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In geometry and topology, crumpling is the process whereby a sheet of paper or other two-dimensional manifold undergo disordered deformation to yield a three-dimensional structure comprising a random network of ridges and with variable density. The geometry of crumpled structures is of interest to mathematicians studying topology. Crumpled paper balls have been studied and found to exhibit surprisingly complex structures with compressive strength resulting from interactions at Local property flat facets between folds. The unusually high compressive strength of crumpled structures relative to their density is of interest in the disciplines of materials science and mechanical engineering.
From a practical standpoint, crumpled balls of paper are commonly used as toys for cat.
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