Epitrochoids
From Math Images
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.
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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
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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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