Talk:Co-cyclic quadrilateral

Duoduoduo, if you agree on my removal of this name as a synonyme for tangential quadrilateral, I suggest that you move this page to a new name (i.e. rename it). Then move it to "Concyclic quadrilateral" and make it redirect to "Cyclic quadrilateral". Circlesareround (talk) 08:16, 5 April 2012 (UTC)


 * Victor Bryant and John Duncan, "Wheels within wheels", Mathematical Gazette 94, November 2010, 502-505 says


 * Dually, a quadrilateral is co-cyclic (or inscribed) if there is a circle that is touched by all of its four sides.


 * Shortly after saying that, they give a "key fact" with a diagram of a tangential quadrilateral referred to as "co-cyclic", and with a citation to Heinrich Dorrie, 100 Great Problems of Elementary Mathematics, Dover, 1965 with no page reference. Unfortunately I no longer have my copy of Dorrie -- if you have a copy, could you check to see if he uses this name? It strikes me as a little unlikely that Bryant and Duncan would have drawn an example from Dorrie and then made up a new name for something that Dorrie called by a different name. If indeed Dorrie uses this name, then I believe that is sufficient to retain it in the lede of Tangential quadrilateral.


 * Terminology varies, as evidenced by Bryant and Duncan also referring parenthetically to them as "inscribed" quadrilaterals. They are circumscribed in the sense of being circumscribed about a circle, and they are inscribed in the sense of being inscribed by a circle. Duoduoduo (talk) 16:32, 5 April 2012 (UTC)


 * I checked Dorrie. On pages 188 and 217 he uses the name tangent quadrilateral, which was added today as a variant of tangential quadrilateral. So for the name co-cyclic quad. there is one paper and one post at mathforum using that name. I don't think it is enough to introduce it as a synonyme, and the main reason is that it is a bad name due to the fact that it is too close to cyclic and concyclic, so it is confusing. I am all for having the relevant facts collected here, but that name is no good in my opinion. There is already some confusion, as you say, on the terms "inscribed" and "circumscribed"; do they refer to the quadrilateral or the circle? The two names tangential quad. and cyclic quad. refers to properties of the quadrilateral, as they should, so they are good. In conclusion, yes, I think they made up that new name when there are several other names to choose from, most of them better. Do you agree? Circlesareround (talk) 07:29, 6 April 2012 (UTC)


 * If that name isn't in Dorrie, then they must have made it up -- a strange thing to do, given that their source had a name for it! (And the mathforum post didn't make it clear what the questioner meant by it, and the responders chose to interpret it provisionally as "cyclic" -- so even that google hit is not a real hit.)


 * So I agree that it shouldn't be in the lede of tangential quadrilateral. But the existence of the 2010 paper alone, I believe, justifies this redirected page, since students might come across it there and come here to find out more. But with a redirect to a page with no mention of it, that would leave the reader to guess that it's a synonym. So how about if we put in a footnote at the end of the opening sentence paragraph saying "Rarely, other names, such as co-cyclic quadrilateral, also have been used." ? Duoduoduo (talk) 16:54, 6 April 2012 (UTC)