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The pedal planes of a tetrahedron

Published online by Cambridge University Press:  24 October 2008

J. H. Grace
J. H. Grace
Affiliation:
Peterhouse
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Extract

The locus of a point the feet of the perpendiculars from which on the faces of a tetrahedron are coplanar is known to be a cubic surface having nodes at the corners: the pedal planes, by which I mean planes containing the feet of four perpendiculars, do not seem to have been much discussed. I propose to prove two theorems concerning them and make some remarks on their envelope.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 23 , Issue 8 , October 1927 , pp. 853 - 858
Copyright
Copyright © Cambridge Philosophical Society 1927

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References

* See, for example, Richmond, , Camb. Phil. Soc. Proc., Vol. XXII. p. 35.Google Scholar

* Cf. the preceding paper § 3. The quadric has triads of perpendicular generators and its linear metrical invariant vanishes.

* The argument will be made clear by considering the analogy in two dimensions.

† Cf. § 3 of the preceding paper.

* Rohn, , Math. Ann. vol. 24 (1884), p. 55.CrossRefGoogle Scholar

* Cf. Somerville, , Proc. International Congress, Cambridge, 1912.Google Scholar