Talk:Ptolemy's inequality
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Alternative statement[edit]
The lead, after giving one statement of the inequality in terms of a quadrilateral, goes on to say
- Alternatively, the three products of opposite sides or of [previously, "opposite"] diagonals must obey the triangle inequality.[1]
I'm not clear on the word "alternatively". Is this a statement of an alternative theorem with the same name? Does it simply mean "equivalently"? Or is this a generalization? It looks to me like a generalization, since the original quadrilateral statement has the product of diagonals isolated on one side. Loraof (talk) 16:19, 9 June 2016 (UTC)
- It's an equivalence. Any ordering of the four points can be interpreted as a quadrilateral, so there is no difference between the sides and the diagonals as far as the inequality is concerned. —David Eppstein (talk) 19:53, 9 June 2016 (UTC)