Heart Curve

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Theorem

The following equations define curves that are more or less heart shaped:

Formulation 1

$r = 1 - \sin \theta$
HeartCurve1.png


Formulation 2

$\left({x^2 + y^2 - 1}\right)^3 = x^2 y^3$
HeartCurve2.png


Formulation 3

$\begin{cases} x = & \map \sin t \map \cos t \ln \size t \\ y = & \size t^{0.3} \sqrt {\cos t} \end{cases}$

where $t \in \hointr {-1} 0 \cup \hointl 0 1$.

HeartCurve3.png


Formulation 4

$\paren {y - \dfrac {2 \paren {\size x + x^2 - 6} } {3 \paren {\size x + x^2 + 2} } }^2 + x^2 = 36$
HeartCurve4.png


Formulation 5

$r = \dfrac {\sin t \sqrt {\size {\cos t} } } {\sin t + \frac 7 5} - 2 \sin t + 2$
HeartCurve5.png


Formulation 6

$\begin{cases} x = & 16 \sin^3 t \\ y = & 13 \cos t - 5 \cos 2 t - 3 \cos 3 t - \cos 4 t \end{cases}$


HeartCurve6.png