On the composition of finite rotations in \({\mathbb E}^4\). (English) Zbl 1342.51021

The authors investigate products of rotations in the Euclidian space \(\mathbb E^4\). They explain simple and double rotations. Working with real quaternions, the authors give conditions under which the product of two rotations is again a rotation. They use H. S. M. Coxeter’s work on quaternions and reflections [Am. Math. Mon. 53, 136–146 (1946; Zbl 0063.01003)]. They also make a number of historical comments; in one of these they refer to Olinde Rodrigues’ paper of 1840 on Transformation groups.


51N20 Euclidean analytic geometry
51F25 Orthogonal and unitary groups in metric geometry
51N30 Geometry of classical groups


Zbl 0063.01003
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