[an error occurred while processing this directive]

Anticycloid Curves I: A Rolling Circle

The curve traced out by a point on the rim of a circle rolling along a straight line is called a cycloid. Now change the situation: the point moves on a straight line when the circle rolls on a suitable trace. What is the shape of this trace? We call this curve an anticycloid.

If is the distance from the point to the center of the circle, a parametrization of an anticycloid is given by
where is an elliptic integral of the first kind and is an elliptic integral of the second kind.


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


The relationship between the the road (the anticycloid) and the wheel (the circle) that rolls smoothly on it is described in detail in the book by H. Dirnböck, Die Antizykloidenbewegung, Klagenfurt, Austria: Verlag Heyn, 1987.
[an error occurred while processing this directive]

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 © 2018 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+