Showing posts with label epitrochoid curves. Show all posts
Showing posts with label epitrochoid curves. Show all posts

28 July, 2023

Shapes Based On Parametric Equations: Epitrochoids

Epitrochoids are curves generated by a point selected on a circle of smaller radius rolling around the outside of a fixed circle of larger radius, and that selected point can be chosen at some distance from the center of the smaller circle. These are then 3-parametric curves. They can be helpful in creating decorative designs and other art applications, and can serve also as pastime and recreation for children. Since 1965 there is available a toy (geometric drawing device) known as spirograph, combining mathematics and art. It allows producing physically numerous curve designs based exactly on epitrochoid and hypotrochoid parametric equations.

However, nowadays the epitrochoids (as well as hypotrochoids - see another post at can be generated quite easily in Excel by using VBA macro like the one provided at the end of this post.

Here are some examples of charts showing epitrochoid curves generated with the macro. Some of them present combined double curves.