Talk:Apollonian circles

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[edit] First merger discussion

I would recommend that the pages of Apollonian circles not be merged with the Apollonian gasket, because they seem to be mathematically distinct. The Apollonian circles constitute two families of mutually orthogonal circles, and extend Apollonius' distance-ratio definition of the circle (see blurb in Circle). By contrast, the Apollonian gasket extends Apollonius' problem, which is to identify a circle that is tangent to three fixed circles. The circles in this case are tangent (not orthogonal) and are constructed by a different method to solve a different problem. The gasket looks nothing like the Apollonian circles, which correspond to the orthogonal bipolar coordinate system. The main thing they have in common is their inventor, Apollonius of Perga. WillowW 21:28, 6 May 2006 (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 06:27, 31 July 2006 (UTC)