Wikipedia:Reference desk/Archives/Mathematics/2013 September 7

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

September 7

3D Protractor

Hello. Is there such thing as a 3D protractor, an instrument that can help one build a physical molecular model? Thanks in advance. --Mayfare (talk) 16:26, 7 September 2013 (UTC)

Positioning goniometer may possibly help. Duoduoduo (talk) 16:53, 7 September 2013 (UTC)

Precise angular positioning is done in Stereotactic surgery. Here is an example of such a three-dimensional protractor. But such devices are not common and tend to be expensive. --Mark viking (talk) 20:05, 7 September 2013 (UTC)

What are you do if I give $ 1 Millon ?

close request for opinion per talk desk consensus
The following discussion has been closed. Please do not modify it.
What are you do if I give $ 1 Millon ? — Preceding unsigned comment added by 37.238.8.188 (talk) 19:43, 7 September 2013 (UTC) Give me ten million dollars, and I will build a math institute in the south of France. With one million, I suppose I would settle for a tenth of a math institute. Sławomir Biały (talk) 00:19, 8 September 2013 (UTC) See here. Count Iblis (talk) 00:48, 8 September 2013 (UTC) Well, in my mind you do raise a point that you may or may not have intended: to what extent do you (in the generic sense) consider the Fields medal—and possibly other similar prizes—to be a fraud? Sławomir Biały (talk) 02:18, 8 September 2013 (UTC) I can't judge this for mathematics, but for theoretical physics the Fields medal is a good thing, you can win this prize for working on mathematical physics subjects like e.g. Edward Witten, Wendelin Werner, Stanislav Smirnov have done, a Nobel Prize is not going to be awarded for such work. Count Iblis (talk) 13:10, 8 September 2013 (UTC) That's interesting. Are you a theoretical physicist, Count Iblis? Widener (talk) 03:31, 9 September 2013 (UTC) Yes, and my subfield field are certain subjects that fall within mathematical physics, so a Nobel Prize is unfortunately not in the cards for me :). A lot of what is now rigorous math that is practiced by "real mathematicians" (instead of physicists who tend to do things less rigorously) originally started out as pure physics subjects in which things were not done rigorously. Take e.g. the results obtained by Stanislav Smirnov that earned him the Field Medal. This is about percolation and the fact that in 2 dimensional systems you have conformal invariance in the scaling limit. A lot of results had been obtained by invoking conformal invariance, but there was not a rigorous mathematical proof that such a system is indeed conformally invariant. Smirnov obtained a proof for percolation the triangular lattice. Count Iblis (talk) 12:51, 9 September 2013 (UTC) There's nothing wrong with stimulating people, but prizes are for children, not grown-ups. Have either Newton, Euler, or Gauss ever won any "medals" or money for their countless results, proofs, and conjectures ? If any of them would've won such a sum for each of their ground-breaking discoveries, global economy would've been plummeted to the ground... :-) — 79.113.209.204 (talk) 19:32, 10 September 2013 (UTC) The OP is free to clarify his request, but we do not provide opinions void of references or links to WP articles. μηδείς (talk) 03:53, 12 September 2013 (UTC)

2D shell theorem?

Shell theorem says it applies to spherically symmetric objects. If I limit it to two dimensions does it apply to radially symmetric objects? (I can't write the problem in a form I can find the integral for.) RJFJR (talk) 21:29, 7 September 2013 (UTC)

There is a version of the shell theorem that holds in any dimension, but with the appropriate Newtonian potential. In three dimensions, this is a 1/r law (for the potential) or equivalently a 1/r² law (for the force). In two dimensions, on the other hand, it's a log(r) law (for the potential) or equivalently a 1/r law (for the force). (In n≠2 dimensions, the potential is $Cr^{n-2}$ for some constant C depending only on the dimension.) You can get from the three dimensional to the two dimensional result by dimensional reduction (extend a two dimensional body to an infinite cylinder in three dimensions by adding a z axis). Hope this helps, Sławomir Biały (talk) 00:16, 8 September 2013 (UTC)

Thank you very much. RJFJR (talk) 01:44, 8 September 2013 (UTC)

Not $Cr^{2-n}$? — Preceding unsigned comment added by 109.144.249.84 (talk) 00:12, 9 September 2013 (UTC)

Yes, I meant $C/r^{n-2}$. Sławomir Biały (talk) 00:30, 9 September 2013 (UTC)

I'd say it applies to any disc as long as the other object in question is also in the plane of the disk. Integrating shouldn't be that hard.--Jasper Deng (talk) 00:27, 9 September 2013 (UTC)

Not with the usual gravitational field, no it doesn't. (It's true with a 1/r force law rather than a 1/r² force law). To see that it doesn't work with the usual gravitational field, take a thin plate of unit mass density concentrated in the plate $r\leq 2R\cos \theta ,-\pi /2\leq \theta \leq \pi /2$ (of radius R, written in polar coordinates). The (standard) gravitational field exerted by this plate on a unit mass concentrated at the origin has y-coordinate zero and x-coordinate given by

$\int _{\text{disc}}{\frac {\cos \theta }{r^{2}}}\,dA=\int _{-\pi /2}^{\pi /2}\int _{0}^{2R\cos \theta }{\frac {r\cos \theta }{r^{3}}}\,r\,dr\,d\theta$

which diverges. Sławomir Biały (talk) 01:03, 9 September 2013 (UTC)