Math in… Pizza

Do you ever find yourself having to brace a particularly floppy pizza slice or position your mouth under it?

As a surface bends without stretching, the product of its principal curvatures at each point remains the same. Since a flat slice of pizza has zero curvature in all directions, a firm bottom crust means that no matter how you pick it up, some direction must still have zero curvature.

If you hold a pizza slice in the middle of the cornicione (outer crust), gravity will decide the slice remains flat across but droops at its tip. If you instead slightly fold the crust and force nonzero curvature across the slice, then the nonzero curvature axis will run from cornicione to tip!