Talk:Ford circle

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A good illustration showing a Farey sequence and associated Ford circles would be an approriate addition to this article. Michael Hardy 01:40, 22 Sep 2004 (UTC)

There was a pic for a while, what happened to it? AnonMoos 00:32, 20 October 2005 (UTC)
It Image:Ford.circles.gif never went away, but sometimes it could not be seen, so I re-uploaded it to the commons as Image:Ford circles.png--Henrygb 00:04, 22 October 2005 (UTC)
Hajor discovered it was due to the policy announced at http://mail.wikipedia.org/pipermail/wikitech-l/2005-October/032030.html ; I uploaded an anti-aliased version. AnonMoos 23:55, 22 October 2005 (UTC)

[edit] "... the line y = 1 is counted as a Ford circle ..."

Is this correct? Surely y = 0 would be more logical, given that this line touches all the other circles. The line at y = 1 only touches two of them. -- Sakurambo 桜ん坊 11:24, 16 May 2007 (UTC)

There is a Ford circle C[n/1] associated with every integer n, with centre at (n, 1/2) and radius 1/2. The diagram in the article is a little misleading, as it only shows parts of two of theses "integer" Ford circles - C[0/1] and C[1/1]. The line y=1 touches all of these "integer" Ford circles. The transformation
z \rightarrow \frac{z-i}{1-iz}
transforms the set of Ford circles into the Apollonian gasket within the circle |z|=1, and shows that the line y=1 is indeed a Ford circle, as it transforms into the circle with centre at (0,1/2) and radius 1/2. Gandalf61 22:38, 16 May 2007 (UTC)

A Ford circle should not touch all of the other Ford circles. Take a close look at the picture. Michael Hardy 00:26, 17 May 2007 (UTC)