01528pamaa2200205 4500 0000049408 20121206090000.0 110726 eng 9780691126777 QA611.A3 RIC 2008 Richeson Euler's gem : the polyhedron formula and the birth of topology David S. Richeson. Princeton, N.J.: Princeton University Press, 2008. xii, 317 p.: ill., maps; 24 cm. 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 Kn̲igsberg -- Cauchy's flattened polyhedra -- Planar graphs, geoboards, and brussels sprouts -- It's a<U+000d><U+000a> 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 Poincar ̌and th ascendance of topology -- The million-dollar question FAS Includes bibliographical references (p. [295]-308) and index Topology -- History Polyhedra www.press.princeton.edu