Euler's Gem: The Polyhedron Formula and the Birth of Topology [Hardcover]

David S. Richeson (Author)

Editorial Reviews

Review

The author has achieved a remarkable feat, introducing a naïve reader to a rich history without compromising the insights and without leaving out a delicious detail. Furthermore, he describes the development of topology from a suggestion by Gottfried Leibniz to its algebraic formulation by Emmy Noether, relating all to Euler's formula. This book will be valuable to every library with patrons looking for an awe-inspiring experience.
(Choice )

I highly recommend this book for teachers interested in geometry or topology, particularly for university faculty. The examples, proofs, and historical anecdotes are interesting, informative, and useful for encouraging classroom discussions. Advanced students will also glimpse the broad horizons of mathematics by reading (and working through) the book.
(Dustin L. Jones Mathematics Teacher )

Review

Euler's Gem is a thoroughly satisfying meditation on one of mathematics' loveliest formulas. The author begins with Euler's act of seeing what no one previously had, and returns repeatedly to the resulting formula with ever more careful emendations and ever-widening points of view. This highly nuanced narrative sweeps the reader into the cascade of interlocking ideas which undergird modern topology and lend it its power and beauty.
(Donal O'Shea, author of "The Poincare Conjecture: In Search of the Shape of the Universe" )

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Product Details

• Hardcover: 332 pages
• Publisher: Princeton University Press; 1 edition (September 8, 2008)
• Language: English
• ISBN-10: 0691126771
• ISBN-13: 978-0691126777
• Product Dimensions: 9.4 x 6.2 x 1.1 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 4.8 out of 5 stars  See all reviews (12 customer reviews)
• Amazon Bestsellers Rank: #51,443 in Books (See Top 100 in Books)

  #3 in	Books > Science > Mathematics > Geometry & Topology > Topology
  #38 in	Books > Science > Mathematics > Geometry & Topology > General Geometry

Customer Reviews

Most Helpful Customer Reviews

41 of 42 people found the following review helpful:

5.0 out of 5 stars More Evidence that Mathematics Is Beautiful, December 22, 2008

By	Gene B. Chase (Grantham, PA USA) - See all my reviews (REAL NAME)

This review is from: Euler's Gem: The Polyhedron Formula and the Birth of Topology (Hardcover)

If you want a popularized book-length treatment of string theory, you have two kinds of choices. Brian Greene uses no equations, save in an occasional endnote. Roger Penrose uses 1136 equation-filled pages to teach you all of mathematics you would need to know--although far too fast for anyone to learn it from Penrose alone. There is not much between Greene and Penrose.

If you wanted a popularized book-length treatment of topology before Dave Richeson's Euler's Gem: The Polyhderal Formula and the Birth of Topology, you had no choice at all.

This is a risky thing that Richeson attempts. Ian Stewart's 2007 book Why Beauty is Truth: The History of Symmetry cites the "conventional wisdom in science writing that every equation halves a book's sales." (34) On this basis, Richeson's book should have only
one ten billionth of the sales of other books popularizing science. Yet Richeson pulls it off with a well-written, nicely illustrated book surveying the history of topology from Plato to Poincaré to Perelman.

Richeson's book is accessible to an academically minded high school student, yet has something to offer the professional mathematican who happens not to be a topologist.

There are no typos in the book. There is a useful, although not comprehensive index. (Richeson mentions flexible polyhedra -- see mathworld.wolfram.com/FlexiblePolyhedron.html -- for example, but the index doesn't.) The only slight confusion that I encountered is at page 157, which says that we have seen V-E+F = 2-2g before. We have not. However, on page 148, we saw V-E+F = 2 - 2T + P + 2C, so let P = C = 0 and rename T as g, and all is clear.

Richeson's book ends on the theme of beauty, and well it should. It's a beautiful book! I bought three as Christmas presents for friends. You should buy one too.

20 of 23 people found the following review helpful:

5.0 out of 5 stars I thoroughly enjoyed this book., December 6, 2008

By	Dave "Srebby" (Massachusetts) - See all my reviews

This review is from: Euler's Gem: The Polyhedron Formula and the Birth of Topology (Hardcover)

I really enjoyed this book. I found that the David Richeson's writing style made this topic very accessible. I thought that there was just the right balance of history and math. Having little experience with topology, learned a lot about it. I was really astounded at some of the unexpected connections between "Euler's Gem" and different branches of math.

Lots of fun!

11 of 13 people found the following review helpful:

5.0 out of 5 stars outstanding read for anyone interested in math, March 4, 2009

By	esm "esm" (LA, CA) - See all my reviews

This review is from: Euler's Gem: The Polyhedron Formula and the Birth of Topology (Hardcover)

i was given this book as a gift after taking a course on algebraic topology. while only some of the material appeared in both the book and the text i used for the course, i developed a much deeper understanding of the subject after finishing richeson's outstanding presentation of a difficult subject.

the writing is efficient and enjoyable throughout. many of the chapters serve as interesting interludes or transitions to help clarify relationships between topics.

i have searched high and low for similar books in topology without luck. richeson seems to have a unique gift for "popularizing" topology without losing the interest of those of us who appreciate the depth and beauty of mathematics.