Re: Soddy gosset theorem


There is a proof of Soddy's formula for mutually touching hyperspheres
in section 7.6.1 , page 145, of my text on A. N. Whitehead's geometric
algebra at: http://www.stebla.pwp.blueyonder.co.uk/papers/Euclid.pdf
The derivation in the text relies on the use of a model of n-d
Euclidean space on the absolute quadric of (n+1)-d elliptic space.
Soddy's formula is then a rewrite of the condition that the point at
infinity of the Euclidean space lies on the absolute quadric by
expanding the point at infinity in terms of a basis of points made from
the touching hyperspheres. Soddy's formula extends to hold in any flat
space.

Hope this helps.

Stephen Blake
http://www.stebla.pwp.blueyonder.co.uk

.