© T Madas

© T Madas

What is an epicycloid?Imagine a circle rolling on the outside of another circle.Pick a fixed point on the rolling circle and follow its path as the circle rolls all the way around.The curve it traces is called an epicycloid

This is not a unique curve.

We can get different epicycloids by:•changing the ratio of the radii of the two circles•changing the tracing point on the rolling circle

© T Madas

cardioid

cusp

epicycloid with 1 cuspHeart-shaped

Radius of rolling circle is equal to the radius of the fixed circle

© T Madas

nephroidepicycloid with 2 cuspskidney-shaped

cusp

cusp

The radius of rolling circle is half the radius of the fixed circle

© T Madas

cardioid nephroid Cremona Curve

Epicycloids with 1 to 5 cusps

© T Madas

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© T Madas

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© T Madas

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© T Madas