The author's point that "curvature imputes stiffness" conflates several different and distinct mechanisms, and offers an inadequate explanation.<p>For the examples of the pizza, the leaf, and the corrugated sheets, the stiffness is due to the fact that the bending moment of inertia of the cross-section increases when we fold the pizza or the sheet in a particular way [1]. The Theorema Egregium shows that such a structure can be made from a flat sheet of material, not that this construction imparts stiffness to the structure.<p>The example of arches show the well-known arch action in mechanics, where forces are carried through pure compression without any tensile stresses, which makes it appropriate for using stones to make the arch [2]. In principle, one could make a triangular "arch", i.e. part of a truss structure, where we use two straight rods joined together at the top [3]. This shows that its not really the curvature that is giving the stiffness.<p>The example of hyperbolic paraboloids shows arch action in one direction and beam bending in the other.<p>The examples of the egg and the can show that it is hard to break a surface when it does not have stress concentrations [4].<p>So the point is that there's a lot of classical solid mechanics at play here, of which the author seems to be unaware.<p>[1] <a href="http://en.wikipedia.org/wiki/Bending" rel="nofollow">http://en.wikipedia.org/wiki/Bending</a><p>[2] <a href="http://en.wikipedia.org/wiki/Arch" rel="nofollow">http://en.wikipedia.org/wiki/Arch</a><p>[3] <a href="http://en.wikipedia.org/wiki/Truss" rel="nofollow">http://en.wikipedia.org/wiki/Truss</a><p>[4] <a href="http://en.wikipedia.org/wiki/Stress_concentration" rel="nofollow">http://en.wikipedia.org/wiki/Stress_concentration</a>