Epicycloids {cardioid} can be curves traced by one circle point rolling on fixed equal-radius-circle outside: r = 2 * a * (l - cos(A)), where r is distance from pole, a is fixed-circle radius, pole is where rolling point meets fixed circle, and A is angle to radius. Cardioids have one loop and are special limaçon-curve cases.
Circle points rolling along straight lines make curves {cycloid}. Circle points rolling on fixed-circle outsides make curves {epicycloid}. Circle points rolling on fixed-closed-curve outsides make curves {pericycloid}. Circle points rolling on fixed-circle insides make curves {hypocycloid}. Fixed circles can have four times rolling-circle diameter {astroid}.
Conchoids {limaçon of Pascal} can have circle for fixed curve: r = 2 * a * cos(A) + b, where r is distance from pole, pole is where rolling point meets fixed circle, A is angle to radius, and a and b are constants. If b < 2*a, limaçon of Pascal has two loops. If b > 2*a, limaçon of Pascal has one loop. If b = 2*a, limaçon of Pascal is a cardioid curve.
Curve points or line envelopes rolling along fixed curves make curves {roulette curve}.
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Date Modified: 2022.0225