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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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
    H. S. M. Coxeter and S. L. Greitzer, Geometry revisited, Random House, New York, 1967.
  • Luis A. Santal√≥, 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
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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