Everybody needs shelter.. Shelter against the sun, the wind, the cold, the heat, animals or other people. One of the things that provide a kind of shelter is a roof. A roof can consist of a flat or a curved surface.

A flat surface is weaker then a curved surface. A flat surface tends to bend and only the thickness of the slab prevents or limits its bending. The material on top of the slab is pressed whereas the material below is stressed. Together they limit the bending and prevent the breaking of the slab.

I use the sheet on which I am going to write this text to illustrate this. I put the sheet on three supports. It bends. Of course it bends, no surprise. Now if I fold the same piece of paper into a cone it suddenly does not bend any more.

Curved surfaces like vaults and double curved surfaces like domes are always stronger and use less material..