Talk:Robbins pentagon
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This article begins as follows:
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- A Robbins pentagon, named after David P. Robbins, is a cyclic polygon with five integer sides and integer area. It also has the property that all its diagonals are rational,
Does that mean: a) Rationality of diagonals is a logical consequence of being cyclic and having integer sides and integer area; or b) A cyclic pentagon with integer sides and integer area fails to qualify as a Robbins pentagon unless it also has integer diagonals? Michael Hardy (talk) 22:38, 26 May 2009 (UTC)
- The first option is correct, even stronger so, correct me if I'm wrond, cyclicality of the pentagon and rationality of the sides implies rationality of the area AND implies rationality of the diagonals, at least, that is my interpretation of Ezra A. Brown and Ralph H. Buchholz, 'Cyclic pentagons with rational sides and area', April 13, 2009. Undoubtly, you can cast your expert opinion on that, or just perfect the wording in english Dedalus (talk) 10:15, 29 May 2009 (UTC)
- No, rationality of diagonals doesn't always follow. Theorem 8 (p. 20) states that, "Any Robbins pentagon has either zero or five rational diagonals." Thus, the authors allow the possibility that all diagonals are irrational. Titus III (talk) 19:13, 17 February 2016 (UTC)
- As I think the article now makes clear (having undergone some improvement since 2009), it is conjectured, but not proven, that the diagonals are always rational. —David Eppstein (talk) 19:26, 17 February 2016 (UTC)
- No, rationality of diagonals doesn't always follow. Theorem 8 (p. 20) states that, "Any Robbins pentagon has either zero or five rational diagonals." Thus, the authors allow the possibility that all diagonals are irrational. Titus III (talk) 19:13, 17 February 2016 (UTC)