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Euler's Gem

The Polyhedron Formula and the Birth of Topology

David S. Richeson

EPUB
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Princeton University Press img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Geometrie

Beschreibung

How a simple equation reshaped mathematics

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 theorem is so simple it can be explained to a child. 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. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical idea’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. This paperback edition contains a new preface by the author.

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Schlagwörter

Bernhard Riemann, Four color theorem, Conjecture, Eulerian path, Planar graph, Complete bipartite graph, Regular polygon, Henri Lebesgue, Cartesian coordinate system, Seifert surface, Orientability, Leonhard Euler, Octahedron, Klein bottle, Paper model, Equilateral triangle, Theory, Knot theory, Exterior angle theorem, Pythagorean theorem, Addition, Euler number, Three-dimensional space (mathematics), Simplicial complex, Molecule, Theorem, Icosahedron, Book, Carl Friedrich Gauss, Line segment, Regular polyhedron, Atomic theory, Knot invariant, Degrees of freedom (statistics), Mathematics, Polyhedron, Tetrahedron, Trefoil knot, Dodecahedron, Right angle, Summation, Mathematician, Combinatorial topology, Pythagoreanism, Calculation, Vector field, David Hilbert, Scientist, Betti number, Complex analysis, Curvature, Euler's formula, Internal and external angles, Analysis Situs (paper), Differential equation, Geometry, Projective plane, Dimension, Complete graph, Archimedean solid, Platonic solid, Textbook, Topology, Quantity, Unknot, Classification theorem, Torus, Graph theory, Total curvature, Number theory