Polar equation: r = a(1 + 2sin(
/2))
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
In the picture above, O is the origin and P is the node where the curve crosses itself three times.
If the line through P parallel to the y-axis cuts the nephroid at A then angle AOP is 3
/7. This can be used to construct a regular 7 sided figure.
T J Freeth (1819-1904) was an English mathematician. In a paper published by the London Mathematical Society in 1879 he described various strophoids, including the strophoid of a trisectrix.
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