Euler's Gem by David S. Richeson

Euler's Gem

Leonhard Euler's polyhedron formula describes the structure of many objects--from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea. From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron...

Details Euler's Gem

TitleEuler's Gem
Release DateSep 28th, 2008
PublisherPrinceton University Press
GenreScience, Mathematics, Nonfiction, History

Reviews Euler's Gem

  • Upom
    I've been dreaming of higher dimensions lately, and this book on topology just enthralled this fascination even more. "Euler's Gem" is really a look at one of the most famous equations you've never heard:V-E+F=2, also known as Euler's Formula. This formula originally described a relationship between the faces, edges, and vertices of the 5 platonic Solids, but actually has a deeper significance as an equation connecting the vast subtopics of topol...
  • Bob Gustafson
    Richeson's "Euler's Gem" is an excellent book. It gives the historical background, going back to ancient Greece, for this equation regarding faces, edges and vertices of polyhedra. It tells us about Euler (as well as more than a dozen other mathematical scholars) and the relationship. It goes on to tell us about various proofs and then extensions of and enhancements to the equation.If this book is excellent, why four rather than five stars? It's ...
  • Erickson
    Nice topology and geometry book. The proof part is especially good. Would recommend this to go along with Weeks' The Shape of Space, or vice versa.
  • Ben Orlin
    A mathematician friend recently asked me, "Do you think pop math books could be a good way for me to learn about other fields?" (He studies partial differential equations.)"Sure!" I said, and handed him this book. "Here's algebraic topology!""Great," he said. "Any others?"I looked at my shelf, saw that the answer was no, and realized in that moment how unusual Richeson's achievement is. This is an engaging, readable, historical tour, covering a l...
  • Tyler
    This is quite an ambitious book for the author, and he does a great job showing the evolution of topology from its roots in geometry, graph theory, and knot theory. The math gets decently high-level by the end, but the author makes a great effort at trying to reach those without a formal understanding of the topics. This book isn’t for people who aren’t interested in mathematics, but for those who are amateurs to probably grad students this s...
  • Richard Holmes
    This book wasn't what I was expecting; rather than a book centered on Euler's formula, it's an introduction to topology with the formula as a recurring theme. As such large parts of the book serve to introduce topics having little to do with the formula and which I was already familiar with. I didn't find Richeson's pedestrian exposition shed much in the way of interesting new light on these topics for the most part. I ended up skipping a lot, be...
  • Hyung Mook Kang
    Excellent book for the overall history of geometry and topology, as well as its motivations behind. The motivations behind the rigorous definitions of modern topology we learn (such as in Munkres) aren't in the book.
  • Matthew Dambro
    Excellent introduction to topology. Much of the math was over my head but the story of how mathematics is done is superb. The step by step accumulation of knowledge with the occasional flash of brilliance shown by a Euler or a Poincare is breathtakingly beautiful.
  • Charles
    A gem of mathematical results produced by one of the masters of mathematicsThe title of the book is derived from the formula V - E + F = 2 that holds for any convex polyhedron. V is the number of vertices, E the number of edges and F the number of faces. First demonstrated by Euler, the proof of this result is surprisingly simple. As is the case with most such formulas and their proofs, there is at least one near miss in the history of mathematic...
  • Koen Crolla
    Euler has arguably produced a lot of gems, but the one Richeson is talking about is the observation that for convex polyhedra, the number of vertices minus the number of edges plus the number of faces is always equal to 2. That this is not true for less sensible polyhedra (it's 0 for a reasonable polyhedral torus, for example) is one of the foundational observations of the field of topology, which is indeed what the book is about.Euler's Gem is m...
  • Gabriel Daleson
    The first two thirds of this book is heavier on the history and geometry, and it's the better part. The back third gets into topology, and, while it's certainly interesting, it's also not for the squeamish. I'm really not sure how one could easily provide a casual treatment of any high-dimensional mathematics, even as casual as Richeson does here, without losing people. I appreciate the effort, certainly, but I can make a good argument that the c...
  • Ruth
    I read this book on the history of topology to my elementary-school-aged son. I cannot really remember when we finished it, but it was some time in the summer of 2011. The idea of a book for a popular audience about topology is absurd. Once I owned a book called Learn Gujrati in 30 Days, and this was something like that. My kid was too young to realize that it was hard to understand and just had a lot of fun. We read about a chapter a night for w...
  • Adam
    This turned out to be an excellent introduction to topology via Euler's second most famous formula, V - E + F = 2. The first 30 pages were a history lesson, and after that it kept ramping up the math, ending at about the same place where my brain stopped working in grad school (homology groups). The proofs are mostly of the "general overview without the nasty tricky details" variety, which is about right for a book like this. Recommended for thos...
  • Aleksandr Jermakov
    "The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living."These are Poincaré's words author quotes at the end of the book. And he very well manages to show the nature's beauty in his book. More of biography/history of science tha...
  • Mohammed Hashem
    Great recap of the history of the relatively new mathematical field of Topology.A quote I liked...“Scientists and engineers have used computers to solve countless problems, but mathematicians have not. Computers are good at making speedy calculations, but not at the kind of precise and subtle arguments that are required in mathematical proof. Like philosophy and art, mathematics has always been a human endeavor, one that cannot be automated.”...
  • Matthewmartinmurray murray
    This was really fun to read at first but then goes heavily into topology and left me in the dust a little. I have a better understanding of some topological ideas but could have used a better explanation of most. I am much more comfortable visualizing the projective plan now which I am glad for. I also was interested in seeing some knot theory tie in. Its a good insight to one of the weirder sides of mathematics. So it was fairly good.
  • Robert
    Very nice book talking about the history of Euler's polyhedron formula and it's applications.Easily accessible with only a bit of mathematical background.My favorite part was learning about Pick's theorem, a beautiful theorem that I didn't know anything about before this.
  • Stephen
    Yes math nuts, this book is for you. Euler's Gem is his mathematical statement that the sum of the vertices and faces of a polygon is equal to the sum of the edges and 2. It shows the relationship to modern topology.
  • Steve Schlutow
    This was an okay book.. I did remind me of Euler's famous formula V-E+F=2 that I used once or twice in one of my math classes back in school (college).. I was interested in the connection of polyhedra and topology, which did not explain anything new.. Oh well.. Not a bad book--pretty easy read..
  • Tox123
    Great book! Before I knew next to nothing on topology, now I know basic knot theory and a little graph theory.
  • Ralph Stoever
    A great, clear and still detailed introduction to topology.
  • gargamelscat
    More interested in geometry than topology but this book is accessible, made up of 23 reasonably digestible chapters.
  • Kari
    I've seen explanations of a number of these topics before, but these are the best. The historical context makes it easier to remember the math and the diagrams are top-notch.
  • Jeff
    An interesting journey through the history of topology, along with the conceptual basics of topology presented in a way that is easy to understand.