Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, Volume 7, Issue 1, Pages 77–84
DOI: https://doi.org/10.21638/11701/spbu01.2020.108 (Mi vspua205) 		 
MATHEMATICS

On the average perimeter of the inscribed random polygon

Ya. Yu. Nikitinab, T. A. Polevayac

a St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
b National Research University Higher School of Economics, ul. Soyuza Pechatnikov, 16, St. Petersburg, 190008, Russian Federation
c St. Petersburg National Research University of Information Technologies, Mechanics and Optics, Kronverkskiy pr., 49, St. Petersburg, 197101, Russian Federation
Full-text PDF (294 kB)
DOI: https://doi.org/10.21638/11701/spbu01.2020.108
Abstract: 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.
Keywords: random polygon, perimeter, convexity, uniform distribution.
Funding agency Grant number
Правительство Российской Федерации 08-08
Saint Petersburg State University 6.65.37.2017
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).
Received: 17.05.2019
Revised: 30.06.2019
Accepted: 19.09.2019
English version:
Vestnik St. Petersburg University, Mathematics, 2020, Volume 7, Issue 2, Pages 58–63
DOI: https://doi.org/10.1134/S1063454120010070
Document Type: Article
UDC: 519.21
MSC: 60D05
Language: Russian
Citation: Ya. Yu. Nikitin, T. A. Polevaya, “On the average perimeter of the inscribed random polygon”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 7:1 (2020), 77–84; Vestn. St. Petersbg. Univ., Math., 7:2 (2020), 58–63
Citation in format AMSBIB
\Bibitem{NikPol20}
\by Ya.~Yu.~Nikitin, T.~A.~Polevaya
\paper On the average perimeter of the inscribed random polygon
\jour Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
\yr 2020
\vol 7
\issue 1
\pages 77--84
\mathnet{http://mi.mathnet.ru/vspua205}
\crossref{https://doi.org/10.21638/11701/spbu01.2020.108}
\transl
\jour Vestn. St. Petersbg. Univ., Math.
\yr 2020
\vol 7
\issue 2
\pages 58--63
\crossref{https://doi.org/10.1134/S1063454120010070}
Linking options:
  • https://www.mathnet.ru/eng/vspua205
  • https://www.mathnet.ru/eng/vspua/v7/i1/p77
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
    Statistics & downloads:
    Abstract page:18
    Full-text PDF :4
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024