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Vertex- and Edge-Altitudes of a Tetrahedron

By Gunter Weiss and Hans Havlicek

Abstract

k-visina nekog n-simpleksa siječe njegovu k-stranicu i njoj nasuprotnu stranicu okomito. Tetraedar T ima četiri "vršne visine" (k = 0) i tri "bridne visine" (k = 1). Visine oba tipa izvodnice su posebnih hiperboloida povezanih s tetraedrom T. Članak obrađuje te hiperboloide na način nacrtne geometrije i daje sintetičke dokaze nekih dobro poznatih svojstava. Pokazuje se, na primjer, da ako se visine jednog tipa sijeku u jednoj točki da se tada i visine drugog tipa sijeku u jednoj točki te da te točke koincidiraju.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

Topics: tetraedar; hiperboloid visina; centralna projekcija, tetrahedron; hyperboloid of altitudes; central projection
Publisher: Croatian Society for Geometry and Graphics
Year: 2003
OAI identifier: oai:hrcak.srce.hr:3943

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