The Love Formula : How to Draw a Heart Shaped Curvy Graph
Ever wanted to know how to draw a heart shaped graph?
Is that real? well yes.
There are a number of mathematical curves that produced heart shapes, some of which are illustrated below.
Is that real? well yes.
The first curve is a rotated cardioid (whose name means "heart-shaped") given by the polar equation
 |
(1)
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The second is obtained by taking the 
cross section of the heart surface and relabeling the 
-coordinates as 
, giving the order-6algebraic equation
cross section of the heart surface and relabeling the -coordinates as , giving the order-6algebraic equation |
(2)
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The third curve is given by the parametric equations
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(3)
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(4)
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where 
(H. Dascanio, pers. comm., June 21, 2003). The fourth curve is given by
(H. Dascanio, pers. comm., June 21, 2003). The fourth 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. And the fifth curve is the polar curve
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(6)
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due to an anonymous source and obtained from the log files of Wolfram|Alpha 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 sixth heart curve can be defined parametrically as
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(7)
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(8)
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The areas of these hearts are
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(9)
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 |  |  |
(10)
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 |  |  |
(11)
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 |  |  |
(12)
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 |  |  |
(13)
|
 |  |  |
(14)
|
where 
can be given in closed form as a complicated combination of hypergeometric functions, inverse tangents, and gamma functions.
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 heart-shaped region as illustrated above.
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