# Talk:Rotor (mathematics)

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Field: Geometry

## Rotor diagram

The diagram illustrates the creation of a rotor as the geometric product of two vectors R=uv, and uses the angle between the vectors as the angle of the rotor. In general, however, the angle we are interested in for a simple rotor (one that rotates vectors in a single plane) is the angle with which it rotates objects, which we would call θ, and MRθMRθ would be a rotation of M through angle θ. The angle between u and v in this case is θ/2, and the diagram should show this. I'm also not too sure that the dot and wedge products are particularly useful here. — Quondum 13:20, 13 November 2012 (UTC)

Well in the link provided they are used to construct the analogue of Euler's formula, and the reader can at least see the simpler case of unit vectors rotated. This article needs extension. I'll remove and fix the diagram soon, can't right now... Maschen (talk) 15:26, 13 November 2012 (UTC)
Euler's formula works but using the half angle: R=eθb/2, R=eθb/2 (or perhaps the other way around), where b is a unit bivector. — Quondum 19:14, 13 November 2012 (UTC)
The angle is corrected:
A rotor that rotates vectors in a plane rotates vectors through angle θ, that is xRθxRθ is a rotation of x through angle θ. The angle between u and v is θ/2. Similar interpretations are valid for a general multivector X instead of the vector x. [1]
Maschen (talk) 20:22, 13 November 2012 (UTC)
This'd need a suitable caption explaining it now, not too sure how I relate to its detail. Come to think of it, this article needs a lot of work before we get too focused on detail. Quondum 11:30, 14 November 2012 (UTC)
I deleted the caption initially since it was confusing the way I previously wrote it... Based on your explanation, and that rotations in GA seem to be generated by double reflections, a new caption has been formed, feel free to change it (well, effectivley you wrote it - not me!)... Maschen (talk) 13:32, 14 November 2012 (UTC)
The idea that the angle of rotation is double because it is two reflections does not work if you go through the detail. If you think of reflecting a vector on a vector, the angle is already doubled in a single reflection. I've tweaked the caption. — Quondum 14:45, 14 November 2012 (UTC)
Ok.. thanks. Maschen (talk) 14:55, 14 November 2012 (UTC)
Is it ok to paste this back into GA? Maschen (talk) 12:08, 15 November 2012 (UTC)
I'll add your modified caption to the GA article (far better than nothing), not this article, and any/everyone can edit from there in mainspace. Feel free to revert. Maschen (talk) 11:09, 18 November 2012 (UTC)
I'm not entirely at ease with the rotor diagram as it stands, but as you say, it's better than nothing. And it'll hopefully prompt suggestions; finding diagrams that intuitively explain rotors is not easy. I have an idea for illustrating reflection on a vector in term of the commuting and anticommuting split, and once we have that nailed we can think of building a rotor out of two reflections. — Quondum 12:52, 18 November 2012 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── Certainly by all means, but are you sure that what you said (illustrating reflection on a vector in term of the commuting and anticommuting split) is not adequately covered in the diagrams already in the GA article (geometric interpretation section)? I assume that you mean to incorperate this into a new rotor diagram, which does sound like a good idea.

Also (I'm hypocritical) but anything more on GA should be in a new thread over there... Maschen (talk) 13:01, 18 November 2012 (UTC)

1. ^ [1]