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An extension of Holditch’s theorem on the area within a closed curve

Published online by Cambridge University Press:  01 August 2016

Mark J. Cooker
Mark J. Cooker*
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ
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While reading a book by David Wells on curious and interesting geometry, I came across the following remarkable theorem named after Holditch.

In Figure 1 the point R divides a straight stick ST into lengths p and q, where p, q 0. We restrict the end points of the stick, S and T, to lie on a plane, simple, closed, convex contour, C 1, and ST slides around C1 . Assuming C 1 is such that ST can pass around C 1 once, the locus of R is another plane closed contour, C, inside C 1.

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Type
Articles
Information
The Mathematical Gazette , Volume 82 , Issue 494 , July 1998 , pp. 183 - 188
Copyright
Copyright © The Mathematical Association 1998

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References

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