Talk:Generalised circle

Schwerdtfeger book

I intend to add material mainly from the earlier chapters of "The Geometry of Complex Numbers" (Hans Schwerdtfeger) . It will discuss

• how the matrix permits right-handed and left-handed circles
• how under stereographic projection to the sphere these can be seen to be equivlent (because the p[oint at infinity is just another point)
• how, also under stereographic projection, a degenerate circle (a line) can also be seen to be a circle like any other
• imaginary radii
• the equations for calculating the points at which two circles intersect (and hence for determining if circles are tangent)
• transformation of generalised circles by mobius transformations

Paul Murray 02:10, 19 April 2007 (UTC)

@Paul Murray – still any interest in working on this? –jacobolus (t) 01:39, 17 July 2023 (UTC)

changes

clines are a reference to the set of lines and circles, thus a reference to generalized circles. cleaned up the expressions of getting a general form of circles using z and it's conjugate and added ${\left|z-\gamma \right|}=r$ , as this is by far the most common form for expressing a circle on the complex plane. — Preceding unsigned comment added by 71.192.107.154 (talk) 02:41, 24 October 2009 (UTC)

Cline has an established and quite different meaning. The meaning "the set of lines and circles" seems not supported by looking at the top items from a Google search. The OED does not give this meaning; it does however mention "conical line" as a synonym for conic section. If no-one contributes a source for this meaning, I plan to remove it. JoergenB (talk) 21:24, 10 August 2010 (UTC)

@JoergenB I added a source for "cline". There are a few others in a Google Scholar search, but you are right that it is a fairly obscure name. –jacobolus (t) 01:29, 17 July 2023 (UTC)

YouTube proofs

This article is atrociously uninspiring, and even a little dejecting. Could you add a proof? See video 1 and video 2? — Preceding unsigned comment added by 50.174.74.32 (talk) 01:31, 19 June 2014 (UTC)

Please feel free to hunt down sources (ideally books / journal papers) and add material. –jacobolus (t) 01:38, 17 July 2023 (UTC)