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Vertex- and Edge-Altitudes of a Tetrahedron

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

Puni tekst: njemački, pdf (197 KB) str. 71-80 preuzimanja: 417* citiraj
APA 6th Edition
Weiss, G. i Havlicek, H. (2002). Ecken- und Kantenhöhen im Tetraeder. KoG, 6. (6.), 71-80. Preuzeto s https://hrcak.srce.hr/3943
MLA 8th Edition
Weiss, Gunter i Hans Havlicek. "Ecken- und Kantenhöhen im Tetraeder." KoG, vol. 6., br. 6., 2002, str. 71-80. https://hrcak.srce.hr/3943. Citirano 19.02.2020.
Chicago 17th Edition
Weiss, Gunter i Hans Havlicek. "Ecken- und Kantenhöhen im Tetraeder." KoG 6., br. 6. (2002): 71-80. https://hrcak.srce.hr/3943
Harvard
Weiss, G., i Havlicek, H. (2002). 'Ecken- und Kantenhöhen im Tetraeder', KoG, 6.(6.), str. 71-80. Preuzeto s: https://hrcak.srce.hr/3943 (Datum pristupa: 19.02.2020.)
Vancouver
Weiss G, Havlicek H. Ecken- und Kantenhöhen im Tetraeder. KoG [Internet]. 2002 [pristupljeno 19.02.2020.];6.(6.):71-80. Dostupno na: https://hrcak.srce.hr/3943
IEEE
G. Weiss i H. Havlicek, "Ecken- und Kantenhöhen im Tetraeder", KoG, vol.6., br. 6., str. 71-80, 2002. [Online]. Dostupno na: https://hrcak.srce.hr/3943. [Citirano: 19.02.2020.]

Sažetak
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.

Ključne riječi
tetrahedron; hyperboloid of altitudes; central projection

Hrčak ID: 3943

URI
https://hrcak.srce.hr/3943

[hrvatski] [njemački]

Posjeta: 1.064 *