On random complete packing by discs

  • Masaharu Tanemura


A computational algorithm for random complete packing by discs is proposed. Monte Carlo simulations using this algorithm give the value 0.5473 for random packing density of discs. It greatly improves the Solomon's result, 04756.


Packing Density Test Particle Cross Point Random Packing Large Disc 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Rényi, A. (1958). On a one-dimensional problem concerning random space filling,Publ. Math. Inst. Hung. Acad. Sci.,3, 109–127.MathSciNetzbMATHGoogle Scholar
  2. [2]
    Page, E. S. (1959). The distribution of vacancies on a line,J. R. Statist. Soc., A,21, 364–374.MathSciNetzbMATHGoogle Scholar
  3. [3]
    Mackenzie, J. K. (1962). Sequential filling of a line by intervals placed at random and its application to linear adsorption,J. Chem. Phys.,37, 723–728.CrossRefGoogle Scholar
  4. [4]
    Bánkövi, G. (1962). On gaps generated by a random space filling procedure,Publ. Math. Inst. Hung. Acad. Sci.,7, 395–407.MathSciNetzbMATHGoogle Scholar
  5. [5]
    Dvoretzky, A. and Robbins, H. (1964). On the “parking” problem,Publ. Math. Inst. Hung. Acad. Sci.,9, 209–225.MathSciNetzbMATHGoogle Scholar
  6. [6]
    Mannion, D. (1964). Random space filling in one dimension,Publ. Math. Inst. Hung. Acad. Sci.,9, 143–154.MathSciNetzbMATHGoogle Scholar
  7. [7]
    Palásti, I. (1960). On some random space filling problems,Publ. Math. Inst. Hung. Acad. Sci.,5, 353–360.MathSciNetzbMATHGoogle Scholar
  8. [8]
    Solomon, H. (1967). Random packing density,Proc. Fifth Berkeley Symp. Math. Statist. Prob.,3, 119–134.MathSciNetGoogle Scholar
  9. [9]
    Blaisdell, B. E. and Solomon, H. (1970). On random sequential packing in the plane and a conjecture of Palásti,J. Appl. Prob.,7, 667–689.CrossRefGoogle Scholar
  10. [10]
    Akeda, Y. and Hori, M. (1975). Numerical test of Palásti's cojecture on two-dimensional random packing density,Nature,254, 318–319.CrossRefGoogle Scholar
  11. [11]
    Akeda, Y. and Hori, M (1976). On random sequential packing in two and three dimensions,Biometrika,63, 361–366.CrossRefGoogle Scholar
  12. [12]
    Mannion, D (1976). Random packing of an interval,Adv. Appl. Prob.,8, 477–501.MathSciNetCrossRefGoogle Scholar
  13. [13]
    Noguchi, K. and Hori, M. (1979). to be published.Google Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1979

Authors and Affiliations

  • Masaharu Tanemura

There are no affiliations available

Personalised recommendations