Plateau Curves

Parametric Cartesian equation:
x = a sin(m + n)t/sin(m - n)t, y = 2a sin(mt)sin(nt)/sin(m - n)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

Click THIS LINK to experiment interactively with this curve and its associated curves.

This curve was studied by the Belgium physicist and mathematician Joseph Plateau.

If m = 2n the Plateau curves become a circle, centre (1, 0) and radius 2.

The particular curves drawn above are with the parameters m = 5, n = 3.

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JOC/EFR/BS January 1997

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