A note on integral geometry in the inversive plane
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- by Jay P. Fillmore PDF
- Proc. Amer. Math. Soc. 78 (1980), 551-554 Request permission
Abstract:
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.References
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H. S. M. Coxeter and S. L. Greitzer, Geometry revisited, Random House, New York, 1967.
- Luis A. Santaló, Integral geometry and geometric probability, Encyclopedia of Mathematics and its Applications, Vol. 1, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976. With a foreword by Mark Kac. MR 0433364
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 78 (1980), 551-554
- MSC: Primary 53C65; Secondary 60D05
- DOI: https://doi.org/10.1090/S0002-9939-1980-0556631-9
- MathSciNet review: 556631