Navel Gazing and the Golden Ratio

What an apple & a belly button have in common

- STEVEN STROGATZ

HIDING INSIDE EVERY apple is a little bit of secret geometry. To reveal it, cut the apple sideways, straight through the core. There you'll find five seeds in the shape of a star.

In its idealized form, this kind of five-pointed star is known as a pentagram. In mathematics, the pentagram is a poster child for "self-similarity," a symmetry that's like worlds within worlds. The shape contains infinitely many smaller and smaller copies of itself.

To see self-similarity in action, imagine connecting the star's points with straight lines. The newly created pentagon immediately calls attention to a smaller pentagon nestled inside itself.