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Holditch's Theorem


HolditchsTheorem

Let a chord of constant length be slid around a smooth, closed, convex curve C, and choose a point on the chord which divides it into segments of lengths p and q. This point will trace out a new closed curve C^', as illustrated above. Provided certain conditions are met, the area between C and C^' is given by pipq, as first shown by Holditch in 1858.

The Holditch curve for a circle of radius R is another circle which, from the theorem, has radius

 r=sqrt(R^2-pq).

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References

Bender, W. "The Holditch Curve Tracer." Math. Mag. 54, 128-129, 1981.Broman, A. "Holditch's Theorem." Math. Mag. 54, 99-108, 1981.Kiliç, E. and Keles, S. "On Holditch's Theorem and Polar Inertia Momentum." Comm. Fac. Sci. Univ. Ankara Ser. A_1 Math. Statist. 43, 41-47, 1996.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, p. 103, 1991.

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Holditch's Theorem

Cite this as:

Weisstein, Eric W. "Holditch's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HolditchsTheorem.html

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