Talk:Quaternion
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There's something messed up with this page, starting after the equation in the history subsection. Using Firefox, everything after that point is rendered in a much smaller font.--Starwed 20:26, 2 May 2005 (UTC)
I wrote a short introduction so that non-mathematicians stumbling across this article, or curious folks wondering what quaternions are, would have something to grasp before being plunged into inaccessible terminology. I think this is important for math articles if they are to serve a purpose other than preaching to the converted (so to speak).
However, that doesn't mean that my introduction is particularly good - I swiped part of it from the History subsection. Any good historians/sociologists of math out there who can improve it? - DavidWBrooks 20:17, 1 Jun 2004 (UTC)
Correction to quaternion argument arg(p) and logarithm ln(p)
The quaternion argument arg(p) was listed as:
<math>\arg(p) = \arccos\left(\frac{\operatorname{Scalar}(p)}{|p|^2}\right)<math>
The norm should not be squared however, so it should be:
<math>\arg(p) = \arccos\left(\frac{\operatorname{Scalar}(p)}{|p|}\right)<math>
The quaternion logarithm ln(p) was listed as:
<math>\ln(p) = \ln(|p|) + \sgn(p)\arg(p)<math>
The sign should be taken from the vector part only not the whole quaterion
<math>\ln(p) = \ln(|p|) + \sgn(\vec{u})\arg(p)<math>
This follow from the exponential notation of quaternions:
<math>p = r\exp([0, \vec{u}]\phi) = r\cos(\phi) + r\sin(\phi)\vec{u} \land |\vec{u}| = 1<math>
Hkuiper 17:34, 30 Oct 2004 (UTC)
ijk = -1 does not imply associativity
The article says the equation ijk = -1 implies the quaternions are associative. Actually it assumes it, but does not imply it.
The statement is now removed. -- Fropuff 01:57, 2005 May 2 (UTC)