10217

# Holditch Curves inside an Ellipse

Around 1858, the Reverend Hamnet Holditch studied the curves generated by a point on a chord of fixed length sliding inside another curve.
This Demonstration is an animation showing the generation of some Holditch curves inside ellipses of different eccentricities. You can see the effect of the chord length and the position of the generating point on the chord.

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

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.