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

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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.

## About book:

## About file:

Security code:

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

- File size:
**12 086 637** - Format:
**pdf**

Security code:

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...

This book traces the recent growth in NGO advocacy. Barbara Rugendyke presents empirical findings about the impacts of NGO advocacy activity on the policies and practices of global and regional institutions. The research reveals the mixed successes of adv...

The State of Democracy in Latin America presents a critical analysis of the contemporary democratic state in Latin America.In a shift away from the more typical analyses of Latin American political change during the 1990s, this book presents a more state-...

Virtually every major media, information and telecommunications enterprise in the world is significantly tied to China. This volume provides the most expert, up-to-date and multidisciplinary analyses on how the contemporary media function in what has rapi...

Surviving the wrath of the fearsome Sauurâ€”a hideous race of invading serpentsâ€”noble Erik and cunning Roo have delivered a timely warning to the rulers of the Midkemian Empire, and are now free to pursue their separate destinies. Erik chooses the armyâ€”and ...

This detailed guide will enable the reader to understand the relative importance of the numerous parameters involved in seismic design and the relationships between them, as well as the motivations behind the choices adopted by the codes. For a structure ...

This introduction to Chinese national cinema covers three 'Chinas': mainland China, Hong Kong and Taiwan. Historical and comparative perspectives bring out the parallel developments in these three Chinas, while critical analysis explores thematic and styl...

What happens to the rural folk--to their power and economic well-being--when development takes place in a democratic framework? Focusing on India where, unlike most of the developing world, a democratic system has flourished for four decades, this book i...

Stuart Greenbaum and Anjan Thakor bring a unique analytical approach to the subject of banks and banking in this completely revised and updated new edition. They expand the scope of the typical bank management course by addressing all types of deposit-typ...

An introductory guide to global magnetic field properties, Earth Magnetism addresses, in non-technical prose, many of the frequently asked questions about Earth's magnetic field. Magnetism surrounds and penetrates our Earth in ways basic science courses c...

Volume 71 of Advances in Cancer Research begins with Morgan and Kastan presenting data on the roles of p53 and ATM in cell cycle progression and cell death in response to DNA damage and how this information may lead to targets for improved cancer therapie...