Talk:Digon

message: "Physically impossible"? Mathworld has an illustration of a digon, along with a very different definition: "The digon is the degenerate polygon (corresponding to a line segment) with Schläfli symbol { 2 } ." Also, Dr. Micah Fogel at the Illinois Mathematics and Science Academy defines digons (and monogons) as "two special curved polygons that have no analogs among polygons with straight edges." Clearly a straight-edged digon would be physically impossible -- but do polygons necessarily have to have straight edges? Could two points connected by two curved lines qualify as a digon?  The University of Wisconsin Oshkosh has a website discussing, "the two-sided polygon called a lune," including illustrations on how to calculate the area of such two-sided polygons. I'm not a mathematician, but after just five minutes of google searches I've found at least three sources that seem to be at-odds with the wikipedia definition. Could someone more knowledgeable about geometry expand (and correct, if need be) this article? 66.17.118.207 16:54, 6 June 2006 (UTC)
thread_title:  comment

message: I don't think it makes sense to distinguish a regular digon. That is to say all digons on the sphere are regular since the edges must be great circles and two nonparallel great circles must intersect on two opposite points.
If there's no opinions, I'll remove the regular claim. Tom Ruen 01:23, 21 December 2006 (UTC)
replies: text: Okay, I got creative, expanded an explantion of digons in polyhedra for Wythoff constructions. It might get a little off topic, but it was a pretty short article with just a definition! Tom Ruen 02:12, 21 December 2006 (UTC)
thread_title:  regular digon? 

message: Didn't we all agree to let digons be bygones? McKay 05:40, 11 January 2007 (UTC)
thread_title:  Oh no! 

message: Someone left this in the main article. I don't really know what to do with it other than shunt it here, perhaps...
"I'm confused. What does a digon look like exactly?"
92.2.100.60 (talk) 08:29, 13 March 2010 (UTC)
thread_title:  Digon images 

message: If a circle is not degenerate then neither is a digon. If a digon was degenerate then why can you project a 3d digon on a 2d screen? Other shapes with two sides can be found in Euclidean geometry, a crescent for example two sides.  —Preceding unsigned comment added by 88.106.85.18 (talk) 14:27, 10 July 2010 (UTC)
replies: text: No, the point is that a digon with straight lines is degenerate. With curves it is not really a polygon (and hence not really a digon). Double sharp (talk) 15:53, 27 March 2013 (UTC)

text: It's a matter of geodesics to define "straight lines". In Euclidean space, there's only a single minimum length path (a straight line) between two points, so a digon can be defined only if it is degenerate. However on curved surfaces, like a sphere or torus, there can be two or more different minimum length paths, and so the digon can be defined with two different edge paths. But even on a sphere, two arbitrary points won't be antipodal, and so will also be degenerate. Tom Ruen (talk) 17:23, 27 March 2013 (UTC)
thread_title:  The digon is not degenerate in Euclidean Geometry 

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thread_title:  External links modified