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Quadritangent spheres

Published online by Cambridge University Press:  23 January 2015

Michael Fox
Michael Fox*
Affiliation:
2 Leam Road, Leamington Spa CV31 3PA e-mail: michaelandjean.fox@btinternet.com
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Extract

Every tetrahedron has a set of quadritangent spheres, that is, spheres that touch the four planes containing its faces. In this article I discuss three questions about them.

1. How many quadritangent spheres does a given tetrahedron have?

2. How can we find their sizes and positions with as little calculation as possible?

3. What relations exist between the vertices and points of contact that lie on anyone of the planes?

Type
Articles
Information
The Mathematical Gazette , Volume 98 , Issue 541 , March 2014 , pp. 24 - 39
Copyright
Copyright © The Mathematical Association 2014

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References

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