Talk:Perko pair
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wouldn't it be nice if ...
[edit]... the article had a picture of the shortest such knot of unit thickness? —Tamfang (talk) 06:21, 10 March 2014 (UTC)
Is the illustration correct?
[edit]Richard Elwes writes that many sources get the Perko pair incorrect, by copying a pair of knots with the numbers of the Perko pair from a source that had been renumbered after the discovery of the Perko pair. Has anyone checked whether ours is one of the correct or the incorrect ones? The drawings in the current version of the article don't look a lot like anything in Elwes' post to me. —David Eppstein (talk) 01:09, 15 April 2014 (UTC)
- The images, created by User:C S, are described as follows:
- "Knot labeled 10_161 in Rolfsen knot table. The first of the infamous Perko Pair."
- "Knot labeled 10_162 in Rolfsen knot table. The second of the infamous Perko Pair."
- and both where made using Knotscape. Hyacinth (talk) 11:36, 23 April 2014 (UTC)
- Yes, but the question is: which edition of the Rolfson table? Before or after the correction and renumbering? —David Eppstein (talk) 15:53, 23 April 2014 (UTC)
[1] Yes, it's one of many correct alternatives illustrated in scores of books and papers. Elwes' book is the only one to get what I call "the Weisstein Pair" instead -- 10-161 and (the mirror of) Rolfsen's original 10-163. The screwed up version is still available for laughing at on Wolfram Web's MathWorld "Perko Pair" page. --Kenneth A. Perko, Jr. (lbrtpl@gmail.com)
- Thanks! Your expertise is very welcome here. —David Eppstein (talk) 21:04, 6 June 2014 (UTC)
There is a special place in Hell for mathematicians who renumber knot tables. --K. Perko.
More images, and chirality
[edit]More images of the Perko pair can be found here, as well as details about its chirality Columbus8myhw (talk) 17:15, 16 December 2018 (UTC)