Talk:Degeneracy (mathematics)

message: I've never heard of the noun "degeneracy" in this context. I think the page should be moved to Degenerate case. nadav (talk) 22:16, 30 May 2007 (UTC)
replies: text: I agree. Any objection to my doing so? Duoduoduo (talk) 22:35, 29 August 2013 (UTC)

text: I agree as well; encyclopedia entries are almost always under a noun if possible, and this should be no exception, for the same reason the page about economies isn't named "Economic". Hppavilion1 (talk) 23:04, 5 April 2017 (UTC)
replies: text: It's already under a noun. Degeneracy is a noun. The adjective is "degenerate". —David Eppstein (talk) 23:25, 5 April 2017 (UTC)
thread_title: Move to better title?

message: Is a regular tetrahedron considered a degenerate antiprism?  It doesn't fit the "usually simpler" of the lede, as its symmetry group is higher. —Tamfang (talk) 19:59, 6 September 2009 (UTC)
replies: text: You could well think of it as one, where the two opposite faces normally found at either end of an antiprism have become line segments. Macbi (talk) 15:16, 27 June 2010 (UTC)
replies: text:  A tetrahedron doesn't follow any of the rules of an anitiprism: It has four vertices so if it has 2p vertices, p=2, but it doesn't have 4p=8 edges. I think a triangular antiprism made of 2+2*3=9 triangles is the degenerate antiprism. If you try to go for smaller p, then you wind up with something other than an antiprism. —Ben FrantzDale (talk) 11:04, 28 June 2010 (UTC)
replies: text:  There's nothing degenerate about the triangular antiprism. —Tamfang (talk) 03:05, 30 June 2010 (UTC)
replies: text:  It doesn't start acting weird if that's what you mean by degenerate, but it seems like it's at least the base case of  an antiprism in that I don't see a well-defined antiprism coming from extruding a line segment. Whereas simply extruding a line segment gives a plane which seems to me like an unambiguous degenerate prism (although one could question whether it is a prism since it has no volume), forming an antiprism from a line segment seems like it would either be a simplicial complex of two triangles or it would be a mess of four triangles back to back with a criss-cross in the middle. The whole thing would be forced to be planar and so the four triangles would really be one quadrilateral (depending on if you are thinking about the topology or an embedding in R^3.  —Ben FrantzDale (talk) 13:47, 30 June 2010 (UTC)
replies: text:  'Degenerate' does not mean 'simplest'; it would be more accurate to say 'degenerate' means lacking some property of the general case. Taking an example from the article's list: a parabola reflects parallel rays into a single point, but a degenerate parabola (line) does not. —Tamfang (talk) 06:05, 1 July 2010 (UTC)
replies: text:  I would say that a regular tetrahedron is a degenerate antiprism. Instead of a shape at the ends, it's a line. The definition of a antiprism is simply that the base is rotated 90 degrees and moved upwards, then connected by triangles right? Do that to a line, and you get a regular tetrahedron, just somewhat rotated. If it fulfills the definitions, it's still part of the group right? I think the definition might need to be changed in the main article to be more clear. 218.186.9.246 (talk) 17:28, 18 July 2010 (UTC)
replies: text:  Not 90° (consider the square antiprism) but 180°/N; for the figure in question, N=2. —Tamfang (talk) 07:56, 23 July 2010 (UTC)

text:  Tamfang, a line reflects parallel rays to the point at infinity. Degenerates preserve properties. 60.230.216.143 (talk) 16:43, 6 April 2015 (UTC)
thread_title:  Antiprisms 

message: [I've extracted this conversation out from the above section to make it easier to follow —Pengo 23:18, 7 October 2010 (UTC)
replies: text: I put  on the torus comment. —Ben FrantzDale (talk) 11:04, 28 June 2010 (UTC)

text: A sphere is a torus whose major radius is zero. —Tamfang (talk) 03:05, 30 June 2010 (UTC)
replies: text:  Isn't a torus (by which I mean a 1-torus) genus 1 whereas a sphere is genus 0? The whole identity of a one-torus hinges on the fact that it can't be continuously deformed into a sphere. Or am I misunderstanding? —Ben FrantzDale (talk) 13:47, 30 June 2010 (UTC)
replies: text:  If self-intersection is forbidden, yes, the torus cannot be deformed to a sphere; but if self-intersection is allowed, then the sphere is the limit case of an "apple" torus. Its surface is "wrapped twice" (the poles are like branch points of a Riemann surface), so it's not a topological sphere, but it is still the set of points at equal distance from a center and the set of points at equal distance from a (degenerate) circle.  —Tamfang (talk) 06:08, 1 July 2010 (UTC)
replies: text: So is this dubious then?  Even torus lists the sphere as a degenerate case.  Both statements are admittedly unsourced, but are they dubious?  Should we remove the example.  Or maybe change it to "In some contexts, a sphere is a degenerate torus."?  ~a (user • talk • contribs) 21:36, 20 July 2010 (UTC)
thread_title:  Degenerate torus 

message: Hi,
is there an "inverse concept" ("generacy"?) or an antonym associated with this concept?
T 88.89.144.233 (talk) 16:01, 29 August 2013 (UTC)
replies: text: I think the most commonly used adjectival antonym would be non-degenerate, as in a non-degenerate parabola. The noun (less commonly used) would be non-degeneracy. It's possible that someone might use proper as in a proper parabola, but I'm not sure about that. Duoduoduo (talk) 16:21, 29 August 2013 (UTC)
replies: text: If "non-degenerate" is commonly used as antonym, then that is a sign that degenerate is not the same as non-generic. Because in that case I guess the antonym of degenerate would be generic? Isheden (talk) 11:54, 30 August 2013 (UTC)
thread_title:  Antonym? 

message: *I have written a program to handle and edit CGI meshes that describe objects, and in it digon and monogon polyhedron faces sometimes arise, and need to be eliminated when I garbage-collect the mesh. Faces where 2 or more vertexes coincide sometimes arise, and at garbage-collection such faces are tidied and if necessary divided into 2 or more polygons. Also, when a new face must be started, it starts as creating a monogon, and the user must insert quickly 2 more vertexes in it. Anthony Appleyard (talk) 05:52, 11 May 2017 (UTC)
thread_title:  A practical case of monogons and digons 

message: the article says a degenerate triangle has two 0 angles and one 180 degree angle, but wouldnt you call it a degenerate triangle too if two vertces are identical? then the angle wouldnt be defined  — Preceding unsigned comment added by 80.187.101.112 (talk) 10:24, 15 January 2018 (UTC)
replies: text: Good remark.  D.Lazard (talk) 11:27, 15 January 2018 (UTC)
thread_title:  Degenerate triangle