Drawing heart in mathematica It's not really a typical math question. Today, while studying graphs, I suddenly got inquisitive about whether there exists a function that could possibly draw a heart-shaped graph. Out of sheer curiosity, I clicked on Google, which took me to this page.
The page seems informative, and I am glad to learn certain new things! Now I am interested in drawing them by my own using Mathematica. So my question is: is it possible to draw them in Mathematica? If yes, please show me how.
 A: A somewhat late addition (I only found my yellowed notebooks containing these just now):
$$\left(2(1+\cos\,\varphi)\sin^3 t\qquad 2\cos\,\theta\;\sin^2 t \sin\,\varphi+\sin\,\theta\cos\,t\left(\cos\,2t-2\cos\,\varphi\;\sin^2 t-3\right)\right)^T$$
is a two-parameter family of curves that generate heart shapes for some values of $\theta$ and $\varphi$. They were derived from projections of a skewed version of the nephroid.
Here for instance is the case $\theta=\pi/4,\quad \varphi=\pi/2$:

A: You can plot Taubin's heart surface using ContourPlot3D:
ContourPlot3D[(2 x^2 + y^2 + z^2 - 1)^3 - (1/10) x^2 z^3 - y^2 z^3 == 0,
              {x, -1.5, 1.5}, {y, -1.5, 1.5}, {z, -1.5, 1.5},
              Mesh -> None, ContourStyle -> Opacity[0.8, Red]]


A: Consider the map $T \colon \mathbb R^2 \rightarrow \mathbb R^2, \ (x,y) \mapsto (x, y+ \sqrt{|x|})$.  With a little examination, you can see that this will define a warping on the plane that will map the unit circle to a heart shaped curve: 

So if you know that a parametrization for the circle is $(\cos(t),\ \sin(t)),\  t\in [-\pi,\pi]$, then the parametrization for its heart-shaped image would be $(\cos(t),\ \sin(t) + \sqrt{|\cos(t)|}),\  t\in [-\pi,\pi]$. You can plot the curve with the following Mathematica code:
ParametricPlot[{Cos[t], Sin[t] + Sqrt[Abs[Cos[t]]]}, {t, -Pi, Pi}]

A: Inigo Quilez has found a polar plot of a heart that doesn't require any of trigonometric functions:

polar plot r = (0.322515 * abs(theta)^3 - 2.22907 * abs(theta)^2 + 4.13803 * abs(theta))/(6.0 - 1.59155 * abs(theta)), theta=-pi to pi

Wolphram Alpha plot
Shadertoy live version
A: A three-dimensional space curve with the shape of a red heart:

The Mathematica code for the image above is:
ParametricPlot3D[{Cos[u]*(4*Sqrt[1 - v^2]*Sin[Abs[u]]^Abs[u]), v, 
  Sin[u]*(4*Sqrt[1 - v^2]*Sin[Abs[u]]^Abs[u])}, 
   {u, -Pi, Pi}, {v, -1, 1}, Axes -> None, Mesh -> False, 
 Boxed -> False, 
   PlotStyle -> {Red, Specularity[White, 10]}]

3D red heart with Mesh and lines:

Mathematica code for the image above:
ParametricPlot3D[{Cos[u]*(4*Sqrt[1 - v^2]*Sin[Abs[u]]^Abs[u]), v, 
  Sin[u]*(4*Sqrt[1 - v^2]*Sin[Abs[u]]^Abs[u])}, {u, -Pi, 
  Pi}, {v, -0.97, 0.97}, PlotPoints -> 50, Axes -> None, 
 Boxed -> False, 
 PlotStyle -> 
  Directive[Glow[Red], Specularity[White, 30], Opacity[0.15]], 
 Mesh -> 50, Background -> Black, MeshStyle -> {Blue, Red}, 
 Lighting -> {{"Directional", Yellow, {{1.5, 1.5, 5}, {1.5, 1.5, 0}}, 
    Pi/6}}]

A variation on the use of the Taubin heart surface with hue:

Mathematica code for the last image above:
ContourPlot3D[(-1/10) x^2 z^3 - 
   y^2 z^3 + (2 x^2 + y^2 + z^2 - 1)^3 == 0, {x, -1.2, 1.2}, {y, -1.4,
   1.4}, {z, -1.5, 1.5}, Mesh -> False, PlotPoints -> 60, 
 Axes -> None, Boxed -> False, 
 ContourStyle -> Directive[Opacity[0.5], Red], 
 ColorFunction -> Function[{x, y, z, f}, Hue[z]]]

For more customized heart images, see the post in my website/blog:
https://knowledgemix.wordpress.com/2014/02/14/heart-to-heart-with-3d-math/
A: For the fifth function in the link you mentioned (which I thought it was the most similar to a heart):
PolarPlot[(Sin[t]Sqrt[Abs[Cos[t]]])/(Sin[t]+7/5)-2Sin[t]+2, {t, 0, 10}]

Similarly, using W|A:

A: This is really about plotting polar plots, parametric plots and implicitly defined functions in Mathematica.
This is the info on how to draw polar plots
http://mathworld.wolfram.com/PolarPlot.html
Parametric plots
http://reference.wolfram.com/mathematica/ref/ParametricPlot.html
This provides info on implicit plots
http://grosz.math.txstate.edu/~dhaz/prob_sets/LTs09cal1lab8.pdf
A: Here is a screen shot from this equation on Wolfram Alpha.  I don't have a license for Mathematica.
(x^2+y^2-1)^3 = x^2


