Hostname: page-component-7dd5485656-k8lnt Total loading time: 0 Render date: 2025-10-31T14:43:53.475Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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?

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1. Semple, J. G. and Kneebone, G. T., Algebraic projective geometry, Oxford University Press (1952).Google Scholar
2. Semple, J. G. and Kneebone, G. T., Algebraic curves, Oxford University Press (1959).Google Scholar
3. http://en.wikipedia.org/wiki/Cubic_plane_curve Google Scholar
4. http://mathworld.wolfram.com/TriangleCubic.html Google Scholar
5. bernard.gibert.pagesperso-orange.fr Google Scholar
6. Altshiller-Court, N., Modern pure solid geometry (2nd edn.), Chelsea (1964).Google Scholar
7. Rouche, E. and de Comberousse, C., Traité de géométric (7th edn.), Gauthier-Villars (1900).Google Scholar