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The Soddy spheres of a 4-ball tetrahedron: Part 1

Published online by Cambridge University Press:  01 August 2016

Michael Fox ,
Adrian Oldknow ,
John Rigby  and
Christopher Zeeman
Michael Fox
Affiliation:
2 Learn Road, Leamington Spa CV32 3PA, e-mail: michaelandjean.fox@btinternet.com
Adrian Oldknow
Affiliation:
Church Lane House, Easter gate, Chichester PO20 3UR, e-mail: aoldknow@yahoo.co.uk
John Rigby
Affiliation:
Flat 5 Cathedral Court, Cathedral Green, Llandaff, Cardiff CF5 2EB, e-mail: rigbycathedralcourt@tiscali.co.uk
Christopher Zeeman
Affiliation:
21 High Street, Woodstock OX20 1TE
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Extract

New discoveries about the Soddy circles of a triangle were published in the Gazette [1] in 1995; they are summarised below. Extensions of wellknown results in the geometry of the triangle to that of the tetrahedron were presented by Zeeman in his 2004 Presidential Address at the Mathematical Association Conference in York [2]. Using the computer software package Cabri 3D, we have discovered new results which extend the Soddy circles of a triangle to Soddy spheres of a special class of tetrahedra. This article is the first of two which present our discoveries, as well as relevant aspects of the established geometry of tetrahedra, together with their proofs.

Type
Articles
Information
The Mathematical Gazette , Volume 92 , Issue 524 , July 2008 , pp. 205 - 213
Copyright
Copyright © The Mathematical Association 2008

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References

1. Oldknow, A., Computer-aided research in the geometry of a triangle, Math. Gaz., 79 (July 1995) pp. 264–276.CrossRefGoogle Scholar
2. Zeeman, E. C., Three-dimensional theorems for schools, The Mathematical Association (2005).Google Scholar
3. Oldknow, A., The Euler-Soddy-Gergonne triangle of a triangle, Amer. Math. Monthly, 103 (1996) pp. 319–329.Google Scholar
4. Coxeter, H. S. M., Introduction to geometry, Wiley (1961).Google Scholar
5. Pedoe, D., A course of geometry for colleges and universities, Cambridge (1970), reprinted as Geometry: a comprehensive course, Dover (1988).Google Scholar
6. Court, N. A., Modern pure solid geometry, Chelsea (1964).Google Scholar
7. Bradley, C. J., Challenges in geometry, Oxford (2005).CrossRefGoogle Scholar