Professional paper

Vertex- and Edge-Altitudes of a Tetrahedron

Gunter Weiss ; Institute of Geometry Dresden University of Technology, Dresden, Germany
Hans Havlicek orcid.org/0000-0001-6847-1544 ; Institute of Geometry Vienna University of Technology, Vienna, Austria

Abstract

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.

Keywords

tetrahedron; hyperboloid of altitudes; central projection

Hrčak ID:

3943

URI

https://hrcak.srce.hr/3943

Publication date:

17.2.2003.

Article data in other languages: croatian german

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