Hidden Harmonies: The Lives and Times of the Pythagorean Theorem by Ellen Kaplan (PDF)

Description

A squared plus b squared equals c squared. It sounds simple, doesn’t it? Yet this familiar expression is a gateway into the riotous garden of mathematics, and sends us on a journey of exploration in the company of two inspired guides, acclaimed authors Robert and Ellen Kaplan. With wit, verve, and clarity, they trace the life of the Pythagorean theorem, from ancient Babylon to the present, visiting along the way Leonardo da Vinci, Albert Einstein, President James Garfield, and the Freemasons-not to mention the elusive Pythagoras himself, who almost certainly did not make the statement that bears his name.How can a theorem have more than one proof? Why does this one have more than two hundred-or is it four thousand? The Pythagorean theorem has even more applications than proofs: Ancient Egyptians used it for surveying property lines, and today astronomers call on it to measure the distance between stars. Its generalizations are stunning-the theorem works even with shapes on the sides that aren’t squares, and not just in two dimensions, but any number you like, up to infinity. And perhaps its most intriguing feature of all, this tidy expression opened the door to the world of irrational numbers, an untidy discovery that deeply troubled Pythagoras’s disciples.Like the authors’ bestselling The Nothing That Is and Chances Are . . .-hailed as “erudite and witty,” “magnificent,” and “exhilarating”-Hidden Harmonies makes the excitement of mathematics palpable.

User’s Reviews

Editorial Reviews: From Publishers Weekly The Kaplans (Out of the Labyrinth) collaborate for a fourth time on this historical and mathematical examination of the Pythagorean Theorem (a2+b2=c2). Going well beyond the typical school treatment of the subject, the Kaplans use proofs and diagrams to demonstrate that “the Pythagorean Theorem…holds even when the most art nouveau shapes flourish on a right triangle’s hypotenuse, along with shapes similar to it on the legs. They can, if you wish, be as lacy as your great-grandmother’s antimacassars, so long as they have areas.” People throughout the ages, from Leonardo da Vinci to President James A. Garfield, have found multiple methods for constructing proofs of this famous and useful theorem, and the Kaplans provide many of them along with background information and context. The Kaplans are wonderfully chatty hosts-“The begottens and begets of mathematics never end-not because of some dry combinatorial play, but because curiosity always seeks to justify the peculiar, and imagination to shape a deeper unity”-often asking questions to inspire thinking. Some readers may wish for a more direct approach, but the Kaplans combine math history and theory with humor, compelling tidbits, and helpful equations (along with an analysis of tangrams) to create an entertaining and stimulating book for the mathematically inclined. Illus. (c) Copyright PWxyz, LLC. All rights reserved. From Booklist The authors of The Art of the Infinite (2003), about mathematical proof, here discuss the equation every high-school grad should know, the famous theorem that relates the sides of a right triangle. Going through many of the apparently hundreds of proofs of it, the Kaplans sinuously weave personalities into the history of proving Pythagoras correct. The brightest-burning controversy concerns who should get the credit for the first proof. Partisans of the Babylonians uphold clay fragments with base-60 numbers, others tout ancient Chinese sages, but the Kaplans are not persuaded. Departing from the theorem’s codification in Euclid’s Elements, they explore proofs proffered by characters historical (James Garfield), obsessive (Elisha Loomis, a teacher who anthologized proofs), and inspiring (a blind woman, E. Coolidge, who devised an original proof). Born of geometry, the theorem proves to be a creature of metamorphosis, appearing in branches of math from number theory to calculus. Showing the theorem’s endless versatility, the Kaplans and their logic- and symbol-permeated text will engage those who delight in doing the math. –Gilbert Taylor Review “Beauty, intrigue, paradox and surprise. Mathematics, in its true essence, is a deeply organic and intensely human enterprise and Bob and Ellen Kaplan are the masters of reveling in its delight and elucidating its richness. Hidden Harmonies is a stunning book, taking the most classic theorem in mathematics and exposing its story, its human story, for what it really is: true poetry.” ―James Tanton, PhD, author and educator, founding director of the St. Mark’s Institute of Mathematics“…The authors succeed in explaining the arcane aspects of the subject, and they are diligent in situating the Pythagorean theorem within the historical rise of mathematics. That they revel in the subject is clear…” ―Wall Street Journal“Showing the theorem’s endless versatility, the Kaplans and their logic- and symbol-permeated text will engage those who delight in doing the math.” ―Booklist“Enthusiasm and wit make the material appealing even to readers who aren’t mathematicians … inspired.” ―Kirkus“The book possesses an alluring lyricism and a good sense of humor, and it’s often as fun to be around…” ―Anthony Doerr, Boston Globe“The Kaplans have given us a wonderful, fun, and entertaining math book.” ―Library Journal About the Author Robert and Ellen Kaplan have taught mathematics to people from six to sixty, at leading independent schools and most recently at Harvard University. Robert Kaplan is the author of the best-selling The Nothing That Is: A Natural History of Zero, which has been translated into 10 languages, and together they wrote The Art of the Infinite. Ellen Kaplan is also co-author of Chances Are: Adventures in Probability and Bozo Sapiens: Why to Err is Human, co-written with her son Michael Kaplan. Read more

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

⭐I enjoy math and science books, but I’m not a professional or holder of a degree in these subjects. I’ve read, enjoyed and at least partially understood a number of books, including on string theory, Einstein, and others. But “Hidden Harmonies” was, for me, lacking in interest and largely beyond my ability (or at least willingness) to follow. There are a few descriptive and human interest stories that are good, and I did get some fun insights. A majority of the book consists, however, of mathematical proofs — beginning simple and getting quite complex — that I was not willing to stop and study and that constituted nothing but page after page of mathematical equations, which were gibberish for me if I did not stop and study them. I think I could have followed more of them if I’d put in the effort (and probably did work some of them back in my geometry, trig and calculus classes), but my reading is for pleasure (e.g. in bed at night), and I don’t want to study advance math a page per evening as my book time. What the authors describe is truly remarkable, and I suppose some avid math readers enjoy working through it. I, however, would have been better served by a short magazine article summarizing the concepts.

⭐This book had some good insights and taught me some things about one of more favorite subjects, the Pythagorean Theorem. I found the writing style a bit too breezy for my taste; I didn’t feel like it was focused, and I found that distracting. Some of the math concepts were beyond my ability, and while I don’t mind getting into the depths of a proof, some of it was too in depth. Especially toward the end, some of the items were too esoteric for my taste. So I learned some things from it, but I think it could have been better.

⭐I had already looked at this book as a library book as I intend to use it as reference material on a book I am doing on Pythagoras although I find the math very hard to follow.

⭐This was not what I expected. For a mathematician it is a good resource, and interestingly put together. But for the general reader, suggest you pass it by.

⭐Good

⭐The book was a good read but it didnt work well on my kindle. There were too many images and figures to read that were distorted on the kindle.

⭐Brilliantly written and thought provoking

⭐This was a very interesting book. You might think it would be hard to have an entire book on the Pythagorean theorem, but the Kaplan’s do make it engaging. The history surrounding its discovery and use is quite interesting. I learned that Neugebauer probably was wrong about Plimpton 322, which I was unaware of before. Instead of being Pythagorean it seems more likely it was creating problem sets for scribe students. You also learn several proofs of the Pythagorean theorem, with the proofs well explained (there was only one proof that left me mystified in the book: the one “proving” the Pythagorean theorem with a torus, with further google searches not helping me see how the proof presented works). And you learn of the many ways of extending the definition for multiple dimensions, different spaces, and just a good amount of generalizations that touch upon the Pythagorean theorem.There is a certain style to the writing that may put off some people in that it makes many allusions and has a semi-mysterious air to some paragraphs. That is it sort of makes grand pronouncements that I’m not sure as grand as they are proclaimed. I found that sometimes it was a little bit too much for my taste, but I still found the vast majority of the book to be interesting. The math is well written with good figures.I would not recommend the Kindle edition because of formatting issues, though. Flipping back and forth to see figures is one thing, but the footnotes are in a strange order, and there are some strange spacings in some of the words like “in e quality” that while not incomprehensible, detract from the readability.One other comment is that they do not dumb down proofs, so if you have little mathematical sophistication, you may find the entire thing unreadable and the generalizations not understandable without putting in a good deal of work. I think they present things well, but it would still be rather daunting without mathematical training. All in all, a fun read, and I will probably try some of the Kaplan’s other books.

⭐Bought for hubby who is estasic about it. Sorry can’t provide further details.

Keywords

Free Download Hidden Harmonies: The Lives and Times of the Pythagorean Theorem in PDF format
Hidden Harmonies: The Lives and Times of the Pythagorean Theorem PDF Free Download
Download Hidden Harmonies: The Lives and Times of the Pythagorean Theorem 2011 PDF Free
Hidden Harmonies: The Lives and Times of the Pythagorean Theorem 2011 PDF Free Download
Download Hidden Harmonies: The Lives and Times of the Pythagorean Theorem PDF
Free Download Ebook Hidden Harmonies: The Lives and Times of the Pythagorean Theorem