r = a(1 + 2sin(θ/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 3π/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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