20 of 21 people found the following review helpful:
4.0 out of 5 stars
Probably the World's Best-Known Theorem, September 24, 2007
This review is from: The Pythagorean Theorem: A 4,000-Year History (Hardcover)
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.
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6 of 6 people found the following review helpful:
5.0 out of 5 stars
Finally!! A book that deals exclusively with the history of one of the most beautiful and most recognized math equations!!, October 11, 2008
This review is from: The Pythagorean Theorem: A 4,000-Year History (Hardcover)
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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)
<<Stephen Pletko, London, Ontario, Canada>>
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