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
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(1)
|
The second is obtained by taking the
cross section of the heart surface and relabeling the
-coordinates as
, giving the order-6algebraic equation



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(2)
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The third curve is given by the parametric equations
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(3)
|
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(4)
|
where
(H. Dascanio, pers. comm., June 21, 2003). The fourth curve is given by
![t in [-1,1]](http://mathworld.wolfram.com/images/equations/HeartCurve/Inline10.gif)
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(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)
|
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)
|
The areas of these hearts are
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(9)
|
![]() | ![]() | ![]() |
(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.

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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