On the Average Perimeter of the Inscribed Random Polygon

被引：0
|
作者：
Nikitin, Ya. Yu. [1 ,2 ]
Polevaya, T. A. [3 ]
机构：
[1] St Petersburg State Univ, St Petersburg 199034, Russia
[2] Natl Res Univ Higher Sch Econ, St Petersburg 190008, Russia
[3] St Petersburg Natl Res Univ Informat Technol Mech, St Petersburg 197101, Russia
来源：
VESTNIK ST PETERSBURG UNIVERSITY-MATHEMATICS | 2020年 / 53卷 / 01期
关键词：
random polygon; perimeter; convexity; uniform distribution;
D O I：
10.1134/S1063454120010070
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Assume that n independent uniformly distributed random points are set on the unit circle. Construct the convex random polygon with vertices in these points. What are the average area and the average perimeter of this polygon? Brown computed the average area several years ago. We compute the average perimeter and obtain quite similar expressions. We also discuss the rate of the convergence of this value to the limit and evaluate the average value of the sum of squares for the sides of the inscribed triangle.
引用
收藏
页码：58 / 63
页数：6
相关论文
共 50 条
  • [1] On the Average Perimeter of the Inscribed Random Polygon
    Ya.Yu. Nikitin
    T. A. Polevaya
    [J]. Vestnik St. Petersburg University, Mathematics, 2020, 53 : 58 - 63
  • [2] Maximum area of inscribed polygon with constant perimeter
    Shu, Yangchun
    [J]. Wuhan Gangtie Xueyuan Xuebao/Journal of Wuhan Iron and Steel University, 2000, 23 (01): : 105 - 107
  • [3] With Random Parametric Equation of Circle Inscribed Polygon Generation Algorithm and Analysis
    Sun, Yanhai
    Song, Laizhong
    Shen, Tao
    [J]. APPLIED MECHANICS AND MATERIALS I, PTS 1-3, 2013, 275-277 : 2506 - 2510
  • [4] ON THE AREA OF A POLYGON INSCRIBED IN A CIRCLE
    Matsumoto, Y.
    Matsutani, Y.
    Oda, M.
    Sakai, T.
    Shibuya, T.
    [J]. ENSEIGNEMENT MATHEMATIQUE, 2007, 53 (1-2): : 127 - 153
  • [5] THE PERIMETER CENTROID OF A CONVEX POLYGON
    KAISER, MJ
    [J]. APPLIED MATHEMATICS LETTERS, 1993, 6 (03) : 17 - 19
  • [6] Maximizing the area of an axially symmetric polygon inscribed in a simple polygon
    Barequet, Gill
    Rogol, Vadim
    [J]. COMPUTERS & GRAPHICS-UK, 2007, 31 (01): : 127 - 136
  • [7] INSCRIBED REGULAR POLYGON OF 13 SIDES
    GOLDBERG, M
    [J]. AMERICAN MATHEMATICAL MONTHLY, 1967, 74 (06): : 720 - &
  • [8] ON QUADRILATERALS OF MINIMAL PERIMETER INSCRIBED IN A GIVEN QUADRILATERAL
    CHAKERIAN, GD
    [J]. AMERICAN MATHEMATICAL MONTHLY, 1963, 70 (03): : 294 - &
  • [9] Largest unit rectangles inscribed in a convex polygon
    Chung, Jaehoon
    Bae, Sang Won
    Shin, Chan-Su
    Yoon, Sang Duk
    Ahn, Hee-Kap
    [J]. COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 2025, 124
  • [10] AREA-PERIMETER DUALITY IN POLYGON SPACES
    Khimshiashvili, Giorgi
    Panina, Gaiane
    Siersma, Dirk
    [J]. MATHEMATICA SCANDINAVICA, 2021, 127 (02) : 252 - 263
12345