Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-05-31T14:03:59.105Z Has data issue: false hasContentIssue false
  • English
  • Français

The expected number of aggregates in a random distribution of n points

Published online by Cambridge University Press:  24 October 2008

C. Mack
C. Mack
Affiliation:
Shirley InstituteManchester
Get access Rights & Permissions [Opens in a new window]

Abstract

When n points are distributed at random (equally likely anywhere) over a large area or volume, they may form small clusters or aggregates. In this paper a k-aggregate is defined more precisely as k points which can be covered by a small figure of given size, shape and orientation, but whose position is not otherwise specified. Exact formulae for the expected number of such k-aggregates are given in some cases, while a good approximate formula (accurate in most practical cases) and limits are stated, covering all cases.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 46 , Issue 2 , April 1950 , pp. 285 - 292
Copyright
Copyright © Cambridge Philosophical Society 1950

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Silberstein, L.Aggregates in random distributions of points. Phil. Mag. (Series 7), 36 (1945), 319.CrossRefGoogle Scholar
(2)Mack, C.An exact formula for Q k(n), the probable number of k-aggregates in a random distribution of n points. Phil. Mag. (Series 7), 39 (1948), 778.CrossRefGoogle Scholar
(3)Berg, W. F.Aggregates in one and two-dimensional random distributions. Phil. Mag. (Series 7), 36 (1945), 337.CrossRefGoogle Scholar