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.


The first curve is a rotated cardioid (whose name means "heart-shaped") given by the polar equation
r(theta)=1-sintheta.
(1)

The second is obtained by taking the y=0 cross section of the heart surface and relabeling the z-coordinates as y, giving the order-6 algebraic equation
(x^2+y^2-1)^3-x^2y^3=0.
(2)

The third curve is given by the parametric equations
x=sintcostln|t|
(3)
y=|t|^(0.3)(cost)^(1/2),
(4)

where t in [-1,1] (H. Dascanio, pers. comm., June 21, 2003). The fourth curve is given by
x^2+[y-(2(x^2+|x|-6))/(3(x^2+|x|+2))]^2=36
(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
r(theta)=2-2sintheta+sintheta(sqrt(|costheta|))/(sintheta+1.4)
Source: HeartCurve

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