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A 24-Point Sphere for the Orthocentric Tetrahedron

Published online by Cambridge University Press:  03 November 2016

F. O’Hara
F. O’Hara*
Affiliation:
Polytechnic of North London
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Extract

Readers familiar with the nine-point circle property of a triangle (Figure 1) may have wondered whether there is a similar result for a tetrahedron.

In general the answer is “No”: there is no equivalent of the orthocentre for a tetrahedron, since the altitudes from the vertices onto the opposite faces do not intersect. There is, however, a special kind of tetrahedron for which these four lines do have a point H in common.

Type
Research Article
Information
The Mathematical Gazette , Volume 56 , Issue 398 , December 1972 , pp. 295 - 298
Copyright
Copyright © Mathematical Association 1972

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