Epitrochoids

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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.


Contents

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.

Teaching Materials

There are currently no teaching materials for this page. Add teaching materials.

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".


Related Links

Additional Resources

http://mathworld.wolfram.com/Epitrochoid.html*)






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