The curve, a botanic
curve, is an extension of Freeth's nephroid (b = 2). This specimen is the strophoid constructed for a circle,
named after the English mathematician T.J. Freeth (18191904).
The Freeth's nephroid (b=2) can be used to construct a regular 7sided figure, as
follows:
Let P be the node where the curve crosses itself three times. Line l parallel
the yaxis through P cuts the nephroid in Q.
Then the angle POQ is 3π/7.
For large b the curve approximates the rhodonea
(c=1/2).
Don't mistake this curve with another nephroid, the (ordinary) nephroid ^{1)}.
notes
1) Nephros (Greek) = kidney
