# Epitrochoids

Epitrochoids

An epitrochoid is a roulette made from a circle going around another circle. A roulette is a curve that is created by tracing a point attached to a rolling figure.

# Basic Description

The basic concept of this is a circle that can't move, and a circle that can. The circle that can't move is fixed onto a surface (like paper). Within the circle that can move is a line that will create a line once this circle is moving around the fixed circle. Think of it as a rabbit that runs around its hole (that's hopefully on the ground) holding a marker while staying in the same position, but twirling.

# A More Mathematical Explanation

Note: understanding of this explanation requires: *Roulettes

Parametric Equations for an epitrochoid: x= (a+b)cos t-h cos(((a+b)/b)t))

y= (a+b)sin t-h sin(((a+b)/ [...]

Parametric Equations for an epitrochoid: x= (a+b)cos t-h cos(((a+b)/b)t)) y= (a+b)sin t-h sin(((a+b)/b)t))

h is distance between the moving line to the center of the circle. b is the radius of the rolling circle. (This equation was found at http://mathworld.wolfram.com/Epitrochoid.html)

# Why It's Interesting

It creates interesting shapes and can be applied to practical daily uses.

# How the Main Image Relates

It show the concept of it.

# About the Creator of this Image

A German artist and mathematician named Albrecht Duerer first discovered the epitrochoid. He lived during the late 15th and early 16th century. He mentioned it first in a book called "Instruction in Measurement with Compass and Straight Edge".