# Anticycloid Curves I: A Rolling Circle

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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

[more]
Contributed by: Ralf Schaper (March 2011)

After work by: Hans Dirnböck

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

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.

## Permanent Citation