Editing Rotation (mathematics) (section)

===In non-Euclidean geometries===
In [[spherical geometry]], a direct motion{{clarification needed|What does the term "direct motion" mean precisely?|date=July 2020}} of the [[n-sphere|{{mvar|n}}-sphere]] (an example of the [[elliptic geometry]]) is the same as a rotation of {{math|(''n'' + 1)}}-dimensional Euclidean space about the origin ({{math|SO(''n'' + 1)}}). For odd {{mvar|n}}, most of these motions do not have fixed points on the {{mvar|n}}-sphere and, strictly speaking, are not rotations ''of the sphere''; such motions are<!-- all of them? --> sometimes referred to as ''[[William Kingdon Clifford|Clifford]] translations''.{{citation needed|reason=Which sources call them that?|date=July 2020}} Rotations about a fixed point in elliptic and [[hyperbolic space|hyperbolic]] geometries are not different from Euclidean ones.{{clarification needed|How are they not different? The definition of rotation given for Euclidean space isn't even defined for those geometries.|date=July 2020}}

[[Affine geometry]] and [[projective geometry]] have not a distinct notion of rotation.