User talk:Maschen

Figures

Hi, your might, or might not be interested in my proposal/plea? User_talk:Cjean42#More, please? to Cjean42. He is scarce on this site, but, if the spirit moved you to do this sort of thing... it could be helpful. Apologies if your past agility has spoiled me with expectations. Cuzkatzimhut (talk) 20:34, 13 February 2017 (UTC)

Sorry for more inactivity, I'll look into this and try and create with something, may take a couple of days... M∧Ŝc²ħεИ_τlk 17:05, 20 February 2017 (UTC)

Thanks, update is perfect. Linked it to a bevy of pages, as you may observe... Cuzkatzimhut (talk) 19:30, 21 February 2017 (UTC)

Nice to know it is useful, thanks for the kind feedback as always! M∧Ŝc²ħεИ_τlk 20:56, 21 February 2017 (UTC)

Me again; no, not greedy. Really, really low priority... for a rainy day... It struck me that Fig 7a or 7b, quadrilateral, or tetrahedron, on p 112 of M E Rose's Elementary theory of angular momentum, ( can you access this? ), might be really instructive for the article Racah W-coefficient. A picture is sometimes worth a thousand words... I could write the label, if desired... something like a=j1, b=j2, d=j3, c=j , f=j23, e=j12, or something more descriptive. Just a thought. Some people with a weak memory buffer like me are helped by geometric thinking... I am suprised I could not find something of the sort in Wikimedia, but maybe I can't search right... Cuzkatzimhut (talk) 16:35, 13 March 2017 (UTC)

Hi, sorry for delay, yes I can access the book (just about, some pages do not show up, but 112 does). I'll reproduce the figure a.s.a.p M∧Ŝc²ħεИ_τlk 13:13, 17 March 2017 (UTC)

Angular momenta in the Racah W coefficients. The top is a 2d plane projection as a quadrilateral, the bottom is a 3d tetrahedral arrangement.

No, you are not greedy, I have hopelessly fallen out of WP routine... Here it is, if you would like to split the image into two or just use one or the other (quad or tetrahedron), let me know. M∧Ŝc²ħεИ_τlk 13:36, 17 March 2017 (UTC)

Wow! Thanks again, on behalf of WP readers... Cuzkatzimhut (talk) 14:06, 17 March 2017 (UTC)

You're very welcome!

All the references you have shown (Whitham's linear/nonlinear waves, Lee's particle physics, now Rose's angular momentum) look brilliant! (YohanN7 often provides excellent refs also). Will read into them more... M∧Ŝc²ħεИ_τlk 17:33, 17 March 2017 (UTC)

Figure request

Hi... it's been a long time! I still don't know how to make 3D pictures with software. If you had the time, could you try something for me? I would like several images based on this diagram. Ideally

• one would just be a cleaned up rendition of what you see
• one would colorize the cube with the label $\mathbb {H}$ in the same color.
• one would colorize the plane through the middle of the cube with the label $\mathbb {R} ^{3}$ in the same color.
• one would colorize the upper hemisphere with the label $SO(3)$ in the same color.
• one would colorize the circular intersection of the hemisphere with the plane with the label $S^{2}$ in the same color.
• one would present all the labels at once with different colors and appropriate translucency, (except for the cube perhaps, which would remain transparent and use a black label.)

What do you think? Might you be able to do this favor for me, even if it is just the last item on the list? It's a diagram for a talk I'm giving to nonmathematicians. Maybe you can even spot inaccuracies in it, but I feel like it will do a good job. Please let me know what might be possible: thank you Rschwieb (talk) 20:09, 22 March 2017 (UTC)

So sorry for late reply, I'll try an SVG version now. Hope it's not too late for your talk... M∧Ŝc²ħεИ_τlk 08:38, 25 March 2017 (UTC)

Here, let me know of improvements/corrections. M∧Ŝc²ħεИ_τlk 09:50, 25 March 2017 (UTC)

Wow, that looks great! I wasn't sufficiently clear about the circle, though. The region that represents $S^{2}$ is actually just the perimeter of the circle and not the whole disc. If you could light up that circle in orange and move the label arrow to point at it, then I think we're good! Rschwieb (talk) 11:11, 25 March 2017 (UTC)

Sure, sorry, fixed now. If R³ is shown as a plane, I should have realized that S² is the circle without interior, since the interior would be the volume of a 3d sphere.

Out of interest what is the figure exactly for? Seems like quaternions and their connection to SO(3), in a lower dimension. M∧Ŝc²ħεИ_τlk 12:07, 25 March 2017 (UTC)

This is awesome! To answer your question, I'm trying to provide a visual aid for my fellow employees (roboticists and software engineers) who might not know how to visualize quaternions and their relationship to 3-dimensional geometry. I want to relate the picture to the ones that can be drawn for 1- and 2- dimensional geometry (which I'm requesting below too.)

The aim is to illustrate what quaternions are the model of 3-space, which ones are doing the transformation, and finally to convey that there are a lot of other quaternions we just don't have to think about when using them for geometry.

You're right: everything in this beautiful diagram you've drawn is "compressed" by a dimension so as not to blow the viewers' minds :) I feel like I might have seen this picture somewhere before, but I couldn't dig it up, and besides that it was probably in black and white in a book.

I will be sure to send you a copy of the presentation (there shouldn't be anything proprietary at all, so that should be fine.)

I feel bad for followup requests, but I really hope they are pretty simple to do:

• First, can you add the point that is the center of the sphere?
• Secondly, two other diagrams:
  • A line with 0 and 1 marked, and labeled $\mathbb {R} =\mathbb {R} ^{1}$, and a label of $SO(1)$ for the point 1.
  • A plane labeled $\mathbb {C} =\mathbb {R} ^{2}$ and a circle with center marked, and a label on the circle $SO(2)$.

I'm purposefully omitting labels for $S^{0}$ and $S^{1}$ in these two diagrams. They aren't really as relevant as $S^{2}$ is in the third diagram. 14:36, 27 March 2017‎ Rschwieb (talk)

That's interesting, had a feeling it was to do with quaternions. As mentioned before, I hope I am not too late creating them.

Please don't worry about the follow up requests! I'll try and get them done this evening.

BTW I added your signature, it wasn't signed. M∧Ŝc²ħεИ_τlk 12:36, 28 March 2017 (UTC)

Had a chance to get them done now. Feedback is welcome. For the SO(2) case are you sure you didn't mean the interior of the circle to be coloured in and labelled SO(2), while the boundary would be S¹? M∧Ŝc²ħεИ_τlk 13:17, 28 March 2017 (UTC)

Also for the SO(1) case, are you sure the interval 0 < x < 1 for real x is not to be a coloured line segment labelled SO(1), while the end points (would be) labelled as S⁰? I can re-colour things to match the original diagram. M∧Ŝc²ħεИ_τlk 16:42, 28 March 2017 (UTC)

No, you are not too late: the talk is in mid April, and I wanted to be sure not to be begging you at the last minute. These are all great!

For both $SO(1)$ and $SO(2)$ I'm pretty sure I mean just the surface of the discs and not the interiors. In the complex plane, it's just the items on the perimeter of the disc which produce rotations (things on the interior rotate and make the plane contract.) Same for the real line: the only orthogonal transformation that preserves the orientation of the line is the identity transformation (-1 produces a reflection.)

In the 3-d diagram I requested, I am also only talking about the surface of that hemisphere :) I can't think of a good way to emphasize that, nor do I think it is very important given that I can clear it up verbally. Rschwieb (talk) 16:02, 2 April 2017 (UTC)

OK, no worries, glad you like them! ^_^ M∧Ŝc²ħεИ_τlk 08:07, 3 April 2017 (UTC)