Problem of the Week

Sept. 5, 2020 to Sept. 12, 2020

Prove that any transformation of the plane which leaves the distances between all points unchanged (called isometries or rigid transformations) can be expressed as compositions of reflections about arbitrary lines. Can you provide and prove a generalization to 3 dimensions? This idea is heavily used in forms of geometric algebras called Clifford Algebras to which Dirac heavily contributed in his study of spinors.

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