9887

Negative Pedal Curves of an Ellipse

The pedal curve of a curve with respect to a point is the curve whose points are the closest to on the tangents of . This Demonstration concerns the inverse of a pedal curve, sometimes called the negative pedal curve. The negative pedal of a curve can be defined as a curve such that the pedal of is . This Demonstration allows you to explore two sets of the negative pedal curves of an ellipse.

SNAPSHOTS

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

DETAILS

An ellipse can be described parametrically by two equations, each of which contains a constant; in this Demonstration these constants have been labeled and : , . The same two constants appear in the parametric equations of the negative pedal curves. The set of negative pedal curves with respect to the origin includes a curve known as "Talbot's curve" which has four cusps and two ordinary double points. The set of curves with respect to one of the foci is called "Burleigh's ovals" and includes a fish-like curve that inspired a paper by H. Martyn Cundy (Mathematical Gazette, 85(504), pp. 439-445).
    • 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+