Geodesic
Maximal Areas of Reuleaux Polygons
Canadian mathematical bulletin, Tome 13 (1970) no. 2, pp. 175-179

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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. 
Sallee, G. T. Maximal Areas of Reuleaux Polygons. Canadian mathematical bulletin, Tome 13 (1970) no. 2, pp. 175-179. doi: 10.4153/CMB-1970-037-1
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     title = {Maximal {Areas} of {Reuleaux} {Polygons}},
     journal = {Canadian mathematical bulletin},
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     year = {1970},
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     number = {2},
     doi = {10.4153/CMB-1970-037-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-037-1/}
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