1. DSpace at Saint Petersburg State University
  2. St.PETERSBURG UNIVERSITY ACADEMIC PRESS
  3. ACADEMIC JOURNALS
  4. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
  5. 2020
  6. Issue 1
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dc.contributor.authorNikitin, Yakov Yu.-
dc.contributor.authorPolevaya, Tatiana A.-
dc.date.accessioned2020-04-10T12:39:55Z-
dc.date.available2020-04-10T12:39:55Z-
dc.date.issued2020-03-
dc.identifier.citationNikitin Ya.Yu., Polevaya T.A. On the average perimeter of the inscribed random polygon. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 1, pp. 77–84.en_GB
dc.identifier.otherhttps://doi.org/10.21638/11701/spbu01.2020.108-
dc.identifier.urihttp://hdl.handle.net/11701/17330-
dc.description.abstractSuppose we put on the unit circumference n independent uniformly distributed random points and build a convex random polygon with the vertices in these points. What are the average area and the average perimeter of this polygon? The average area was calculated by K. Brown some years ago. We calculatе the average perimeter and obtain quite similar formulae. In the same time we discuss the rate of convergence of this value to the limit. We evaluate also the average value of the sum of squares for the sides of the inscribed triangle.en_GB
dc.description.sponsorshipThe work of Ya.Yu.Nikitin is supported by St. Petersburg State University (grant SPbSU–DFG 6.65.37.2017), the work of T.A.Polevaya is supported by Government of the Russian Federation (grant 08-08).en_GB
dc.language.isoruen_GB
dc.publisherSt Petersburg State Universityen_GB
dc.relation.ispartofseriesVestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 7 (65); Issue 1-
dc.subjectrandom polygonen_GB
dc.subjectperimeteren_GB
dc.subjectconvexityen_GB
dc.subjectuniform distributionen_GB
dc.titleOn the average perimeter of the inscribed random polygonen_GB
dc.typeArticleen_GB
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