Curves of High Degree

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The epitrochoid is the roulette traced by a point attached to a circle rolling about the outside of a larger fixed circle.
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Similar to the epitrochoid, the hypotrochoid is defined to be the roulette traced by a point attached to a circle rolling on the inside of a larger fi...
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The epicycloid is an epitrochoid where the point being traced is on the circumference of the circle being rolled around.
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An Astroid is a four-cusped hypocycloid.
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Cayley's sextic is the locus of the equations shown below.
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The Hypocycloid is the hypotrochoid where the point generating the locus lies on the circumference of the small, rotating circle.
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The Nephroid is a two-cusped epicycloid. It is also the catacaustic of rays that reflect in a cardioid and originate in the curve's cusp. Furthermor...
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The Nephroid of Freeth is the nephroid of a circle with its pole at the circle's center and its fixed point on the circumference of the circle.
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