For those who are in love and (or) those who like maths, this post might be interesting. For those who don’t, be aware: this post is about maths and hearts ;)

Some time ago, I designed a heart with mathematical functions. 14th of February seems the perfect day to offer something like this. It is original, cheap and easy to do. So if you’re in a hurry and forgot to buy a present to your girl/boyfriend, take a piece of paper and write him/her down the Heart Curve.

The Heart Curve is a mathematical relation that, when plotted, has the shape of a heart. This is easily accomplished by the use of several implicit functions.

Let $ H(x)$ be the Heart relation defined on $ [\frac{-\sqrt{13}-3}{5}, \frac{\sqrt{13}+3}{5}],$ $ (x, y) \in \mathbb{R}\times\mathbb{R}$ by:

$ H(x): \left\{ \begin{array}{clcr} (x+\frac{3}{5})^2 + (y-\frac{8}{5})^2 = \frac{13}{25}, & \text{if } y > x +2 \\ (x-\frac{3}{5})^2 + (y-\frac{8}{5})^2 = \frac{13}{25}, & \text{if } y > -x + 2\\ y^3 = x^2, & \text{if } x \in [-1,1]\\ \end{array} \right. $

The resulting plot without using the functions' definitions:

And the Heart curve, restricted and filled with a nice color.

There’s an even more incredible curve :

$ (x^2 +y^2-1)^3 = x^2y^3 $

Its curve plotted with wolfram alfa here.

Happy St. Valentine’s day !

PS : More info about Heart Curves here.