Talk:Ford circle

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)[reply]

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)[reply]

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)[reply]

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

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)[reply]

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)[reply]

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)[reply]

a little nutty question[edit]

is it just me or do the Ford Circles resemble the relative sizes of the Planets? Decora (talk) 04:09, 21 September 2012 (UTC)[reply]

That is a pretty nutty question indeed....RockvilleRideOn (talk) 00:55, 31 December 2012 (UTC)[reply]

equation from the centers[edit]

what is the equation of the curve going through the centers of the circles, at least for the left-handed set of circles? I could not quite infer this from the article... is it asymptotic towards epsilon (near zero) ? — Preceding unsigned comment added by 207.96.202.138 (talk) 22:34, 6 May 2016 (UTC)[reply]

So you're looking at the circles whose numerator is one? The answer is given in the first line of the article. If x=p/q=1/q and y=radius=1/2q^2, then the curve is y=x^2/2. —David Eppstein (talk) 22:48, 6 May 2016 (UTC)[reply]