Euclid's Window : The Story of Geometry from Parallel Lines to Hyperspace

by Leonard Mlodinow

Book Overview

Through Euclid's Window Leonard Mlodinow brilliantly and delightfully leads us on a journey through five revolutions in geometry, from the Greek concept of parallel lines to the latest notions of... This description may be from another edition of this product.

• Format: Paperback
• Language: English
• ISBN: 0684865246
• Release Date: April 2002
• Publisher: Free Press
• Length: 320 Pages
• Weight: 0.70 lbs.
• Dimensions: 9.3" x 0.9" x 5.3"

Customer Reviews

The Shape of Our Universe

As a teacher of geometry, I always keep an eye out for books that offer coherent explanations of the importance of this most intriguing and ancient branch of mathematics. This books offers that in spades. In fact, it is one of the best basic overviews of the field I have ever come across.Mlodinow divides the history of the development of geometry into five major "revolutions." Starting first with Euclid and his Greek contemporaries, Mlodinow traces the field through Descartes and the development of analytic geometry, Gauss and the development of "non-Euclidean" geometries, Einstein and the physical application of these geometries, to Witten and the development of string theory--the attempt to understand the universe as a consequence of geometry. In high school we teach the basics of plane and analytic geometry but few people are aware of how the field has matured since then. This book takes us on that journey.And it is a wonderful one. Along the way he gives insight not only into the mathematics but also into the personalities that created it. We too often forget that it is people who created this magnificent structure and that it was not just handed down to us perfectly formed. Even more, we need to be reminded that the development continues and people are still contributing to it.The real achievement of this book, however, is its acessiblity. Despite the fact that most people will only have experience with the material from the first two sections of the book (Euclid and Descartes), Mlodinow's writing is understandable by anyone who has successfully navigated a course in high school geometry. In my view, he offers one of the most lucid explanations of Einstein's work and string theory that I have ever read. His style is engaging and very readable. The ability to bring the importance of mathematics to a general audience is a great gift that Mlodinow seems to have. I hope he continues to exploit it.If I have a complaint about this book, it is that it could have used a few more diagrams to help the less mathematically minded visualize his explanations. This is a minor point, however. Overall, this book is a great piece of work.

Brilliantly written

Euclid's Window is an astounding book. It takes you on a ride through History, where you explore the origins of Geometry & Mathematics. From the early Babylonians to the Egyptians who used Geometry & Mathematics, but didn't ask the deeper questions which the Greeks did. With the Greeks came Thales, Pythagoras, and Euclid (Not necessarily in that order) who changed our view of the world by developing Geometry as we know it today in High School books. Than came the Dark Ages, and Europe plummeted into more than 1000 years of intellectual silence. The book than talks about the revolutions led by Galileo, Descartes, Gauss, and Riemann. Finally the Author describes the later developments in physics. The revolution that Einstein made with the Special Theory or Relativity and the General Theory of Relativity. From then on we knew that mass curves space creating gravity, that nothing can travel at the speed of light, and that time is a privet matter rather than universal. Than the Revolution of Quantum Physics which, was developed in particular by Heisenberg and Schrodinger. Leonard Mlodinow explains the conflicts that arise when quantum physics and the General Theory of Relativity are combined, they fail. Quantum Mechanics works perfectly on the small scale, General Relativity works fine on the large scale, yet there is no way physicist and mathematicians could combine the two. And then came the birth of the String Theory, rather five different String theories that turn out to be approximations to the much larger M-Theory, the theory that would be able to describe everything in the Universe, from subatomic particles to distant galaxies in the Universe. There is only one problem nobody knows what it looks like, and mathematicians and physicist can only calculate approximations of the theory. Leonard Mlodinow takes the reader on a fascinating ride through the history of Mathematics and Physics, the book is enlightening, even to me who constantly tries to keep up with new developments in Physics. A must read for anybody interested in Mathematics & Science, or just plain old History, this book is essential.

A work both charming and profound

I found Euclid's Window charming and profound. Though Mlodinow's topic is ambitious, his ability to explain with incredible clarity some of the world's most abstruse thinking reminded me of Jim Gleick's work on Chaos. Mlodinow's storytelling seemed something altogether different--a lot more fun than Gleick.Building on historical anecdote, Mlodinow has stitched together a history of human thought for me in a way no one else has, explaining how millenia of physical observation have translated into conceptual thought. I worried that this might be heavy going, but Mlodinow glories in the fine line of tale and humor;it spills over in his prose with such ease that it appears unconscious. I suspect this may become something of a classic.

Math Turned Adventure

Mlodinow's book does the nearly impossible, translating key moments in mathematical understanding into the stuff of gripping drama. The fact that he's written extensively helps; but his choice of subjects, his vision and understanding, takes us away. It's the kind of book to read--and recommend. We live in a world of points, and lines, and space...but Mlodinow shows how understanding..conquering that world...was a real intellectual adventure. Oh, and it is--amazingly--a page turner of the highest order!

This adds up to some great writing!!!

What a terrific book. Not only does take me from Euclidean geometry to the string theory of today -- but it does so in a clear, understandable way. And, lo and behold, its a math book that is written with a real sense of humor. Who would have guessed this was even possible? I strongly recommend this.