Wikipedia:Reference desk/Mathematics

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July 3[edit]

July 5[edit]

How to categorize these images?[edit]


I recently uploaded these two images to supplement the four referenced in the Fundamental polygon article. What categories should I put them in? In particular, I don't know if they're actually fundamental polygons or not: it's been a while since I've proven that something is a closed surface. Jbeyerl (talk) 17:37, 5 July 2014 (UTC)

It's not definite, but I lean against those ending up being manifolds. The group representation for the first would be A2 = 1, and the second would be A2B−2 = 1. — Arthur Rubin (talk) 01:17, 8 July 2014 (UTC)
A2 = 1 is the projective plane. For the second, by cutting diagonally from the top left to the bottom right, then gluing along A, you get the standard presentation of the Klein bottle.--Antendren (talk) 04:42, 8 July 2014 (UTC)

July 6[edit]

July 7[edit]

July 8[edit]

How does this graph work? How is it possible?[edit]

This is the weirdest real-life graph I've ever seen: [[1]]
IMF Staff Discussions Note: Emerging Markets in Transition: Growth Prospects and challenges.
[2] (bottom of page 4)
— Preceding unsigned comment added by (talk) 11:32, 8 July 2014 (UTC)

Graphical representations of parametric equations often look like that. Dolphin (t) 12:22, 8 July 2014 (UTC)
Thank you for that. It did help shed a bit of light and introduced me to paramtric vs non-parametric equations :) I guess there wasn't a proper function in this graph, it was just simply data points plotted and therefore the line we see in the graph is a bit misleading because we could join the 'dots' in any way we like. (talk) 14:22, 8 July 2014 (UTC)
The dots are joined in chronological order. You can see the years marked next to each location in the graph. -- Meni Rosenfeld (talk) 15:45, 8 July 2014 (UTC)
That graph doesn't seem to show a case where one axis variable is strongly dependent on the other, which is what is most familiar (for example, population is strongly dependent on time). If you plot two largely independent values, the graph will take on a rather random look (for example, sound volume versus frequency in a piece of music). Such graphs seem less useful, to me. I'm not sure how you are supposed to use it to predict anything. StuRat (talk) 14:30, 8 July 2014 (UTC)
Such a graph can help you tell whether the variables are independent. —Tamfang (talk) 04:52, 9 July 2014 (UTC)
It isn't intended to predict anything; it simply provides an easily read display of how the two variables related to each other at different times. It's no different in principle than plotting the path followed by a vehicle or a person over time, like this map or this map... except that with a map, latitude and longitude are obviously related, whereas with a graph showing two functions over time, their relationship may not be obvious. — Preceding unsigned comment added by (talk) 06:22, 9 July 2014 (UTC)

July 9[edit]

July 10[edit]

Lie algebras of U(p, q)[edit]


Which, if any, is correct?

\mathfrak{u}(p, q) = \left\{\left .\left(\begin{matrix}X_{p \times p} & Z_{p \times q} \\ -\overline{Z}^{\rm{T}} & Y_{q \times q}\end{matrix}\right)\right| \overline{X}^{\rm T} = -X,\quad \overline{Y}^{\rm T} = -Y\right\}.
\mathfrak{u}(p, q) = \left\{\left .\left(\begin{matrix}X_{p \times p} & Z_{p \times q} \\ +\overline{Z}^{\rm{T}} & Y_{q \times q}\end{matrix}\right)\right| \overline{X}^{\rm T} = -X,\quad \overline{Y}^{\rm T} = -Y\right\}.

I have one opinion and my reference another about the +/- sign in the lower left. YohanN7 (talk) 21:29, 10 July 2014 (UTC)

July 11[edit]