Unfortunately, the last serious book on this subject was written over 80 years ago by an Ohio school teacher, Elisha Loomis. Enter Dr. Eli Maor! He has written an absolutely marvelous book about 'The Crown Jewel' that will captivate anyone with a good high school mathematics background. Read it and behold a wonder!
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