This is the most wonderful thing I learned this week (though I don’t truly understand it), from the Wikipedia article on Gauss’s Theorema Egregium (Remarkable Theorem) about the curvature of surfaces. “The theorem says that the Gaussian curvature of a surface does not change if one bends the surface without stretching it,” says the article, and then gives an example:
An application of the Theorema Egregium is seen in a common pizza-eating strategy: A slice of pizza can be seen as a surface with constant Gaussian curvature 0. Gently bending a slice must then roughly maintain this curvature (assuming the bend is roughly a local isometry). If one bends a slice horizontally along a radius, non-zero principal curvatures are created along the bend, dictating that the other principal curvature at these points must be zero. This creates rigidity in the direction perpendicular to the fold, an attribute desirable when eating pizza, as it holds its shape long enough to be consumed without a mess.