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

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 hyperspace. Here is an altogether new, refreshing, alternative history of math revealing how simple questions anyone might ask about space — in the living room or in some other galaxy — have been the hidden engine of the highest achievements in science and technology.
Based on Mlodinow's extensive historical research; his studies alongside colleagues such as Richard Feynman and Kip Thorne; and interviews with leading physicists and mathematicians such as Murray Gell-Mann, Edward Witten, and Brian Greene, Euclid's Window is an extraordinary blend of rigorous, authoritative investigation and accessible, good-humored storytelling that makes a stunningly original argument asserting the primacy of geometry. For those who have looked through Euclid's Window, no space, no thing, and no time will ever be quite the same.

ISBN-13: 9780684865249

Media Type: Paperback

Publisher: Free Press

Publication Date: 04-09-2002

Pages: 320

Product Dimensions: 5.30(w) x 9.18(h) x 0.68(d)

Leonard Mlodinow, Ph.D., was a member of the faculty of the California Institute of Technology before moving to Hollywood to become a writer for numerous television shows ranging from Star Trek: The Next Generation to Night Court. He has also developed many bestselling and award-winning educational CD-ROMs, and delivered technical and general lectures in ten countries. He is currently Vice President, Emerging Technologies and R&D, at Scholastic Inc. He lives in New York City.

Read an Excerpt

Chapter One: The First Revolution

Euclid was a man who possibly did not discover even one significant law of geometry. Yet he is the most famous geometer ever known and for good reason: for millennia it has been his window that people first look through when they view geometry. Here and now, he is our poster boy for the first great revolution in the concept of space — the birth of abstraction, and the idea of proof.

The concept of space began, naturally enough, as a concept of place, our place, earth. It began with a development the Egyptians and Babylonians called "earth measurement." The Greek word for that is geometry, but the subjects are not at all alike. The Greeks were the first to realize that nature could be understood employing mathematics — that geometry could be applied to reveal, not merely to describe. Evolving geometry from simple descriptions of stone and sand, the Greeks extracted the ideals of point, line, and plane. Stripping away the window-dressing of matter, they uncovered a structure possessing a beauty civilization had never before seen. At the climax of this struggle to invent mathematics stands Euclid. The story of Euclid is a story of revolution. It is the story of the axiom, the theorem, the proof, the story of the birth of reason itself.

Copyright © 2001 by Leonard Mlodinow

Show More

What People are Saying About This

Edward Witten

Edward Witten, California Institute of Technology
Mlodinow leads the reader on a fascinating tour through the history of geometry, from ancient times to our modern-day fumblings in trying to understand string theory. The book is written with grace and charm.

Amir Aczel

Euclid's Window is a very good introduction to geometry, from Euclid to Einstein. Readable and entertaining.
—(Amir Aczel, author of Fermat's Last Theorem)

Amy Brunvand

Amy Brunvand, University of Utah Lib, Salt Lake City
This surprisingly exciting history of how mathematicians and physicists discovered geometric space beyond Euclid's three dimensions ... does an excellent job of explaining the importance of the study of geometry without making the reader learn any geometry. For all math and science collections.

Michael Guillen

How often can you say that a book on math-on math!-is a real page-turner? Well, this one is. As engaging as a soap opera, as fascinating as a whodunnit, as funny as the Sunday comics, Mlodinow's book is story-telling at its best.
—(Michael Guillen, Ph.D., author of Five Equations That Changed the World)

David Berlinsky

This is an exhilarating book, one that celebrates geometry as one of mathematics' shining suns. And it is an important book, if only because that sun has for too long been covered by a numver of scudding clouds. And it is, finally, a lovely book, one that reflects the radiance of its subject and so warms even as it instructs.
—(David Berlinski, author of A Tour of the Calculus)

Brian Greene

If there is one thing that progress in physics confirms again and again, it is that geometry is a powerful conceptual framework for describing and understanding the universe. In Euclid's Window, Leonard Mlodinow tells the intriguing story of geometry, from antiquity through the exciting and mind-bending developments of superstring theory. There is perhaps no better way to prepare for the scientific breakthroughts of tomorrow than to learn the language of geometry, and Euclid's Window makes this task lively and enjoyable.
—(Brian Greene, author of The Elegant Universe)

Show More

Table of Contents

Contents

Introduction

I THE STORY OF EUCLID

1. The First Revolution

2. The Geometry of Taxation

3. Among the Seven Sages

4. The Secret Society

5. Euclid's Manifesto

6. A Beautiful Woman, a Library, and the End of Civilization

II THE STORY OF DESCARTES

7. The Revolution in Place

8. The Origin of Latitude and Longitude

9. The Legacy of the Rotten Romans

10. The Discreet Charm of the Graph

11. A Soldier's Story

12. Iced by the Snow Queen

III THE STORY OF GAUSS

13. The Curved Space Revolution

14. The Trouble with Ptolemy

15. A Napoleonic Hero

16. The Fall of the Fifth Postulate

17. Lost in Hyperbolic Space

18. Some Insects Called the Human Race

19. A Tale of Two Aliens

20. After 2,000 Years, a Face-lift

IV THE STORY OF EINSTEIN

21. Revolution at the Speed of Light

22. Relativity's Other Albert

23. The Stuff of Space

24. Probationary Technical Expert, Third Class

25. A Relatively Euclidean Approach

26. Einstein's Apple

27. From Inspiration to Perspiration

28. Blue Hair Triumphs

V THE STORY OF WITTEN

29. The Weird Revolution

30. Ten Things I Hate About Your Theory

31. The Necessary Uncertainty of Being

32. Clash of the Titans

33. A Message in a Kaluza-Klein Bottle

34. The Birth of Strings

35. Particles, Schmarticles!

36. The Trouble with Strings

37. The Theory Formerly Known As Strings

Epilogue

Notes

Acknowledgments

Index Show More