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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.

MSC:

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

Citations:

Zbl 0063.01003
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