A Note on Integral Geometry in the Inversive Plane

Jay P. Fillmore
1980 Proceedings of the American Mathematical Society  
The density for circles in the Euclidean plane, which is invariant under the group of similitudes, is in fact invariant under the inversive group. The fundamental invariants of the inversive plane, angle and inversive distance, can be obtained from the measures of certain sets of circles.
doi:10.2307/2042430 fatcat:wu5sma4elbhddebxd6x7k5sxwa