Talk:Rotation (mathematics)

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Contents 1 Move 3D matrix to rotation matrix 2 Merging 3 Name/redirect 4 Sense typo 5 4 dimensional rotation 6 point, axis, hyper-plane?

[edit] Move 3D matrix to rotation matrix

I've moved the matrix for rotation in 3D to rotation matrix, it, and its derivation are a bit long-winded for this article when we have another article dealing with the subject.

User:KSmrq, you reverted me, which I presume was just because you saw this page after I'd removed a bit but before I'd added it to the other page. Appologies for that, I should have done it in the other order.

If anyone disagrees with this move, then there's no point having the article rotation matrix at all. If you think that, then please recommend that it (together with the new content that I've written) be merged into this page, rather than just reverting this page, which creates duplicaton which is uncalled for, IMHO. TomViza 16:52, 21 May 2006 (UTC)

[edit] Merging

Disagree about merging this with rotation. The article Coordinate rotation is mathematical, the article rotation is very physical/intuitive. Merging them would create an article rather not understandable to the general public.

These two articles overlap little, and describe two different perspectives. They are also big and rather well-written. I feel there is no necessity to merge, and much could be lost as result of merging. Oleg Alexandrov 01:26, 13 August 2005 (UTC)

[edit] Name/redirect

It is wrong to name the article "coordinate rotation", since a mathematical rotation — of all things — can be defined and used quite well without coordinates, thank you very much. A rotation is a geometric idea, a direct isometry with a fixed point. Coordinates are handy in applications, but there is no excuse for letting them dominate the name of the article.

In fact, there is a beautiful way to approach geometry using involutions, which is to say, reflections. Discussions can be found in Coxeter's Introduction to Geometry, 2/e (ISBN 0471504580) and in Behnke et al.'s Fundamentals of Mathematics, Volume II:Geometry (ISBN 026252094X). Rotations in 2D or 3D are merely two intersecting reflections, which clearly produces a direct isometry with a fixed point at the intersection.

Therefore I propose to move the article where it belongs, to "Rotation (mathematics)", and redirect "Coordinate rotation" (and links here) to there. --KSmrq^T 12:55, 16 May 2006 (UTC)

Looking at the history of "Rotation (mathematics)", first it was split out from the Rotation page (which I fully support). Later, I suggested a merge with Coordinate rotation (see that version), thinking co-ordinate rotation could be a section on a larger page about mathematical rotations, but didn't really get merged, just redirected. I thought "coordinate rotation" was just an alternate way to describe a rotation, e.g. in computer graphics ray-tracing where sometimes it's easier to move the co-ordinates around than to move the camera or the items. Ewlyahoocom 14:35, 16 May 2006 (UTC)

I would support moving this to rotation (mathematics). You'd be most welcome if you would like to merge this and the text at rotation (mathematics) before I did the redirect. Oleg Alexandrov (talk) 15:04, 16 May 2006 (UTC)

I'm probably not qualified to do the actual merge cause I'm not a mathmagician. And I prefer your version which (to borrow your phrase) replaced the crap with normal English explaining the basic math behind rotations. Ewlyahoocom 22:49, 18 May 2006 (UTC)

Well, I moved the coordinate rotation article to rotation (mathematics). Any improvements to this article are welcome. Oleg Alexandrov (talk) 02:20, 19 May 2006 (UTC)

[edit] Sense typo

It looks like there is a typo. the rotation shown is clockwise, where it says that it is counter clockwise. I am not sure if the equation or the definition should be changed. It would be nice to clean this up. I would do so, but I do not know the best way to do so. —Preceding unsigned comment added by 169.237.42.82 (talk • contribs) 05:26, 2006 July 19

(Please add comments at end of page. Use "+" tab at top to start a new section. Thanks. --KSmrq^T 08:32, 19 July 2006 (UTC))

[edit] 4 dimensional rotation

why is there nothing about 4 dimensional rotation? Granpa31 (talk) 16:27, 18 December 2007 (UTC)

[edit] point, axis, hyper-plane?

As I see it, only in 2D a rotation can be said to be a transformation around a point.

In 3D shouldn't it be around an axis?

In 4D shouldn't it be around an hyper-plane????

Can anyone put some light on this? Mitus08 (discussion) —Preceding comment was added at 13:59, 13 January 2008 (UTC)

The 3D rotation is also around a point. It so turns out though, that any 3D rotation is not only around a point, but around an entire axis. In 4D one can again find rotations which leave just one point fixed, no more. But of course, you can always find 4D rotations which leave an entire axis fixed, or even an entire plane or hyperplane. Oleg Alexandrov (talk) 16:20, 13 January 2008 (UTC)