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Beautiful Geometry Hardcover – January 19, 2014


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Editorial Reviews

Review

Honorable Mention for the 2015 PROSE Award in Popular Science & Popular Mathematics, Association of American Publishers

"Mathematicians sometimes compare well-constructed equations to works of art. To them, patterns in numbers hold a beauty at least equal to that found in any sonnet or sculpture. In this book, Maor, a math historian, teams with Jost, an artist, to reveal some of that mathematical majesty using jewel-like visualizations of classic geometric theorems. . . . The result is a book that stimulates the mind as well as the eye."--Lee Billings, Scientific American

"The combination of art and exposition was quite effective. The writing is accessible to most reasonably well-educated laypeople, and I imagine that many such people would derive considerable pleasure dipping into this attractive and interesting book."--Mark Hunacek, MAA Reviews

"Eli Maor's lively writing benefits in equal parts from the geometry of ancient Greece and the eye-popping images conjured by artist Eugen Jost."--Bill Cannon, Scientist's Bookshelf

"Graphic illustrations serve as both beautiful abstract art and helpful explanations in this overview of geometric theorems and patterns."--Science News

"[The book] achieves its aim to demonstrate that there is visual beauty in Mathematics. I heartily recommend it for anyone to at least page it through, and for anyone interested in geometry to read, especially mathematics students who want to broaden their horizons and teachers of mathematics at school level."--Konrad Swanepoel, LSE Review of Books

"[A] book where art and mathematics are in perfect harmony. . . . [A]nyone with any interest in visual mathematics will love this book, which, given the quality of the reproductions, is very attractively priced. It will inspire interest in a wide variety of mathematics, and should be a compulsory purchase for sixth-form libraries."--Tony Mann, Times Higher Education

"A good-looking, large-format book suitable for the coffee table, but with lots of mathematical ideas packed in among the colorful illustrations. . . . [A] handsome book for browsing and for some deep thought, and would be a superb gift for anyone (especially a young person) who has interest in mathematics."--Rob Hardy, Columbus Dispatch

"It is a handsome book for browsing and for some deep thought, and would be a superb gift for anyone (especially a young person) who has interest in mathematics."--Rob Hardy, Dispatch

"The book by Maor and Jost should be given to everyone--young or old--embarking on the study of mathematics or anyone teaching mathematics. The book will act as a source of inspiration and as a reminder of why it is that mathematics has fascinated the human race for millennia."--Henrik Jeldtoft Jensen, LMS Newsletter

"The content is accessible to anyone with even a high school course in geometry. The writing is very clear."--Choice

"The text is easily readable--accessible to a bright high-school student--but is good for anyone with an interest in the subject and who wants a visual approach. The book rises to the level of a coffee-table art book, only with a lot more depth."--Mary Long, Mathematical Reviews

"[E]erily captivating book. . . . Maor's style of writing is conversational, and the writing is engaging."--Annalisa Crannell, Journal of Mathematics and the Arts

"At a very reasonable price, this is a book which would grace the coffee-table of any mathematics department, and many of the ideas in it will stimulate valuable discussions in the classroom."--Gerry Leversha, Mathematical Gazette

"It presents as a coffee-table book for mathematicians and would be a good addition to a classroom library, available for students of all ages to explore."--Susan Mielechowsky, Mathematics Teaching in the Middle School

From the Back Cover

"Mathematicians always claim their subject is beautiful. Eli Maor and Eugen Jost prove it. This is geometry as you've never seen it before. A feast for the eyes."--Ian Stewart, author of Visions of Infinity

"This book shows that math is more than theorems and proofs--it is full of history, philosophy, and glimpses of different cultures. I was immediately attracted by the book's intriguing and beautiful illustrations, and once I started reading the text, I could not stop following its fascinating stories about the origins of geometrical theorems."--Carlo H. Séquin, University of California, Berkeley

"Reading Beautiful Geometry is like touring a personal art collection, except the masterpieces here are elegantly presented theorems and constructions by ancient and modern mathematicians. Eli Maor teaches the thought process of a geometry connoisseur as he highlights important details in each of these gems, and Eugen Jost illustrates these ideas with colorful and creative artworks. Readers who like to see real math in their math books will enjoy how Beautiful Geometry brings these enduring mathematical achievements to life."--George Hart, mathematical sculptor

"Beautiful Geometry teaches and delights with its marriage of art and mathematics. The lovely illustrations range from conversation starters to dazzling Proofs Without Words--clever diagrams that explain why something is true. A feast for the eye and mind."--Frank Farris, Santa Clara University

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Product Details

  • Hardcover: 208 pages
  • Publisher: Princeton University Press (January 19, 2014)
  • Language: English
  • ISBN-10: 0691150990
  • ISBN-13: 978-0691150994
  • Product Dimensions: 0.8 x 9 x 9.5 inches
  • Shipping Weight: 1.8 pounds (View shipping rates and policies)
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (19 customer reviews)
  • Amazon Best Sellers Rank: #75,151 in Books (See Top 100 in Books)

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Customer Reviews

The book is full of beautiful art work and mathematics.
Charles H. Rosa
Well selected geometry topics that are highlighted and presented to the reader.
W. D. Partridge
Wonderful book, well illustrate, always something new to learn.
Eric Joyall

Most Helpful Customer Reviews

18 of 20 people found the following review helpful By David Wineberg TOP 500 REVIEWER on January 17, 2014
Format: Hardcover
When I was a single digit prime number, I bought a ten cent comic book that was different from all the rest. It was called Donald Duck in Mathematics Land, and it was all about the absolute magic of numbers in geometry. It was a treasure and I still have it, carefully pressed flat and kept from the ravages of light.

Now just 50 years later, come a couple of number theory heavyweights, one in math and one in math-based art, one-upping Donald. Beautiful Geometry makes art of science and sense of math.

The science dates back to the golden age of Greece, that less-than-hundred year period where the Greeks ruled the intellectual world, spent their time racking up truckloads of discoveries, and elevating science to unheard of heights. Interestingly, there were no generalizations in the approach of the Greeks. Each time they discovered a variation or new instance, it became a new theorem, even though it might describe the same phenomenon as another theorem. Nothing was insignificant in the golden age. And though they did not have a real number system to work with (that had to wait till 1200 AD), and a lot of what they proposed was (ultimately) incorrect, they made remarkable contributions and remarkable progress.

There are 51 three page chapters, each illustrating magic of some sort in numbers and their geometric origin and/or display. The middle page of each chapter is a full page color work of art employing the topic of the chapter.

For those not mathematically inclined, it will be work to understand it all. But it is written as simply and basically as mathematics can be, and the overall effect is one of childlike fascination with the magic of it all. From equivalence to symmetry to infinity, it’s all here, updating and collecting facets of number theory that have occupied and obsessed the minds of mathematicians and philosophers for more than 2000 years.

David Wineberg
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14 of 16 people found the following review helpful By Dr. Bojan Tunguz HALL OF FAMETOP 50 REVIEWER on January 28, 2014
Format: Hardcover
Geometry remains one of the most intuitively appealing subfields of Mathematics. However, as anyone who has studied geometry at any length will attest, the visual beauty of geometry oftentimes belies its underlying intellectual complexity. Like in many other parts of Mathematics, sometimes it’s the things that are easy to visualize and state, which can be fiendishly hard to understand and prove.

In “Beautiful Geometry” Eli Maor and Eugen Jost aim to give the reader a sampler of some of the most interesting problems and ideas from the almost three thousand years long history of Geometry. The book is designed to inform and educate the reader, and even though it’s not written as a traditional math textbook, it does require an active engagement on the part of the reader. There are many proofs and other fairly rigorous demonstrations, which, although not terribly long nor complex, do require that the reader is comfortable and used to going through rigorous mathematical reasoning. Many of the proofs can be found in most elementary geometry textbook, but if you are like me you probably haven’t seen them in many, many years and I appreciate a gentle reintroduction to this material. Maor is a great pedagogue, and this is probably as good of an elementary exposition of geometry as they come.

This is a beautifully designed hardbound book that would be right at home in almost any library. However, it doesn’t quite rise to the level of a math “coffee table” book. For one, even the most die-hard math enthusiast will not just casually pick up this book for the most absent-minded perusal. Furthermore the illustrations, although nice enough, have higher pedagogical than artistic value.
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16 of 19 people found the following review helpful By Ursiform TOP 1000 REVIEWERVINE VOICE on January 15, 2014
Format: Hardcover
Perhaps unfairly, I expected this book to delve more generally into how math has influenced art. In fact, the author presents various mathematical symmetries and theorems, and the artist creates artwork based on them. Each mathematical topic is a chapter, with a few page explanation of the math, a plate of artwork, and often additional drawings.

Although presented clearly and at an introductory level, the math is serious. If you have no interest in math you probably won't enjoy this book, and if you have no basic understanding of math, at least through introductory algebra and geometry, you may have trouble following it.

Likewise, if you don't enjoy art, and specifically art based on symmetrical patterns, the artsy part of the book may not interest you.

This is a case where the Amazon "Look Inside" feature can be used to good value. You can read a chapter or two, and look at some of the pictures. If you want to read more, this is a good book for you. If you aren't engaged you don't want this book.

This book is definitely a niche book, aimed at the math/science lover who also likes art. You know who you are ...

I was provided a copy for review by the publisher.
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4 of 5 people found the following review helpful By Richard Murphy on March 11, 2014
Format: Hardcover Verified Purchase
The author has a clear sense of geometry and other mathematical areas, along with a fascinating feel for artistic representations of the concepts embodied in each particular theorem or property. This book would be interesting to anyone who likes math, art, or simply good writing.
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By Grant Cairns on January 6, 2015
Format: Hardcover Verified Purchase
This delightful book has 51chapters each devoted to a classical topic in geometry. Each chapter includes a beautiful colour plate and many chapters include additional illustrations. The topics are well chosen and the text is logical and eloquent. The book should be accessible to a very broad audience (there is an appendix with more mathematical details for those inclined). The attention to detail and the standard of production are both outstanding. This would make an excellent gift and would be enjoyed by anyone interested in math, the history of math, art or architecture.

Here are 4 comments/observations:

p. 44. It is often stated that there is no formula for the primes, but this is actually not the case. There are many explicit formulas. (To my mind the nicest is Ghandi's formula). For example, see Underwood Dudley's "Formulas for primes", Math. Mag. 56 (1983), no. 1, 17-22. There have also been other formulas obtained since Dudley's paper.

p.101. For a geometric derivation of the formula for ln(2), see the proof without words by Matt Hudelson, Math. Mag. vol 83 (2010) p.294.

p.120. Fig 36.3; in the 2nd and 4th figure the red dot should be in the centre of the figure, not on the rim of the circle.

Chap 49. In my opinion the common popular treatment of the Koch curve is not entirely satisfactory, in that it may be unclear to the reader that its length is infinite, or in fact, what its length means. To clarify my concern, let alpha>0 and consider the curve: gamma_n : [01]->R^2 whose graph on each interval [m/n,(m+1)/n] is a little tent of height alpha/n, where m=0,1,2,...n-1. As n-> infty, the curve converges (in the sup norm) to the unit interval on the x-axis (which is a curve of length 1).
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