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From the definition looks like the angle is 2*arccos(q_r). Why it is now a different expression including atan? Is it a different angle now? Is it w no longer cos(w/2)?
: <math>2 \arccos(q_r)</math> is correct only assuming a unit length quaternion, and has stability issues near <math>q_r = \pm 1</math>. Using the two-argument arg-tangent yields the correct angle for any non-zero quaternion in a numerically stable fashion. [[User:Ybungalobill|bungalo]] ([[User talk:Ybungalobill|talk]]) 17:28, 19 November 2018 (UTC)
== Last section on 4D rotations needs rewriting ==
* The section '''Pairs of unit quaternions as rotations in 4D space''' has too many problems and needs to be rewritten from scratch.
* It is never mentioned that the '''z''''s have as coordinates the a's, b's, c's, and d's.
* It is never mentioned that the quaternion '''v''' has as coordinates w, x, y, and z (z again?).
* The statement
<div style="text-align: center;">"''Note that since <math>(\mathbf{z}_{\rm{l}} \vec{v}) \mathbf{z}_{\rm{r}} = \mathbf{z}_{\rm{l}} (\vec{v} \mathbf{z}_{\rm{r}})</math>, the two matrices must commute.''"</div>
:seems entirely unjustified and incorrect. (I think the author really means that '''left multiplication''' commutes with '''right multiplication''' (whether by matrices or anything else). It is '''not true''', however, that the two matrices commute.
* It is never mentioned that there are two pairs of '''z''''s that result in the identical 4D rotation.
* And it is never mentioned which quaternions {{math|'''z'''<sub>l</sub>}} and {{math|'''z'''<sub>r</sub>}} must be used to achieve a desired rotation in 4-space, or what rotation is achieved using those '''z''''s.
[[Special:Contributions/50.205.142.35|50.205.142.35]] ([[User talk:50.205.142.35|talk]]) 20:45, 13 January 2020 (UTC)
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