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Regular polygons and a propellor problem for convex sets in the plane

Published online by Cambridge University Press:  17 April 2009

P.R. Scott
P.R. Scott
Affiliation:
Department of Pure Mathematics, The University of Adelaide, South Australia 5005, Australia e-mail: [email protected]
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We find the convex planar set of maximal area which is partitioned into subsets of equal area by a given propellor. The argument depends on the characterisation of an n-sided polygon which is circumscribed about a regula n-gon Pn, and inscribed in a regula n-gon Qn, where Pn and Qn are homothetic about their common centre.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 55 , Issue 3 , June 1997 , pp. 483 - 487
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Davis, C., ‘An extremal problem for plane convex curves’, Proc. Sympos. Pure Math. VII (1963), 181–186.CrossRefGoogle Scholar