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文章基本信息

  • 标题:The Parabola in Universal Hyperbolic Geometry I
  • 本地全文:下载
  • 作者:Alkhaldi, Ali ; Wildberger, Norman John
  • 期刊名称:KoG
  • 印刷版ISSN:1331-1611
  • 电子版ISSN:1846-4068
  • 出版年度:2014
  • 卷号:17
  • 期号:17
  • 页码:14-42
  • 语种:English
  • 出版社:Croatian Society for Geometry and Graphics
  • 摘要:We introduce a novel definition of a parabola into the framework of universal hyperbolic geometry, show many analogs with the Euclidean theory, and also some remarkable new features. The main technique is to establish parabolic standard coordinates in which the parabola has the form xz = y^2. Highlights include the discovery of the twin parabola and the connection with sydpoints, many unexpected concurrences and collinearities, a construction for the evolute, and the determination of (up to) four points on the parabola whose normals meet.
  • 关键词:universal hyperbolic geometry; parabola
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