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The King of Infinite Space: Euclid and His Elements Hardcover – January 29, 2013


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Editorial Reviews

From Booklist

*Starred Review* “As dazzling as first love” is how Bertrand Russell described his initial encounter with Euclid. As a mathematician who understands what Russell felt, Berlinski guides his readers through the intellectual wonderland that the ancient Greek geometer created in his epoch-making treatise, the Elements. In writing at once geometrically precise and disarmingly conversational, Berlinski explores the imposing edifice that Euclid erected on a foundation of just five deceptively simple axioms. Each of these axioms receives careful scrutiny, allowing readers to share in the excitement of mapping out the dimensions of an audacious new human enterprise, inscribing sharp boundaries around key concepts yet opening onto the infinite. Only an author who thinks both mathematically and philosophically could infer—as Berlinski does—the intellectual and even moral substance of the mental perspective that Euclid unfolds. Readers thus come to realize how Euclid’s pioneering thought made possible the rigor of a mathematical proof—and the discipline of a mathematical life. Even in the revolutionary modern theorizing of non-Euclidian geometers such as Lobachevsky, Bolyai, and Poincaré, readers will discern Euclid’s abiding influence as a visionary who glimpsed the mathematical unities hidden beneath chaotic appearances. An impressively concise distillation of the wizardry that transforms points, lines, and planes into sheer genius. --Bryce Christensen

Review

The Wall Street Journal
“Reading this brief, lively work is like sitting with the author in a French café with too many carafes of red wine and the smoke of hundreds of Gauloises swirling inside your head."

The New Yorker
“Lively….Berlinski guides us through an austere world of shapes and numbers with enthusiasm, assurance, and mischievous humor. He presents difficult ideas in straightforward terms, even when he moves into the strange and forbidding realm of non-Euclidean geometry.”

Publishers Weekly, Starred Review
“In this brief, accessible foray, popular math/science writer Berlinski breathes life into an ancient mathematician and the world of axioms and theorems he created—a geometric world that became the basis for much of modern math, from analytic geometry to the idea of curved space-time…. Even the most math-averse [will] be enthralled by Berlinski’s rich, vibrant language…. Berlinski’s book succeeds not only as a history of geometry but also as an exploration of the power of ideas, masterfully replacing cold abstraction with humor and humanity.”

Booklist, Starred Review
“In writing at once geometrically precise and disarmingly conversational, Berlinski explores the imposing edifice that Euclid erected on a foundation of just five deceptively simple axioms…. An impressively concise distillation of the wizardry that transforms points, lines, and planes into sheer genius.”

Library Journal
“Berlinski has produced a volume that will entertain and enlighten many of today’s readers—even those who do not treasure their memories of geometry class.”

The Weekly Standard
“Written with David Berlinski's characteristic mix of hothouse prose and standup comedy.”

Nature
“[A] pared and elegant homage to the peerless geometer [Euclid] and his magnum opus.”

New York Journal of Books
“For anyone who cares about Euclid, geometry, the philosophy of mathematics and most especially, for those who appreciate fine writing.”

American Scientist
"The King of Infinite Space is not a crib for the lazy student who can’t be bothered to read all 13 books of the Elements. Neither is it a line-by-line exegesis for the diligent student who wants help with specific propositions in Euclid. Instead Berlinski offers a meditative monologue on Euclid’s place in the history of mathematics and the history of ideas. Berlinski speaks to you one-on-one, taking you into his confidence, never preachy or teachy."

Kirkus Reviews
“A playful yet deep excursus through Euclid’s Elements, from veteran mathematician Berlinski. It is a pleasure to follow the author as he grasps the logistical tail of Euclid’s mathematics and follows it to this day…. It is a profound investigation, as math was synthesized and refined and Euclid broke out with his axiomatic system… as a way of seeing, a way of life…. The author’s storytelling is clear, crisp and emotive, and he brings Euclid’s little-known life alive.”
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Product Details

  • Hardcover: 192 pages
  • Publisher: Basic Books; 1st edition (January 29, 2013)
  • Language: English
  • ISBN-10: 046501481X
  • ISBN-13: 978-0465014811
  • Product Dimensions: 8.3 x 5.8 x 1.1 inches
  • Shipping Weight: 11.2 ounces (View shipping rates and policies)
  • Average Customer Review: 3.4 out of 5 stars  See all reviews (20 customer reviews)
  • Amazon Best Sellers Rank: #844,081 in Books (See Top 100 in Books)

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Customer Reviews

3.4 out of 5 stars

Most Helpful Customer Reviews

30 of 33 people found the following review helpful By Arash Farzaneh on February 9, 2013
Format: Hardcover
If you are already familiar with Euclid's work or if you really like math and geometry, then this book will be delightful and delicious. For those, who like me, shy away from math, it is a rather arduous process. And do not be fooled by the length of the book; there is a lot of condensed thought and reflection that have gone into it.

I cannot say that I fully enjoyed this book, nor would I say that I disliked it. In fact, it made me think, and it awoke my curiosity not only for Euclid, the man and the work, but also for the field of geometry itself and that is quite a feat!

Even if you do not like all the abstract language and the geometrical shapes and forms, there are some very interesting observations on time and space, including a chapter on paintings frozen both in time and space! It may not be an entertaining read, but it is educational and rewarding in the end.
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9 of 9 people found the following review helpful By Mark Twain on June 17, 2013
Format: Hardcover Verified Purchase
As a fan of David Berlinski's Devil's Delusion, I found myself drawn to dip into this fascinating book om Euclid. I was rewarded with Berlinski's clarity and wit, his elegant writing style. He converted me to a newfound interest in mathematics. Anyone would pick this book up with pleasure and leave it with regret. Mary Karr
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9 of 10 people found the following review helpful By J D Roberts on February 21, 2013
Format: Hardcover
This book does quite an astounding job portraying the works of Euclid and how he has laid the stepping stones for his predecessors, spanning more than two thousand years ago. The effort and skill that Euclid devoted his many years of life into his eternally thriving axiomatic system is adorned in this book. This book captivates no only the mathematical perspective of Euclid's admirable commission but also how it is applied into everyday life. The appreciation of space and an understanding of it's presence is the sole foundation of any readers credentials, making it congenial for all classifications of readers alike.
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12 of 15 people found the following review helpful By Blueboy on June 14, 2014
Format: Paperback
I am a retired PhD in engineering and have written, read, and reviewed papers for technical journals. I am accustomed to reading through proofs and pulling them apart as part of the review process. Papers are rejected for lack of rigor or for not making a contribution to the field, and for any number of reasons.

I saw this little book in the library, read the jacket, and took it home thinking it might be a fun read. Wrong!

With Euclid's 2300 year old proof, you would expect someone in the 21st century with all our history of rigor in math and and modern technology to GET THE PYTHAGOREAN THEOREM CORRECT. On page 75 (paperback) in the third paragraph he drivels into confusion: "The square BDEC is equal in its parts to EL and CL. But CL is equal to the square GL; and EL to the square AK. When reassembled, the square BDEC, having been divided for purposes of proof, is equal to GL and AK." This is a mess. There is no square GL and the rest is misdescribed. What is intended, I believe, is: The square BDEC is equal in its parts to BL and CL. But BL is equal to the square GB; and CL to the square AK. When reassembled, the square BDEC, having been divided for purposes of proof, is equal to GB and AK.

While explaining the proof's generic approach correctly, he misses with the details. If he doesn't get the nomenclature of the proof right, did he copy it from somewhere else perpetuating an earlier error, did an editor slip in a well-meaning "correction", or is it a mere typo? I suspect it is not a typo because there are too many letters involved. Somebody somewhere involved in the production of the book didn't understand the proof.
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4 of 4 people found the following review helpful By GM on July 6, 2013
Format: Hardcover Verified Purchase
This is not the book to learn Euclidean Geometry. It requires some basic knowledge of Mathematics; it is not a fast read. It is a good discussion of some of the assumptions and limitations of Euclidean Geometry. One of the points it makes is to show how, for all the reputation for being a logically rigorous system in which all assumptions are defined and justified; Euclidean Geometry includes a good dose of plain "common sense" and "self-evident truths" baked into its foundations. The book also moves on to discussing other geometries, of which one gets a flavor, but not much more. The style is a bit quirky, the author often doesn't tell you where he is going; lets things be revealed. I am not a mathematician, so who knows whether I got the right message or not; I enjoyed it and consider it time well spent.
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3 of 3 people found the following review helpful By Michael George on October 15, 2013
Format: Hardcover
Who was Euclid? What little passes to us through the ravages of time often leaves us with a puzzle. Certainly, one is curious about Euclid: His books on geometry have been standard textbooks for students for many hundreds of years. And yet the man, Euclid, has been lost in time. I felt that this little book has somehow captured someone, certainly a teacher, perhaps Euclid, commenting on the grand panorama of geometry, and discussing with some intimacy a few of the results from The Elements. I felt like a 10-year old, listening to the great geometer, come back to life, discussing geometry as he knew it, and geometry as it became, for example through the work of Poincare and other modern mathematicians. Dr. Berlinski's account presents the old teacher speaking to us through the centuries about the beautiful subject geometry was, and still is.
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