Area of Epicycloid and Hypocycloid

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

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

This Demonstration shows that the area under the first hump of a epicycloid is when the radii of the generating circle and greater circle are and respectively. When you slide the "roll" slider, slices form a circle of radius and a circular hole of radius . Therefore the area is the difference of areas of the two circles. In other words, .


For the hypocycloid, the same result holds with negative.

As the number of slices goes to infinity, the dark figure approaches a region bounded by a perfect epicycloid or hypocycloid.


Contributed by: Okay Arik (March 2011)
Open content licensed under CC BY-NC-SA



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.