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.

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