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Solitary Solarians and densely packed spheres - from Stephen Hales to Thomas Hales

Published online by Cambridge University Press:  01 August 2016

Paul Stephenson
Paul Stephenson*
Affiliation:
The Magic Mathworks Travelling Circus, Old Coach House, Penypwllau, Holywell, Flintshire CH8 8HB
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Extract

In Isaac Asimov's novel Foundation and Earth (Grafton 1987) the inhabitants of the planet Solaria have evolved from early Earth space explorers. They have developed a society with many robots and few people. The small population of Solarians live as far from each other as possible. These solitary people are confined to their estates, which are distributed evenly across the planet. In this article I investigate the pretty problem of even distribution of points on a sphere. With the exception of one piece of spherical trigonometry the work needed to derive my (admittedly restricted) set of results is routine for sixth-form mathematicians but has the interesting pay-off announced in the title.

Type
Articles
Information
The Mathematical Gazette , Volume 83 , Issue 498 , November 1999 , pp. 426 - 432
Copyright
Copyright © The Mathematical Association 1999

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References

1. Coxeter, H. S. M. Introduction to geometry (1961).Google Scholar
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3. Thomson Kelvin, Baron William On the division of space with minimum partitional area, Acta Mathematica 1887.CrossRefGoogle Scholar