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)[reply]

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

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)[reply]

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)[reply]

@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)[reply]

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)[reply]

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