# Holditch Curves inside an Ellipse

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Around 1858, the Reverend Hamnet Holditch studied the curves generated by a point on a chord of fixed length sliding inside another curve.

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Contributed by: Erik Mahieu (April 2012)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The parametric equation of the ellipse is used with the semimajor axis equal to 1 and eccentricity : .

Since there is no simple formula for the chord length along the circumference of an ellipse, you have to continuously solve the equation expressing the intersection of the ellipse and a circle with radius equal to the chord length.

For a description of Holditch's theorem, see [1] and [2].

[1] C. Pickover, *The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics*, New York: Sterling, 2009 pp. 250–251.

[2] J.-P. Truc, Le Théorème de Holditch, *Quadrature*, 75, 2010 pp. 10–18.

## Permanent Citation

"Holditch Curves inside an Ellipse"

http://demonstrations.wolfram.com/HolditchCurvesInsideAnEllipse/

Wolfram Demonstrations Project

Published: April 30 2012