9846

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.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

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.
    • 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 »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+