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The Inversive Distance Between Two Circles

Published online by Cambridge University Press:  20 November 2018

O. Bottema
O. Bottema*
Affiliation:
Technological University, Delft, Netherlands
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H. S. M. Coxeter (3) has recently studied the correspondence between two geometries the isomorphism of which was well known, but to which he was able to add some remarkable consequences. The two geometries are the inversive geometry of a plane E (the Euclidean plane completed with a single point at infinity or, what is the same thing, the plane of complex numbers to which ∞ is added) on the one hand, and the hyperbolic geometry of three-dimensional space S.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 1149 - 1152
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Casey, J., A sequel to the first six books of the elements of Euclid, 5th ed. (Dublin and London, 1888), pp. 101–105.Google Scholar
2. Coolidge, J. L., A treatise on the circle and the sphere (Oxford, 1916). pp. 36–38.Google Scholar
3. Coxeter, H. S. M., The inversive plane and hyperbolic space, Abh. Math. Sem. Univ. Hamburg, 29(1966), 217–242.Google Scholar
4. Coxeter, H. S. M., Non-Euclidean geometry, 5th ed. (Toronto, 1965), p. 266.Google Scholar
5. Johnson, R. A., Advanced Euclidean geometry (New York, 1960). p. 99.Google Scholar
6.F. and Morley, F. V., Inversive geometry (London, 1933).Google Scholar