File:Fanosingercycle.svg
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Size of this PNG preview of this SVG file: 580 × 570 pixels. Other resolutions: 244 × 240 pixels | 488 × 480 pixels | 781 × 768 pixels | 1,042 × 1,024 pixels | 2,084 × 2,048 pixels.
Original file (SVG file, nominally 580 × 570 pixels, file size: 13 KB)
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| Description |
English: Fano plane. The numbers for the points (black) and the lines (blue) are chosen thus, that the plane appears to be the plane generated by a perfect difference set, see the article A THEOREM IN FINITE PROTECTIVE GEOMETRY AND SOME APPLICATIONS TO NUMBER THEORY by JAMES SINGER. The arrows (red) show a generator of a so called Singer cycle, a cyclic permutation of all points of the plane.
Deutsch: Die Fano-Ebene erweist sich bei geeigneter Nummerierung der Punkte (schwarz) und Geraden (blau) als eine Ebene, die von einer Differenzmenge abstammt. Siehe dazu den Artikel von James Singer (PDF) in der englischsprachigen Beschreibung. Die Pfeile (rot) stehen für eine erzeugende Kollineation eines Singer-Zyklus, d. i. eine Kollineation, die die gesamte Punktmenge der Ebene zyklisch vertauscht. |
| Date | |
| Source | Own work |
| Author |
KlioKlein (original by Watchduck) |
| Other versions |
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I, the copyright holder of this work, hereby publish it under the following license:
 
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 11:39, 28 July 2022 | | 580 × 570 (13 KB) | Watchduck (talk | contribs) | Arial 0 |
| 20:39, 3 April 2012 |  | 580 × 570 (12 KB) | KlioKlein (talk | contribs) | Clipping | |
| 20:38, 3 April 2012 |  | 600 × 600 (12 KB) | KlioKlein (talk | contribs) | Background, Clipping | |
| 20:14, 3 April 2012 |  | 600 × 600 (12 KB) | KlioKlein (talk | contribs) | Contrast, Clipping | |
| 23:05, 2 April 2012 |  | 700 × 700 (12 KB) | KlioKlein (talk | contribs) | {{Information |Description ={{en|1=Fano plane. The numbers for the points (black) and the lines (blue) are chosen thus, that the plane appears to be the plane generated by a ''perfect difference set'', see the article [http://www.ams.org/journals/tr... |
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