Thin objects are easy to deform, as we see in everyday life: a piece of paper crumples, while an umbrella may invert in the wind. It is also clear that such thin structures choose to bend, rather than compress/stretch, whenever possible. Gauss’ "Remarkable Theorem” severely restricts what types of pure bending deformations can happen with consequences from how best to eat pizza to the domed roofs of buildings. Nevertheless, as I will show, Gauss’ Theorem can be subtly subverted by objects that have a small, but non-zero, thickness.
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