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Altitudes of a general n–simplex*

Published online by Cambridge University Press:  09 April 2009

Sahib Ram Mandan
Sahib Ram Mandan
Affiliation:
Indian Institute of Technology, Kharagpur
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Abstract

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The purpose of this paper is to prove that the altitudes of an n-simplex (a simplexin an n-space) S form an associated set of n+1 lines (see Baker, [4] for n = 4) such that any (n–2)-space meeting n of them meets the (n+1)th too. As an immediate consequence 2 quadrics are associated with S, one touching its primes at the respective feet of its altitudes and the other touching n(n+1) primes, n parallel to each of its altitudes and 2 through each of its (n−2)-spaces. Certain special cases are also mentioned.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 5 , Issue 4 , November 1965 , pp. 409 - 415
Copyright
Copyright © Australian Mathematical Society 1965

References

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