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Conditions equivalent to central symmetry of convex curves

Published online by Cambridge University Press:  24 October 2008

P. C. Hammer  and
T. Jefferson Smith
P. C. Hammer
Affiliation:
University of Wisconsin, Madison and Carnegie Institution, Washington
T. Jefferson Smith
Affiliation:
University of Wisconsin, Madison and Carnegie Institution, Washington
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Extract

In this paper we establish that a convex planar body C is centrally symmetric provided either one of the following conditions hold:

(1) Each line halving the circumference of the boundary γ of C is a diametral line.(A diametral line is a line intersecting C in a chord of maximal length in the family of parallel chords.)

(2) Each line halving the area of C is a diametral line.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 4 , October 1964 , pp. 779 - 785
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

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