Reflections, rotations, and Pythagorean numbers (Q1027967)

The authors discuss reflections and rotations of \(\mathbb R ^{n}\) in terms of Clifford algebras. They give a new proof of Cartan's Theorem which states that every orthogonal transformation of \(\mathbb R ^{n}\) can be decomposed by at most \(n\) reflections. They also describe all Pythagorean triples (\(x^2+y^2=z^2\)) and boxes (\(x^2+y^2+z^2=w^2\)) in the framework of Clifford algebras.