Wikipedia:Featured picture candidates/Inner radius

Inner radius

Voting period is over. Please don't add any new votes. Voting period ends on 12 Nov 2012 at 10:51:44 (UTC)

Original – The circumradius (blue) and inner radius (green) of a set (dark red, with its convex hull shown as the lighter red dashed lines). The inner radius is smaller than the circumradius except for subsets of a single subset (a disc), for which they are equal.

Reason: Best illustration and perhaps the only illustration in the literature, which simply uses the definitions (without illustration). The distinction between inner radius and circumradius explains why the Shapley–Folkman–Starr theorem is an improvement over the Shapley–Folkman theorem.
Articles in which this image appears: Shapley–Folkman lemma
FP category for this image: Mathematics
Creator: David Eppstein

Support as nominator --Kiefer.Wolfowitz 10:51, 3 November 2012 (UTC)[reply]
Support, educational and encyclopedic. Also, SCIENCE! — Cirt (talk) 17:17, 3 November 2012 (UTC)[reply]
Comment: I'd like to see some verification provided. I assume there is some academic paper or textbook that could be cited to show that the information presented is correct. Grandiose (me, talk, contribs) 11:44, 4 November 2012 (UTC)[reply]
Reply The information is correct because it simply applies the definitions found in the original article (Starr). I understand that supremum and infimum operators are difficult to understand for persons who've not studied university mathematics; you could ask at the WikiProject Mathematics for additional confirmations. However, Jacob Scholbach, Geometry guy, and other mathematicians have scrutinized the article as it went through GA and A class nominations (successful) and its FA nomination (unsuccessful, because of failure on "brilliant prose"): Perhaps you could first scan those nominations and judge the comments about the content and its being based on reliable sources, before asking for new confirmations? (In response to your query, I left a notice at the WikiProject Mathematics.) Sincerely, Kiefer.Wolfowitz 10:13, 5 November 2012 (UTC)[reply]
There is a little more detailed explanation of correctness that can be given. The outer circle is optimal because it has three points forming an acute triangle on its boundary; enclosing all three of these points by a different circle would be larger, regardless of whether it contains any of the other points. For the same reason the inner circle can't be changed to be near to its current position without making it smaller. and in the other parts of the point set the points are placed so densely as to make it obvious that there is no larger inner circle anywhere else. —David Eppstein (talk) 15:51, 6 November 2012 (UTC)[reply]
Comment A (now retired) member of the WikiProject Images and Media wrote "All I can say about its illustrations is that 'I am impressed'. Excellent.", in response for a request for an evaluation. Kiefer.Wolfowitz 11:14, 5 November 2012 (UTC)[reply]

Hmm, the criteria were a little more lenient on this point than I'd expected - they allow for verification in the article. Whilst I am uncertain whether that ought to be allowed, it clearly is. I'm certain this is supported by the sources in the article. Support. Grandiose (me, talk, contribs) 11:47, 5 November 2012 (UTC)[reply]
This seems to me to be a self-evident illustration of the concepts. The set is finite (and hence compact), and so the extrema are attained: The radii can be confirmed using a protractor (as in sophomore geometry in US high schools). The inequality of the radii is obvious. What is your concern? Kiefer.Wolfowitz 12:14, 5 November 2012 (UTC)[reply]

Sorry, I should have replied sooner. My concern is with verifiability. One man's self-evident is different to another man's, surely a princple we apply to articles all the time. For me to be able to verify the image, I'd need to look at an outside work, a book or article. Now I was under the impression, when I first commented, that such verification had to be given on the image page, but I was mistaken. In this case, it is clearly provided in the article and its sources. Grandiose (me, talk, contribs) 16:31, 6 November 2012 (UTC)[reply]

Not Promoted --Makeemlighter (talk) 00:22, 13 November 2012 (UTC)[reply]