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MULTICARDIOID


Curve proposed in a special case by Brocard in 1894, called "Brocard trefoil" by G. de Longchamps.
Homemade name.

 
Polar equation: obtained by replacing x by  and y by  in the equation  of the cardioid.

The multicardioids are the images of the cardioid by the Brocard transformation.
 

Some examples with :
 
 
n = 2 n = 3 n =  5 n = 3/2
=3a
=2a

(Brocard trefoil)
=3/2a
= a
=a/2
=0
= a

 
 
=2a , n = 4/3 =3/2 a , n = 4/3 = a, n = 3/4 =3a, n = 3/4

The original article by Brocard, Nouvelles annales 1894, page 58

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© Robert FERRÉOL 2017