Beyond Gauss' Pizza Theorem: From wrinkly isometry to snap-through
Thin objects are easy to deform, as we see in everyday life: a piece of paper crumples, while bridges may vibrate in the wind. It is also clear that such thin structures choose to bend, rather than compress, whenever possible. Gauss’ "Remarkable Theorem” has a lot to say about how such bending deformations can happen, and its consequences are everywhere from pizza slices to the domed roofs of buildings. Nevertheless, I’ll show how Gauss’ Theorem can be subverted by thin sheets and how finite thickness can cause a surprisingly slow snap-through.
