文章基本信息

标题：Vertex- and Edge-Altitudes of a Tetrahedron
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作者：Weiss, Gunter ; Havlicek, Hans
期刊名称：KoG
印刷版ISSN：1331-1611
电子版ISSN：1846-4068
出版年度：2003
卷号：6
期号：6
页码：71-80
出版社：Croatian Society for Geometry and Graphics
摘要：A k-altitude of an n-simplex meets a k-face and its opposite face orthogonally. A tetrahedron T possesses four "vertexaltitudes"( k = 0) and three "edge-altitudes" (k = 1). The altitudes of each type are generators of special hyperboloids connected with T. The paper treats these hyperboloids in terms of descriptive geometry and gives synthetic proofs for some well-known properties. It turns out, for example, that if the altitudes of one type intersect in one point, then so do the others, and the points of intersection coincide.
关键词：tetrahedron; hyperboloid of altitudes; central projection