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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Universal measure for Poncelet-type theorems
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by Evgeny A. Avksentyev and Vladimir Yu. Protasov PDF
Proc. Amer. Math. Soc. 146 (2018), 4843-4854 Request permission


We give a simple proof of the Emch closing theorem by introducing a new invariant measure on the circle. Special cases of that measure are well known and have been used in the literature to prove Poncelet’s and the zigzag theorems. Some further generalizations are also obtained by applying the new measure.
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Additional Information
  • Evgeny A. Avksentyev
  • Affiliation: Department of Mechanics and Mathematics of Moscow State University, Moscow, 111991 Russia
  • Email:
  • Vladimir Yu. Protasov
  • Affiliation: DISIM of the University of L’Aquila, 67100 L’Aquila, Italy and Department of Mechanics and Mathematics of Moscow State University, Moscow, 111991 Russia
  • MR Author ID: 607472
  • Email:
  • Received by editor(s): June 10, 2015
  • Received by editor(s) in revised form: March 22, 2017
  • Published electronically: August 10, 2018
  • Additional Notes: The second author was supported by RFBR grants no. 16-04-00832 and 17-01-00809, and by RSCF grant no. 17-11-01027
  • Communicated by: Michael Wolf
  • © Copyright 2018 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 146 (2018), 4843-4854
  • MSC (2010): Primary 53A04, 28A25, 51N15
  • DOI:
  • MathSciNet review: 3856151