File:"Knot with 48 crossings" on a clock face.svg
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Original file (SVG file, nominally 750 × 750 pixels, file size: 3 KB)
Captions
Captions
The integers from 1 to 12 written on the image number either the twelve hours of half a day on a clock face or the twelve bends of a race track. There are forty‑eight bridges along the route, no dangerous crossings. Interesting loop in arithmetic.
Summary[edit]
| Description |
English: The integers from 1 to 12 written on the image number either the twelve hours of half a day on a clock face or the twelve bends along a race track. Along the loop there are forty‑eight bridges. Every straight line crosses eight other parts of the track, passing alternatively under and above. The twelve bends are parts of parabolas produced by 'q' commands in SVG language. Through this drawing of knot, it is easy to explain arithmetic modulo 12. For example, if it is eleven o'clock now, five hours later the clock hand will indicate four o'clock, because 11 + 5 = 4 modulo 12. By turning clockwise, we pass through the terms of an arithmetic progression with common difference +5 or –7. This also explains "{12,5}": a Schläfli notation that denotes nonconvex regular dodecagons, all similar. For more informations see another version.
Français : Les nombres entiers de 1 à 12 inscrits dans l’image numérotent soit les douze heures d’une demi‑journée sur un cadran d’horloge, soit les douze virages d’une piste de course. Le long du circuit il y a quarante‑huit ponts. Chaque ligne droite croise huit autres parties de la piste, en passant alternativement en dessous et au‑dessus. Les douze virages sont des portions de paraboles produites par des commandes 'q' en langage SVG. Avec ce dessin de nœud, il est facile d’expliquer l’arithmétique modulo 12. Par exemple, si maintenant il est onze heures, dans cinq heures l’aiguille de l’horloge indiquera quatre heures, parce que 11 + 5 = 4 modulo 12. En tournant dans le sens des aiguilles d’une montre, on passe par les termes d’une progression arithmétique de raison +5 ou –7. Cela explique aussi "{12,5}" : une notation de Schläfli qui désigne des dodécagones réguliers étoilés, tous semblables. Pour plus d’informations voir une autre version. |
| Date | |
| Source | Own work |
| Author | Baelde |
| Other versions |
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| SVG development |  This /Baelde was created with a text editor. |
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 06:48, 7 August 2012 | | 750 × 750 (3 KB) | Baelde (talk | contribs) | central ornament more interesting |
| 19:35, 2 August 2012 |  | 750 × 750 (3 KB) | Baelde (talk | contribs) | knot with lines more thick | |
| 04:51, 15 July 2012 |  | 750 × 750 (3 KB) | Baelde (talk | contribs) | the PNG conversion was bad | |
| 04:26, 15 July 2012 |  | 750 × 750 (2 KB) | Baelde (talk | contribs) | SVG code improved by using transform ="rotate (…)" | |
| 09:23, 13 July 2012 |  | 750 × 750 (3 KB) | Baelde (talk | contribs) | {{Information |Description ={{en|1=We can consider that the integers from 1 to 12, written on the clock face, are the twelve hour numbers, or the numbers of twelve bends along a race track. Along the loop, there are forty-eight brid... |
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File usage on Commons
The following 6 pages use this file:
- User:OgreBot/Watercraft/2012 July 11-20
- File:48 crossings on clock face.svg
- File:Abyss of regular dodecagons on a clock face.svg
- File:Academ Arithmetic progressions along a knotted loop.svg
- File:Academ Arithmetic progressions modulo 12 on a clock face.svg
- File:Academ Bijection between angles and 12 positions of a clock hand.svg
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