# The Heart Curve present

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 :