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Pi-optimal polygons

Published online by Cambridge University Press:  22 September 2016

David Griffiths  and
David Culpin
David Griffiths
Affiliation:
CSIRO Division of Mathematics & Statistics, Sydney, Australia
David Culpin
Affiliation:
CSIRO Division of Mathematics & Statistics, Sydney, Australia
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Extract

The number π (as all—or very nearly all—the world doth know) signifies the ratio of the circumference of a circle to its diameter and is also equal to the ratio of the area to the square of the radius. This suggests two generalisations of π which apply to plane figures of any shape:

Type
Research Article
Information
The Mathematical Gazette , Volume 59 , Issue 409 , October 1975 , pp. 165 - 175
Copyright
Copyright © Mathematical Association 1975

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References

1. Ball, D. G. A generalisation of π, Mathl Gaz. 57, 298–303 (No. 402, December 1973).Google Scholar
2. Rademacher, H. and Toeplitz, O. The enjoyment of mathematics. Princeton University Press (1957).CrossRefGoogle Scholar
3. Toussaint, G. Generalisations of π: some applications, Mathl Gaz. 58, 289–291 (No. 406, December 1974, Classroom note 313).Google Scholar