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On sweeping out an area

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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Extract

In a previous article I wrote about the remarkable theorem of Holditch, about areas generated by a sliding or sweeping motion. While thinking further on this topic I discovered some relations concerning the areas within closed curves and the lengths of the perimeters of curves.

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Type
Articles
Information
The Mathematical Gazette , Volume 83 , Issue 496 , March 1999 , pp. 69 - 73
Copyright
Copyright © The Mathematical Association 1999

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References

1. Cooker, M.J., An extension of Holditch’s Theorem on the area within a closed curve, Math. Gaz. 82 (July 1998) pp. 183–188.CrossRefGoogle Scholar
2. Holditch, H., Geometrical theorem, Q. J. Pure and Applied Mathematics 2, (1858) p. 38.Google Scholar
3. Hardy, G.H., Pure Mathematics, Cambridge University Press, (10th edition, 1952) pp. 271–272.Google Scholar
4. Edwards, J., A treatise on the integral calculus, Vol. 1, Chelsea (1922).Google Scholar