There are a number of mathematical curves that produced heart shapes, some of which are illustrated above. A "zeroth" curve is a rotated cardioid (whose name means "heartshaped") given by the polar equation
(1)

The first heart curve is obtained by taking the cross section of the heart surface and relabeling the coordinates as , giving the order6 algebraic equation
(2)

A second heart curve is given by the parametric equations
(3)
 
(4)

where (H. Dascanio, pers. comm., June 21, 2003).
A third heart curve is given by
(5)

(P. Kuriscak, pers. comm., Feb. 12, 2006). Each half of this heart curve is a portion of an algebraic curve of order 6.
A fourth curve is the polar curve
(6)

due to an anonymous source and obtained from the log files of WolframAlpha in early February 2010. 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.
A fifth heart curve can be defined parametrically as
(7)
 
(8)

A sixth heart curve is given by the simple expression
(9)

(noted on a greeting card by J. Schroeder, pers. comm., Oct. 16, 2021). When properly nondimensionalized with scale paramaters and , the curve becomes
(10)

which can be written as a sextic equation in and .
A seventh heart curve can be defined parametrically as
(11)
 
(12)

which arises through modifying the parametric equations of a nephroid (J. Mangaldan, pers. comm., Feb. 14, 2023).
The areas of these hearts are
(13)
 
(14)
 
(15)
 
(16)
 
(17)
 
(18)
 
(19)
 
(20)

where can be given in closed form as a complicated combination of hypergeometric functions, inverse tangents, and gamma functions.
The Bonne projection is a map projection that maps the surface of a sphere onto a heartshaped region as illustrated above.