Timeline for How to solve geometry problems using involutions
Current License: CC BY-SA 3.0
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| Aug 23, 2020 at 9:10 | comment | added | user11235 | And yes, the projective transformations of the complex line are exactly the Möbius transformations. | |
| Aug 23, 2020 at 9:06 | comment | added | user11235 | A projective transformation of the complex line is any function from the complex numbers plus infinity to the complex numbers plus infinity that preserves the complex cross ratio (i.e. plug in complex numbers in the cross ratio formula). This does NOT include reflections about a fixed line or inversions because they conjugate the cross ratio. Up to a reasonable choice of coordinate system, all involutions of this kind are $z$, $-z$ and $1/z$. Since the first two already have other names, this is really about $1/z$ after an appropriate choice of origin, axis and scaling. | |
| Feb 15, 2012 at 15:48 | vote | accept | Beni Bogosel | ||
| Jul 13, 2011 at 22:17 | history | edited | Will Jagy | CC BY-SA 3.0 |
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| Jul 13, 2011 at 21:03 | history | edited | Will Jagy | CC BY-SA 3.0 |
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| Jul 13, 2011 at 20:45 | history | answered | Will Jagy | CC BY-SA 3.0 |