**Polar equation: **

*r* = *a*(1 + 2sin(*θ*/2))

**Click below to see one of the Associated curves.**

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This is a strophoid of a circle with the pole

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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JOC/EFR/BS January 1997

The URL of this page is:

http://www-history.mcs.st-andrews.ac.uk/Curves/Freeths.html