Talk:Circles of Apollonius

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It was on the requested list...will add more tommorow, not much time tonight. Robbjedi 01:47, 18 October 2005 (UTC)

[edit] Second merger discussion

I'm willing to merge these articles on the Apollonian circles, the Circles of Apollonius and the Apollonian gasket, but I'll confess that the motivation is murky to me. Despite their similar name, these concepts seem as mathematically alien as "linear regression" and "linear dynamical system". Perhaps the motivating idea for merger is that non-professionals might become confused by their similar names? Or that we can make one good-length article from a handful of overly short articles? Please help me understand your reasoning. Willow 06:28, 31 July 2006 (UTC)

I disagree with merging with Apollonian circles. Two different problems. --Salix alba (talk) 23:40, 17 September 2006 (UTC)

Hi! Apollonian circles article is about one of four "definitions" which occur in literature. The same definition is included in the article Circles of Apollonius - see the second bulleted paragraph on the page. I definitely agree that the articles should be merged. Mh liv01 (talk) 16:00, 19 February 2008 (UTC)

[edit] An additional meaning?

I just removed the following section from the article:

The following definition has been suggested as a "circle of Apollonius":

• The circle that touches all three excircles of a triangle and encompasses them.

This circle can be constructed by solving Apollonius' problem for the three excircles of a given triangle. One of the solutions should be the nine-point circle, which is externally tangent to all three excircles. Intriguingly, the circle described here is internally tangent. A reference for this "circle of Apollonius" and some of its properties would be welcome! :)

This has been unsourced since the first version of this article in October 2005. Apparently no one has been able to find a source for this definition. —Bkell (talk) 15:51, 6 March 2008 (UTC)