Mathematical Intentions logo

Quadrivium logo

The Tangent Vector to the Cycloid

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)


A cycloid is the curve traced by a point on a circle as the circle rolls along a line.

Roberval (1634) found the velocity vector (this is modern terminology) that describes both the tangent direction for a point on the cycloid, and the velocity of the point moving along the curve as the circle rolls at a constant rate.

See the lecture notes on the cycloid for the proof.

Technical details: use the "Roll" slider, or click the "Play" triangle in the lower left of the window to roll the circle.

Susan Addington, Created with GeoGebra


Mathematical Intentions
Measuring the World


Contact us

Last updated November 29, 2010

Copyright 2009-10 David Dennis and Susan Addington. All rights reserved.