Talk:Steiner chain

Images
This article begs for a picture of a typical case. It might be difficult to make with something simple like xfig, since getting the circles positioned correctly is pretty delicate. Michael Hardy (talk) 16:28, 15 August 2008 (UTC)

Two illustrations of interest appear in Ogilvy's Excursions in Geometry, on pages 52 and 53. The second is a typical Steiner chain of eight circles touching two non-concentric circles. The first is a case in which the condition fails and no Steiner chain exists. Michael Hardy (talk) 17:21, 15 August 2008 (UTC)


 * I'll try to put some images together over the weekend. I've been meaning to for Soddy's hexlet, and this would be an excellent dry run! :) Willow (talk) 00:15, 16 August 2008 (UTC)

I think in a good illustration, the inner bounding circle would take up most of the area of the outer one, and the chain would be fairly long&mdash;maybe eight circles, so that the viewer would instantly see that it's a "chain". Michael Hardy (talk) 16:56, 17 August 2008 (UTC)


 * New images

Sorry I'm a week late, but I wrote a little computer program that makes SVG images of arbitrary Steiner chains. The given circles are shown in red and blue; the chain circles are in black. So now we can Talk among ourselves about what we would like for this little article! :)

The inside-out Steiner chain was surprising and a fun discovery. That's why I colored the given circles, because initially I couldn't figure which was which in these configurations. In reading up for the problem of Apollonius, I remember hearing that there were some nifty theorems on the properties of circles that are tangent to four circles, but I neglected to read up on them. :P



I also experimented with making animations, which was fun. This GIF animation has 60 frames, one for each degree of rotation (a 60-degree rotation returns you to your starting place, as I guess you all see). After "optimization", the animation shrank from 2 MB to 1.3 MB, but it's still pretty big. I was thinking of adding the ellipse on which the centers move, and maybe the circle through which the tangent points pass, but I was worried that those additions might make the diagram too busy. Maybe we should show those separately? I'd be grateful for any advice - thank you! :) Willow (talk) 10:39, 28 August 2008 (UTC)

Orphan article?
Excluding redirects, discussion pages, pages that list new articles, pages that list "stubs", etc., only the following now link here:


 * List of geometry topics
 * Jakob Steiner
 * List of mathematics articles (S)
 * List of circle topics

Not a complete "orphan", but somewhat link-deficient, maybe? Michael Hardy (talk) 21:54, 15 August 2008 (UTC)


 * I added a connection in both directions with Pappus chain. —David Eppstein (talk) 22:16, 15 August 2008 (UTC)


 * I did likewise with Soddy's hexlet. Our little orphan is gradually being adopted ;) Willow (talk) 00:15, 16 August 2008 (UTC)

Typo ?
for ywo given circles - Erik Baas (talk) 22:49, 12 September 2008 (UTC)


 * Thank you, Erik, for catching that typo and thank you, Michael, for fixing it so swiftly. :) Willow (talk) 11:27, 13 September 2008 (UTC)

given circles
1st paragraph: the smaller circle may lie completely inside or outside of the larger circle. In the latter case the circles need not be of different size, innit? --Mosmas (talk) 09:18, 3 April 2012 (UTC)

Types of tangency
Figure 2: "In this configuration, the Steiner-chain circles have the same type of tangency to both given circles, either externally or internally tangent to both". How is "internally tangent to both" possible? --Mosmas (talk) 10:57, 3 April 2012 (UTC)