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

© Robert FERRÉOL 2017