File:Fano plane binpoints.svg
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Summary[edit]
| Description |
Deutsch: Die projektive Fano-Ebene, visualisiert als gleichseitiges Dreieck mit Inkreis und Winkelhalbierenden. Die Dreiecksseiten, der Inkreis und die Winkelhalbierenden sind die 7 projektiven Geraden der Ebene, deren 7 Schnittpunkte, in denen sich immer genau drei dieser Geraden treffen, sind die 7 Punkte der Ebene. Die Ebene lässt sich als P^2(Z/2Z) mit dem Koordinatenvektorraum K^3 versehen, wobei K=Z/2Z der Körper mit 2 Elementen ist.
Die in der Zeichnung angegebenen Punktkoordinaten sind die binären Abkürzungen für die Koordinatenvektoren, die den projektiven Punkt in K^3 erzeugen. Z.B. steht 011 für den Vektor (0,1,1). English: Projective Fano-plane. The straight blue lines together with the circle stand for the 7 projective lines, the intersection of these lines stand for the projective points. The coordinates of these points (red) are short forms of the vector, which generates the point in the vector space K^3, where K is the field with 2 elements (K= Z/2Z) |
| Date | |
| Source | Own work |
| Author | KlioKlein |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 03:46, 25 January 2012 | | 320 × 240 (3 KB) | KlioKlein (talk | contribs) | typo corrected |
| 03:09, 25 January 2012 |  | 320 × 240 (3 KB) | KlioKlein (talk | contribs) | Exchanged the names of two base-points to meet the decimal numbered Fano-plane in file:Fano_plane_nimbers.svg. | |
| 23:30, 24 January 2012 |  | 320 × 240 (3 KB) | KlioKlein (talk | contribs) | clipping | |
| 23:19, 24 January 2012 |  | 300 × 240 (3 KB) | KlioKlein (talk | contribs) |
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