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Maximal Areas of Reuleaux Polygons

Published online by Cambridge University Press:  20 November 2018

G. T. Sallee
G. T. Sallee*
Affiliation:
University of California, Davis, California
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In this paper we provide new proofs of some interesting results of Firey [2] on isoperimetric ratios of Reuleaux polygons. Recall that a Reuleaux polygon is a plane convex set of constant width whose boundary consists of a finite (odd) number of circular arcs. Equivalently, it is the intersection of a finite number of suitably chosen congruent discs. For more details, see [1, p. 128].

If a Reuleaux polygon has n sides (arcs) of positive length (where n is odd and ≥ 3), we will refer to it as a Reuleaux n-gon, or sometimes just as an n-gon. If all of the sides are equal, it is termed a regular n-gon.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 2 , June 1970 , pp. 175 - 179
Copyright
Copyright © Canadian Mathematical Society 1970

Footnotes

(2)

The author wishes to thank the referee for suggesting several improvements in this paper.

(1)

Research supported in part by the National Science Foundation Grant GP-8188.

References

1. Eggleston, H. G., Convexity, Cambridge Univ. Press, Cambridge, 1958.Google Scholar
2. Firey, W. J., Isoperimetric ratios of Reuleaux polygons, Pac. J. Math. 10 (1960), 823-830.Google Scholar
3. Sallee, G. T., The maximal set of constant width in a lattice, Pac. J. Math. 28 (1969), 669-674.Google Scholar
4. Yaglom, I. M. and Boltyanskii, V. G., Convex figures, Holt, Rinehart and Winston, New York, 1961.Google Scholar