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Euler's Gem

The Polyhedron Formula and the Birth of Topology

David S. Richeson

EPUB
ca. 18,99
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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

Eulerian path, Imre Lakatos, Internal and external angles, Klein bottle, Number theory, Leonhard Euler, Complex analysis, Hairy ball theorem, Proofs and Refutations, Euler characteristic, Frederick the Great, Proofs from THE BOOK, Curvature, Trefoil knot, Regular polyhedron, Mathematics, Addition, Betti number, Exterior angle theorem, Conjecture, Unknot, Knot theory, Icosahedron, Torus, Planar graph, Atomic theory, Platonic solid, Science, Bernhard Riemann, Astronomy, Joseph-Louis Lagrange, Paper model, Parity (mathematics), Scientist, Euler number, Molecule, Pure mathematics, Projective plane, Seifert surface, Theorem, Differential equation, Tetrahedron, David Hilbert, Jordan curve theorem, Three-dimensional space (mathematics), Topology, Book, Equilateral triangle, Differential geometry, Right angle, Augustin-Louis Cauchy, Calculation, Theory, Simplicial complex, Quantity, Counterexample, Complete graph, Henri Lebesgue, Dimension, Johannes Kepler, Philosopher, Philosophy, Pick's theorem, Pythagorean theorem, Graph theory, Pythagoreanism, Complete bipartite graph, Four color theorem, Fermat's Last Theorem, Summation, Triangular face, Octahedron, Cartesian coordinate system, Clockwise, Homology (mathematics), Regular polygon, Writing, Vector field, Euclidean space, Princeton University Press, Tangent vector, Archimedean solid, Degrees of freedom (statistics), Euler's formula, Textbook, Geometry, Classification theorem, Mathematician, Line segment, Knot invariant, Special case, Carl Friedrich Gauss, Dodecahedron, Total curvature, Analysis Situs (paper), Orientability, Riemann surface, Combinatorial topology, Polyhedron, Hauptvermutung