Talk:Inversion (geometry)
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[edit] QBAsic
Isn't the QBasic program a bit out of place? Hardly anyone uses QBasic anyway. Phys 05:31, 1 Jan 2005 (UTC)
I agree. It would be neat to have a link to a web page with a java program that would let someone do this but this takes up a lot of room and is a program besides, which doesn't seem to fit an encyclopedia. Gene Ward Smith 07:51, 3 May 2006 (UTC)
- Agree too. I removed that text. The external link
in the article seems to have a script at the other end illustrating inversions, that should be enough. Oleg Alexandrov (talk) 14:53, 3 May 2006 (UTC)
[edit] My reversions
I just reverted Patrick's recent changes. There are there goodies to keep maybe, but that can be figured out later.
Invertive geometry is an elementary geometry topic, acessible (and sometimes taught to) high school students. It is highly useful in sinthetic geometry for doing proofs. One can do invertive geometry knowing nothing about analytic geometry, all one needs to know is again, elementary geometry, what is a circle, line, what is a reflection, symmetry etc.
Starting this article with the full-blown generalization to n dimensions adds very little value to the aricle (if you are a mathematician, the generaliation is obvious). However, starting with the generalization greatly reduces its value for undergraduate students or for people who only know elementary geometry.
Please remember an important lesson. Keep articles accessible. One can read in the math style manual about that. This is a general purpose encyclopedia. Keep your math genius ego in check, and start an article at the most acessible place to the reader. If you got the reader hooked on, he/she might be willing to read on. If you start an article with "in n-dimensional space" the reader will stop here, unless the reader is at least as smart as you to start with. Oleg Alexandrov (talk) 17:20, 8 October 2005 (UTC)
[edit] Change to the introduction
I removed some stuff from the introduction. Introduction is meant to be a very simple description of what the article is about. Inversive geometry is about treating circles and lines the same, and tranformations which map these "generalized circles" to themselves. So why not just say that? Whether that eventually turns out to be conformal geometry, reflections and all that, is not that important to put it in the very first sentence. Oleg Alexandrov (talk) 13:03, 17 October 2005 (UTC)
[edit] Anti-deSitter stuff removed
Someone might want to fix this, but it's hardly clear this is the best place for it in any case:
This is the Wick-rotated version of the AdS/CFT duality. In fact, since most calculations are performed in the Wick-rotated model, this is the duality which is really being used.
See also AdS/CFT. Gene Ward Smith 21:57, 4 May 2006 (UTC)
[edit] critical but missing topics: sph inv, mob trans, stereo proj
The following contents, about how sphere inversion, stereographic projection being a special application of sphere inversion, and how circle inversion is the gist of mobius transform, should be written. I started with the following in the article, but it got deleted thru political struggle. By the outcome of a diplomatic relation, a request is made that i put them here. Here they are:
[edit] Inversions in three dimensions
The 3-dimensional version of inversion is analogous to the 2-dimentional case.
The inversion of a vector P in 3D with respect to a sphere centered on the origin with radius r is a vector P' such that 
and P' is a positive multiple of P.
As with the 2D version, a sphere inverts to a sphere, except that if a sphere passes through O, then it inverts to a plane. Any plane not passing through 0, inverts to a sphere touching at O.
Stereographic projection is a special case of sphere inversion. Suppose, we have a stereographic projection with a sphere S of radius 1 sitting on the origin O of plane P, and the north pole N being the projection point. Then, consider a sphere S2 of radius 2 centered at N. The inversion in respect to S2 transforms S into its stereographic projection.
Xah Lee 16:09, 15 July 2006 (UTC)
- hi Oleg. Thanks for the edit. This phrase: “P' is a positive multiple of P.” i didn't understand in the first reading. Perhaps we can say that “P' has the same direction as P”. This way, the phrasing gives it a more geometric interpretation inline with sphere inversion. Xah Lee 22:17, 17 July 2006 (UTC)
[edit] relation to mobius trans
here's a proposed gist of the content:
Circle inversion plays a critical role in Möbius transformation. A mobius transformation can be decomposed into a sequence of rotation, dilation, translation, and circle inversion. Of these, the circle inversions gives mobius transformation a critical characteristics. In particular, circle inversion is the only map among the composition that is a non-trivial conformal map.
Xah Lee 16:22, 15 July 2006 (UTC)
