Editing Euler angles (section)

===Higher dimensions===
It is possible to define parameters analogous to the Euler angles in dimensions higher than three.<ref>{{Citation
  |last = Hoffman
  |first = D. K.
  |title = Generalization of Euler Angles to N-Dimensional Orthogonal Matrices
  |journal = Journal of Mathematical Physics
 |publisher = [J. Math. Phys. 13, 528–533]
  |year = 1972
  |volume = 13
 |issue = 4
 |pages = 528–533
 |doi = 10.1063/1.1666011
  |bibcode = 1972JMP....13..528H
 |url = https://pubs.aip.org/aip/jmp/article/13/4/528/440286/Generalization-of-Euler-Angles-to-N-Dimensional
|url-access = subscription}}</ref>
<ref>{{in lang|it}} [http://ansi.altervista.org A generalization of Euler Angles to ''n''-dimensional real spaces]</ref>{{unreliable source?|date=December 2022}} In four dimensions and above, the concept of "rotation about an axis" loses meaning and instead becomes "rotation in a plane." The number of Euler angles needed to represent the group {{math|SO(''n'')}} is {{math|''n''(''n'' − 1)/2}}, equal to the number of planes containing two distinct coordinate axes in ''n''-dimensional Euclidean space.

In [[SO(4)]] a rotation matrix [[Rotation (mathematics)#In four dimensions|is defined by two unit quaternions]], and therefore has six degrees of freedom, three from each quaternion.