## Thursday, February 14, 2013

### Happy Valentine!

We wish you all a happy Valentine's day with origami hearts and an equation.

Let's make a plot in polar coordinates, of $$r = |\phi|^p$$. The angle $$\phi$$ goes from $$-\pi$$ to $$\pi$$,  and $$p \approx 1$$. Here is the plot, in processing, with $$\phi = 0$$ pointing up. Move the mouse to change $$p$$!

Mathworld has more equations for hearts, but none of them is as simple as ours. As $$p = 1$$ gives a nice shape, $$p$$ can be left out for an even simpler equation.