A hypotrochoid is a roulette traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is a distance d from the center of the interior circle.
The parametric equations for a hypotrochoid are:
Where is the angle formed by the horizontal and the center of the rolling circle (these are not polar equations because is not the polar angle).
- J. Dennis Lawrence (1972). A catalog of special plane curves. Dover Publications. pp. 165–168. ISBN 0-486-60288-5.
- Gray, Alfred. Modern Differential Geometry of Curves and Surfaces with Mathematica (Second ed.). CRC Press. p. 906. ISBN 9780849371646.
- Flash Animation of Hypocycloid
- Hypotrochoid from Visual Dictionary of Special Plane Curves, Xah Lee
- Interactive hypotrochoide animation
- O'Connor, John J.; Robertson, Edmund F., "Hypotrochoid", MacTutor History of Mathematics archive, University of St Andrews.