2012年4月15日 · 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 …

How a simple equation reshaped mathematics Leonhard Euler's polyhedron formula describes the structure of many objects-from soccer balls and gemstones to...

2019年7月23日 · 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.

Euler’s polyhedron formula. A polyhedron is a three-dimensional object such as those found in figure I.1. It is composed of flat polygonal faces. Each pair of adjacent faces meets along a line segment, called an edge, and adjacent edges meet at a corner, or a vertex. Euler observed that the numbers of vertices, edges,

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.

Euler’s gem is the formula, V – E + F = 2, relating the vertex, edge, and face counts of a polyhedron. Richeson carefully describes Euler’s proof, as well as later more rigorous proofs.

2019年7月23日 · 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.

of mathematics. ‘‘It’’ is ‘‘Euler’s Gem,’’ Euler’s polyhedron formula, one of the most beautiful formulas of mathematics (in fact, the author informs us, a survey of mathematicians found its beauty to be second only to epi + 1 = 0, also Euler’s). ‘‘They’’ refers to …

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.

Euler’s gem : the polyhedron formula and the birth of topology/David S. Richeson. p. cm. Includes bibliographical references and index. ISBN-13: 978-0-691-12677-7 (alk. paper) ISBN-10: 0-691-12677-1 (alk. paper) 1. Topology–History. 2. Polyhedra. I. Title.