There are a number of mathematical curves that produced heart shapes, some of which are illustrated above. The first curve is a rotated cardioid (whose name means "heart-shaped") given by the polar equation.
The second is obtained by taking the 
cross section of the heart surface and relabeling the 
-coordinates as 
, giving the order-6 algebraic equation.
The third curve is given by the parametric equations.
The fourth curve is given by (P. Kuriscak, pers. comm., Feb. 12, 2006). Each half of this heart curve is a portion of an algebraic curve of order 6.
And the fifth curve is the polar curve. Each half of this heart curve is a portion of an algebraic curve of order 12, so the entire curve is a portion of an algebraic curve of order 24.
The Bonne projection is a map projection that maps the surface of a sphere onto a heart-shaped region as illustrated above.
above.
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