Euler's Gem : The Polyhedron Formula and the Birth of Topology /

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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...

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Detalles Bibliográficos
Autor principal: Richeson, David S. (David Scott)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, N.J. : Princeton University Press, 2008.
Colección:Book collections on Project MUSE.
Temas:
Polyeder
Euler-Poincare-Charakteristik
Algebraische Topologie
Topology.
Polyhedra.
Topología > Historia
Poliedros
MATHEMATICS > Geometry > General.
MATHEMATICS > Topology.
polyhedra.
Polyedres.
Topologie > Histoire.
Topology > History.
History.
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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 Poincare and the ascendance of topology
  • The million-dollar question.

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