Crumpling, buckling, and cracking: Elasticity of thin sheets

crumple, stretch, or tear it. Sometimes the sheet can spring right back to its original form, as with a roll of paper, while other times it is permanently changed, as with torn plastic. Much can be learned from such everyday acts. The subtle mathematics of differential geometry is needed to make sense of the deformed sheets, and along the way it offers insights into issues such as the shapes of flowers and the speed of earthquakes.