عنوان

Euler's gem :the polyhedron formula and the birth of topology

Euler's gem :the polyhedron formula and the birth of topology

Princeton, N.J.

Princeton University Press

2008

xii, 317 p. : illus, maps, tables

Includes bibliographical references )p. ]295[-308( and index

David S. Richeson

1

Leonhard Euler and his three "great" friends -- What is a polyhedron? -- The five perfect bodies -- The Pythagorean brotherhood and Plato's atomic theory -- Euclid and his elements -- Kepler's polyhedral universe -- Euler's gem -- Platonic solids, gold balls, Fullerenes, and geodesic domes -- Scooped by Descartes? -- Legendre gets it right -- A stroll through Konigsberg -- Cauchy's flattened polyhedra -- Planar graphs, geoboards, and brussels sprouts -- It's a colorful world -- New problems and new proofs -- Rubber sheets, hollow doughnuts, and crazy bottles -- Are they the same, or are they different? -- A knotty problem -- Combing the hair on a coconut -- When topology controls geometry -- The topology of curvy surfaces -- Navigating in n dimensions -- Henri Poincare and th ascendance of topology -- The million-dollar question

History ، Topology

، Polyhedra

Richeson, David S. )David Scott(

AU

TI