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—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)