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# ðŸ“™ Euler's Gem: The Polyhedron Formula and the Birth of Topology by David S. Richeson â€” free epub

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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 formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of *V* vertices, *E* edges, and *F* faces satisfies the equation *V*-*E*+*F*=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map.

Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, *Euler's Gem* will fascinate every mathematics enthusiast.

- Author:
**David S. Richeson** - Year:
**2008** - Publisher:
**Princeton University Press** - Language:
**English** - ISBN:
**0691126771,9780691126777**

- File size:
**4 848 191** - Format:
**epub**

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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 t...

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 tel...

I used to think math was no fun'Cause I couldn't see how it was doneNow Euler's my heroFor I now see why zeroEquals e[pi] i+1 --Paul Nahin, electrical engineer In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula ...

Euler's Gem is a fascinating & well written book. However, it is also a pretty challenging read, one can not really sit back & read it straight through. But this is also what mathematics & learning is all about, as you often have to stop, re-read, & thi...

2 DVD set with 24 lectures 30 minutes each for a total of 720 minutes...Performers: Taught by: Professor Edward B. Burger, Williams College.Annotation Lectures 1-12 of 24."Course No. 1495"Lecture 1. Number theory and mathematical research -- lecture 2. Na...

From the Preface by J. E. Littlewood: "All [Hardy's] books gave him some degree of pleasure, but this one, his last, was his favourite. When embarking on it he told me that he believed in its value (as well he might), and also that he looked forward to th...

Unusually clear and interesting classic covers real numbers and sequences, foundations of the theory of infinite series and development of the theory (series of valuable terms, Euler's summation formula, asymptotic expansions, other topics). Exercises thr...

An ideal text for an advanced course in the theory of complex functions, this book leads readers to experience function theory personally and to participate in the work of the creative mathematician. The author includes numerous glimpses of the function t...

Following their introduction in the early 1980s, o-minimal structures have provided an elegant and surprisingly efficient generalization of semialgebraic and subanalytic geometry. This book gives a self-contained treatment of the theory of o-minimal struc...

The sister cities of the southwestern United States border are challenged by widespread environmental and health issues and limited access to help. And while different initiatives have been set up to improve health outcomes and lessen inequities in the bo...

The proceedings consists of 30 papers which have been selected and invited from the submissions to the 2nd International Conference on Computer Science, Applied Mathematics and Applications (ICCSAMA 2014) held on 8-9 May, 2014 in Budapest, Hungary. The co...

Covering the complete design cycle of nanopositioning systems, this is the first comprehensive text on the topic. The book first introduces concepts associated with nanopositioning stages and outlines their application in such tasks as scanning probe micr...

This book constitutes the proceedings of the 9th International Computer Science Symposium in Russia, CSR 2014, held in Moscow, Russia, in June 2014. The 27 full papers presented in this volume were carefully reviewed and selected from 76 submissions. In a...

This book is the outcome of the Dagstuhl Seminar 13201 on Information Visualization - Towards Multivariate Network Visualization, held in Dagstuhl Castle, Germany in May 2013. The goal of this Dagstuhl Seminar was to bring together theoreticians and pract...

This book constitutes the refereed proceedings of the 10th VLDB Workshop on Secure Data Management held in Trento, Italy, on August 30, 2013. The 15 revised full papers and one keynote paper presented were carefully reviewed and selected from various subm...

This book constitutes the revised selected papers of the workshops of the 11th International Conference on Service-Oriented Computing (ICSOC 2013), held in Berlin, Germany, in December 2013. The conference hosted the following five workshops: 3rd Internat...

The thesis represents the development of an entirely new experimental platform for generating and studying converging radiative shock waves. It was discovered that the application of large magnetic pressures to gas-filled cylindrical metallic tubes could ...

Low voltage unearthed (IT) AC and DC systems are commonly applied for supply of power and control circuits in industry, transportation, medical objects etc. The main reasons for their use are high reliability and numerous advantages offered by isolating t...

DepCoS â€“ RELCOMEX is an annual series of conferences organized by WrocÅ‚aw University of Technology to promote a comprehensive approach to evaluation of system performability which is now commonly called dependability. In contrast to classic analyses which...