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On closest packing by equilateral triangles

Published online by Cambridge University Press:  24 October 2008

H. G. Eggleston
H. G. Eggleston
Affiliation:
University CollegeSwansea
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Extract

The problem with which this paper is concerned is that of packing non-overlapping plane figures into a given plane figure. It is of a different type from the usual packing problem in which equal figures are used in the whole plane, and the aim is to calculate the limit of the ratio of covered area to the total area inside a large circle, as the radius of the circle tends to infinity. A closest packing in this problem is an arrangement of the figures in such a way that this limit attains its largest value.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 1 , January 1953 , pp. 26 - 30
Copyright
Copyright © Cambridge Philosophical Society 1953

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References

* The words square, circle, etc., are used to mean either the bounding curve or the bounded domain according to the context.

* X τY τ and E jF j are both to be parallel to AB.