Non-euclidean geometries : János Bolyai memorial volume
著者
書誌事項
Non-euclidean geometries : János Bolyai memorial volume
(Mathematics and its applications, v. 581)
Springer, c2006
大学図書館所蔵 全15件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references
内容説明・目次
内容説明
"From nothing I have created a new different world," wrote Janos Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture.
The papers in this volume, which commemorates the 200th anniversary of the birth of Janos Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of Janos Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics.
目次
History.- The Revolution of Janos Bolyai.- Gauss and Non-Euclidean Geometry.- Janos Bolyai's New Face.- Axiomatical and Logical Aspects.- Hyperbolic Geometry, Dimension-Free.- An Absolute Property of Four Mutually Tangent Circles.- Remembering Donald Coxeter.- Axiomatizations of Hyperbolic and Absolute Geometries.- Logical Axiomatizations of Space-Time. Samples from the Literature.- Polyhedra, Volumes, Discrete Arrangements, Fractals.- Structures in Hyperbolic Space.- The Symmetry of Optimally Dense Packings.- Flexible Octahedra in the Hyperbolic Space.- Fractal Geometry on Hyperbolic Manifolds.- A Volume Formula for Generalised Hyperbolic Tetrahedra.- Tilings, Orbifolds and Manifolds, Visualization.- The Geometry of Hyperbolic Manifolds of Dimension at Least 4.- Real-Time Animation in Hyperbolic, Spherical, and Product Geometries.- On Spontaneous Surgery on Knots and Links.- Classification of Tile-Transitive 3-Simplex Tilings and Their Realizations in Homogeneous Spaces.- Differential Geometry.- Non-Euclidean Analysis.- Holonomy, Geometry and Topology of Manifolds with Grassmann Structure.- Hypersurfaces of Type Number 2 in the Hyperbolic Four-Space and Their Extensions To Riemannian Geometry.- How Far Does Hyperbolic Geometry Generalize?.- Geometry of the Point Finsler Spaces.- Physics.- Black Hole Perturbations.- Placing the Hyperbolic Geometry of Bolyai and Lobachevsky Centrally in Special Relativity Theory: An Idea Whose Time has Returned.
「Nielsen BookData」 より