title: On the average perimeter of the inscribed random polygon
metadata.name: dc.contributor.author
metadata.value: Nikitin, Yakov Yu.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Polevaya, Tatiana A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-04-10T12:39:55Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-04-10T12:39:55Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Nikitin 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.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2020.108
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17330
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Suppose 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.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The 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).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 7 (65); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: random polygon
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: perimeter
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: convexity
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: uniform distribution
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On the average perimeter of the inscribed random polygon
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 77-84.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17330/1/77-84.pdf
resources.format: Adobe PDF
resources.size: 294 kB