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What's up with the random picture of the J-invariant? The connection to this page is pretty opaque, although it's a beautiful picture. -- Dylan Thurston ( talk) 23:44, 4 June 2009 (UTC)
One might also point out that the upper half plane is effectively a disk of infinite diameter.
There's a lot more information on the disk model over at Poincaré disk model. These two pages seem similar enough that I don't see a great need for two separate articles. -- Dantheox 22:20, 30 April 2006 (UTC)
Currently the article defines cross-ratio as which is inconsitent with the order defined in cross-ratio. I'll tag this inconsistency. I'm not sure whether the formula after that refers to the common definition of cross-ratio or actually relies on this non-standard definition. It might need adjustment as well. Someone should verify this. -- Martin von Gagern ( talk) 15:31, 11 July 2011 (UTC)
I inserted a factor of 2 in the formula for . With the old formula we would have for small positive , which is clearly inconsistent with the formula for . The formula for is the right one if we want to have curvature . Neil Strickland ( talk) 13:07, 8 January 2015 (UTC)
Though Poincare's name is attached to two models of the hyperbolic plane, the metric in these planes is named after Arthur Cayley and Felix Klein. Appropriate use of references may preserve this article for some applications in Riemann surface theory, but the reference to the hyperbolic plane models is incorrect. Currently there are no in-line references. Inaccurate statements are subject to change. — Rgdboer ( talk) 21:30, 10 January 2016 (UTC)
My search for "Poincare metric" led to an article careful in use of terminology: H.S. Bear (1991) "Part metric and hyperbolic metric", American Mathematical Monthly 98: 109–123. In this case "metric of the Poincare model" does not translate to "Poincare metric". — Rgdboer ( talk) 01:25, 11 January 2016 (UTC)
The source of this article is M%C3%A9trique_de_Poincar%C3%A9. One of our standards is WP:SET (search engine test) which yielded five times more for Poincare than Cayley-Klein, but then SET is known to be unreliable in cases like this. — Rgdboer ( talk) 01:09, 13 January 2016 (UTC)
There is a serious mathematical error on this page. The metric
is not equal to
The former is the Poincare metric. The latter is the Cayley-Klein metric. Mosher ( talk) 14:33, 29 February 2016 (UTC)
The Poincaré volume form (called "invariant volume element" in the page) is written as a tensor or symmetric product (depending on convention) of differential forms , instead of an antisymmetric product . One may assume that is implicitly antisymmetrized but higher in the page the wedge notation is used, which may cause confusion. Plm203 ( talk) 22:46, 9 July 2023 (UTC)
![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
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What's up with the random picture of the J-invariant? The connection to this page is pretty opaque, although it's a beautiful picture. -- Dylan Thurston ( talk) 23:44, 4 June 2009 (UTC)
One might also point out that the upper half plane is effectively a disk of infinite diameter.
There's a lot more information on the disk model over at Poincaré disk model. These two pages seem similar enough that I don't see a great need for two separate articles. -- Dantheox 22:20, 30 April 2006 (UTC)
Currently the article defines cross-ratio as which is inconsitent with the order defined in cross-ratio. I'll tag this inconsistency. I'm not sure whether the formula after that refers to the common definition of cross-ratio or actually relies on this non-standard definition. It might need adjustment as well. Someone should verify this. -- Martin von Gagern ( talk) 15:31, 11 July 2011 (UTC)
I inserted a factor of 2 in the formula for . With the old formula we would have for small positive , which is clearly inconsistent with the formula for . The formula for is the right one if we want to have curvature . Neil Strickland ( talk) 13:07, 8 January 2015 (UTC)
Though Poincare's name is attached to two models of the hyperbolic plane, the metric in these planes is named after Arthur Cayley and Felix Klein. Appropriate use of references may preserve this article for some applications in Riemann surface theory, but the reference to the hyperbolic plane models is incorrect. Currently there are no in-line references. Inaccurate statements are subject to change. — Rgdboer ( talk) 21:30, 10 January 2016 (UTC)
My search for "Poincare metric" led to an article careful in use of terminology: H.S. Bear (1991) "Part metric and hyperbolic metric", American Mathematical Monthly 98: 109–123. In this case "metric of the Poincare model" does not translate to "Poincare metric". — Rgdboer ( talk) 01:25, 11 January 2016 (UTC)
The source of this article is M%C3%A9trique_de_Poincar%C3%A9. One of our standards is WP:SET (search engine test) which yielded five times more for Poincare than Cayley-Klein, but then SET is known to be unreliable in cases like this. — Rgdboer ( talk) 01:09, 13 January 2016 (UTC)
There is a serious mathematical error on this page. The metric
is not equal to
The former is the Poincare metric. The latter is the Cayley-Klein metric. Mosher ( talk) 14:33, 29 February 2016 (UTC)
The Poincaré volume form (called "invariant volume element" in the page) is written as a tensor or symmetric product (depending on convention) of differential forms , instead of an antisymmetric product . One may assume that is implicitly antisymmetrized but higher in the page the wedge notation is used, which may cause confusion. Plm203 ( talk) 22:46, 9 July 2023 (UTC)