Engineering the Perfect Heart with Math

Is there such thing as a perfectly engineered heart shape? This Valentine’s Day, we did a little research and experimentation to find out.


The mathematical term, cardioid, means "heart-shaped." It is created by plotting the function r(θ) = 1 – sin(θ) on a graph, or by tracing a point on the perimeter of a circle that is rolling around a fixed circle of the same radius.

The result is maybe more apple-shaped than heart-shaped, having a rounded base rather than the iconic pointed tip one usually associates with the heart graphic.

To get a truer heart shape, you can try a few of the functions below. There are many different rectangular, polar and parametric functions you can use to create countless variations of this universal symbol for love. 


If you want to learn more about cardiods and their uses in mathematics, check out Wikepedia's impressively detailed page on the subject. We hope your Valentine's Day is full of cardioids!

Fun tip: you can also create a heart symbol with your keyboard by pressing Alt+5 on the numpad (on the right-side of the keyboard), like this: ♥

The pure mathematician, like the musician, is a free creator of his world of ordered beauty
— Bertrand Russell / philosopher, mathematician, writer, social critic, political activist, and Nobel laureate