Talk:Diagonal

message: We know the pattern for the number of diagonals in an n-gon, but how about the number of regions determined by the number of diagonals??
To make sure you know what I mean, here are some examples:
*A circle determines 2 regions, the inside and the outside.
*A checkerboard determines 65 regions, the squares and the area outside the lines.
A regular hexagon has 25.  A general hexagon, assumed to have no more than two diagonals intersecting at any point (other than a vertex) has 26.  The general position is already done for us http://www.research.att.com/projects/OEIS?Anum=A027927 . -- Smjg 11:08, 26 May 2004 (UTC)
replies: text: The formula will depend on whether n is even or odd.  We need to look at the number of common intersections of three or more diagonals.  Each point where three diagonals intersect loses one region, each point where four diagonals intersect loses three regions, and where d diagonal meet there are ½(d-1)(d-2) regions lost.  For the regular hexagon this is simple because the only multiple intersections (other than at the vertices) are the three diagonals in the centre, where just one region gets lost.  I'm trying to prove that when n is odd it is not possible for more than two diagonals to intersect at a point inside the polygon, and I'm thinking about a formula for bigger regular n-gons where n is even, but the situation gets more complicated as further symmetries emerge.  For example, I think 82 regions are lost for the regular dodecagon, but this reduces to 57 regions lost for a regular 14-sided shape because 14 has fewer factors than 12.  There are some experts on the Mathematics reference desk who will soon solve this if you wish to copy it there.  Dbfirs 10:02, 10 April 2011 (UTC)
thread_title: Challenging Question: 2 for a triangle, 5 for a square, 12 for a pentagon...

message: I've made a new section on diagonal functors.  These are not very related to other more geometrical notions of diagonals.  If I could find enough stuff to write about them to fill an article, I wouldn't mind splitting to diagonal functor (currently a redirect to here).  What you guys think? -lethe talk [ +] 23:01, 2 April 2006 (UTC)
replies: text: Yeah, I think you're right.  It doesn't belong in this article.  I've moved it to its own article, and left a "see also" link.  -lethe talk [ +] 04:21, 23 April 2006 (UTC)
thread_title:  split diagonal functors 

message: The following was removed wholesale. I thought some of it could be saved and put into the "non-mathematical" use, but I couldn't find a general quote that it was a term used by more than one eccentric director. If it is a term in general use in the theatre, then I think it would be worth listing under the "non-mathematical uses" Mike 10:20, 19 March 2007 (UTC)
thread_title:  Theatre 

message: This user recently discovered the general use for the diagonal formula. It's pretty insane to think of streaming to dimensions above three.
http://www.mathhelpforum.com/math-help/f13/general-diagonal-formula-191707.html
Scroll down until you see proofs.
Is this valid for the article?  — Preceding unsigned comment added by Briandiaz (talk • contribs) 18:25, 13 November 2011 (UTC)
thread_title:  General Diagonal Formula 

message: I have reverted the following nonsense which was added to this article:
45^\circ\sum_{n=1}^346x\begin{array}{|c|c|c|} a & b & S \\ \hline 0&0&1\\ 0&1&1\\ 1&0&1\\ 1&1&0\\ \end{array}\underbrace{ a+b+\cdots+z }_{10478}A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C\alpha\left ( \frac{1\! t}{2} \right )\textstyle \lim_{6 \to 103} \displaystyle\overbrace{ 1+2+\cdots+100 }^{5050}{}_pF_q\left({a_1, \ldots, a_p \atop b_1, \ldots, b_3}; z\right)\log_{13}(63)343\! 102\overbrace{ 1+2+\cdots+100 }^{\mu}f(n) = \begin{cases} n/2, & \text{if }n\text{ is even} \\ 3n+1, & \text{if }n\text{ is odd} \end{cases}\phi
Samboy (talk) 06:59, 26 March 2022 (UTC)
thread_title:  Nonsense reverted 

message: User  (talk · contribs) has recently made several edits to this article. They introduced at least one clear error: the article previously noted that the longest diagonals of a regular n-gon coincide at its circumcentre when n is even, but the edit removed this qualification.
I nearly reverted all of the edits, for this reason and for some issues with formatting (like using asterisks for multiplication), but then I thought that this might be a bit hasty, not to mention hostile to a relatively new editor. So instead I (re-)added a mention of n needing to be even, and I'm bringing the matter here for discussion.
It should perhaps be noted that other edits by this user to related articles (Face diagonal, Space diagonal) have been reverted, with reverter comments "WP:OR, nonstandard use of terms" and "Dubious, uncited, & very broken formatting". -- Perey (talk) 14:47, 1 July 2023 (UTC)
thread_title:  Edits by AvrhUFfvr