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  "body": "\n## Summary\n\nRigidity theory studies when a framework of rigid bars joined at flexible joints cannot be deformed except by moving it as a whole.\nA framework is a [[graph|00C0BR7D7H]] together with positions of its vertices in [[Euclidean space|0XPR1E85W0]], with each edge a bar of fixed length.\nThe subject links geometry, combinatorics and linear algebra, and it is used in engineering, chemistry and robotics.\nClassical results include Cauchy's rigidity theorem for convex polyhedra and Laman's characterisation of generically rigid graphs in the plane.\n\n## Explanations\n\n### L1 human\n\nBuild a shape out of sticks and hinges and ask whether it wobbles.\nA square of four sticks wobbles: it can be pushed into a rhombus.\nA triangle of three sticks does not, since three side lengths fix a triangle.\nAdding one diagonal stick to the square splits it into two triangles and makes it rigid.\nRigidity theory turns this into precise mathematics and counts how many sticks a rigid structure needs.\n",
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