Talk:Tangential quadrilateral
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Minimum area text
[edit]I removed a lot of the text on maximum area since it was getting to long, I think, for an encyclopedia. Please don't take it as critisism on your additions, Fjackson and Duoduoduo. (Of course, you can always get it back if you disagree on my edit.) Circlesareround (talk) 14:47, 9 September 2011 (UTC)
Non-convex tangential quadrilaterals
[edit]
Why are non-convex quadrilaterals excluded here? They can also have all four sides tangent to a circle, and all of the theorems and properties described in this article either hold directly or hold in close analogy after some minor tweaking (I think there are some sign flips needed in a few of the identities). –jacobolus (t) 19:06, 21 August 2023 (UTC)
What makes a formula "trigonometric" vs. "non-trigonometric"
[edit]These two categories of formulas do not seem obviously distinct to me. The semiperimeter, inradius, diagonals, and tangent lengths all seem just as "trigonometric" to me as the side lengths or angle measures. –jacobolus (t) 04:05, 22 August 2023 (UTC)
- Formula is trigonometric if it has trigonometric functions. Trigonometric functions are explained in https://en.m.wikipedia.org/wiki/Trigonometric_functions . So only functions involving angles are considered trigonometric. 77.219.1.85 (talk) 03:54, 6 October 2023 (UTC)
- I don't think this is a meaningful categorical difference. Really the distinction being made here is between formulas involving angles (and optionally sides) vs. formulas involving only sides (but no angles). But if you examined the corresponding formulas in spherical/hyperbolic geometry, all of these formulas would have "trigonometric functions" (assuming you used angle measures and side lengths as your basic quantities), whereas if you looked at the corresponding formulas in the Galilean plane, none of them would have. On the other hand, if you used half-tangent or chord lengths as your basic representation for angles, none of these formulas would need trigonometric functions in any of these geometries. –jacobolus (t) 03:57, 6 October 2023 (UTC)