Parametric Cartesian equation:
x = (a - b) cos(t) + c cos((a/b -1)t), y = (a - b) sin(t) - c sin((a/b -1)t)
Click below to see one of the Associated curves.
|Definitions of the Associated curves||Evolute|
|Involute 1||Involute 2|
|Inverse curve wrt origin||Inverse wrt another circle|
|Pedal curve wrt origin||Pedal wrt another point|
|Negative pedal curve wrt origin||Negative pedal wrt another point|
|Caustic wrt horizontal rays||Caustic curve wrt another point|
For the hypotrochoid, an example of which is shown above, the circle of radius b rolls on the inside of the circle of radius a. The point P is at distance c from the centre of the circle of radius b. For this example a = 5, b = 7 and c = 2.2.
These curves were studied by la Hire, Desargues, Leibniz, Newton and many others.
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