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Mid-Circles and Loxodromes

Published online by Cambridge University Press:  03 November 2016

H. S. M. Coxeter
H. S. M. Coxeter*
Affiliation:
Dept. of Mathematics, University of Toronto, Canada
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Extract

Any two distinct circles a and b (in the real inversive plane) have one or two mid-circles which may be described as the locus of the point of contact of a variable pair of tangent circles that touch a and b [8, p. 31; 4, p. 74]. We easily see by inversion that two non-intersecting or tangent circles have a unique mid-circle, but two intersecting circles have two orthogonal mid-circles, bisecting the angles of intersection. The circles a and b are interchanged by inversion in their mid-circle (or in either of their mid-circles). This subject has been surprisingly neglected, possibly because of the terrifying name “circles of antisimilitude” [1, p. 28].

Type
Research Article
Information
The Mathematical Gazette , Volume 52 , Issue 379 , February 1968 , pp. 1 - 8
Copyright
Copyright © Mathematical Association 1968

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References

[1] Coolidge, J. L., A treatise on the circle and the sphere (Oxford, 1916).Google Scholar
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