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Euler's gemthe polyhedron formula and the birth of topology /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Euler's gemDavid S. Richeson.
其他題名:	the polyhedron formula and the birth of topology /
作者:	Richeson, David S.
出版者:	Princeton, N.J. :Princeton University Press,2012.
面頁冊數:	1 online resource (xii, 317 p.) :ill., maps.
標題:	TopologyHistory.
電子資源:	http://www.jstor.org/stable/10.2307/j.ctt7sqb7
ISBN:	9781400838561 (electronic bk.)

Euler's gemthe polyhedron formula and the birth of topology /
Richeson, David S.

Euler's gemthe polyhedron formula and the birth of topology /[electronic resource] :David S. Richeson. - Princeton, N.J. :Princeton University Press,2012. - 1 online resource (xii, 317 p.) :ill., maps.

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

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 Königsberg -- 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 Poincaré and the ascendance of topology -- The million-dollar question.

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 formula is so simple it can be explained to a child. 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. In 1750, Euler observed that any polyhedron composed of V vertices, E edges.

ISBN: 9781400838561 (electronic bk.)Subjects--Topical Terms:

537131
Topology
--History.

LC Class. No.: QA611.A3 / R53 2012

Dewey Class. No.: 514.09

Euler's gemthe polyhedron formula and the birth of topology /
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260 $a Princeton, N.J. : $b Princeton University Press, $c 2012.
300 $a 1 online resource (xii, 317 p.) : $b ill., maps.
504 $a Includes bibliographical references (p. 295-308) and index.
505 0 $a 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 Königsberg -- 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 Poincaré and the ascendance of topology -- The million-dollar question.
520 $a 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 formula is so simple it can be explained to a child. 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. In 1750, Euler observed that any polyhedron composed of V vertices, E edges.
588 0 $a Print version record.
650 0 $a Topology $x History. $3 537131
650 0 $a Polyhedra. $3 189600
856 4 0 $u http://www.jstor.org/stable/10.2307/j.ctt7sqb7