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Proceedings of the American Mathematical Society

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A note on integral geometry in the inversive plane


Author: Jay P. Fillmore
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
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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 [Enhancements On Off] (What's this?)

  • [1] H. S. M. Coxeter and S. L. Greitzer, Geometry revisited, Random House, New York, 1967.
  • [2] Luis A. Santaló, Integral geometry and geometric probability, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976. With a foreword by Mark Kac; Encyclopedia of Mathematics and its Applications, Vol. 1. MR 0433364

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0556631-9
Article copyright: © Copyright 1980 American Mathematical Society