Science Puzzle
Which Shape Holds the Most Weight?
Take three identical sheets of A4 paper. Roll one into a square tube, one into a triangular tube, and one into a cylinder, all the same height. Stand each on a table and stack books on top until it collapses.
Same paper, same height, same amount of material. Which shape holds the most books?
The Answer
The cylinder, usually by a wide margin. A paper cylinder can carry a surprising stack of books.
Thin columns almost never fail by being crushed. They fail by buckling: bowing sideways and folding over. A flat panel is easy to bow, so the square tube gives way as soon as one of its four flat sides begins to bulge, and the rest follows instantly. The triangle does better because it has fewer, narrower panels and its corners are stiff, but it still has flat faces waiting to bow.
A cylinder has no flat faces at all. Every part of its wall is curved, and to buckle inward at any point the paper must stretch around the curve, which paper strongly resists. The load runs smoothly down the whole wall with no weak line to fold along.
This is why drinks cans, submarine hulls, gas cylinders, tree trunks and your own leg bones are round. The triangle is unbeatable for a framework of struts, but for a hollow column carrying a load from above, the circle wins.
The principle: Buckling and cross-section. Slender columns fail by buckling rather than crushing, and a curved wall with no flat panels resists buckling far better than a faceted one.