File:Academ Translations depicted on a wallpaper.svg
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Summary[edit]
| Description |
English: Two drawings of similar tilings are overlaid. An article calls "Pythagorean tiling" such a periodic tiling by squares of two different sizes, where any tile, by any edge, adjoins exactly one square of another size. The tiling with red tiles is enlarged to scale √2: square root of two. Its colors are changed, its orientation too, in manner that any tile of the second tiling has the same center as a red square. And we see all tiles with the same slope, equal to the dimension ratio of a small tile to a large tile of a same tiling: √2 – 1 = tan 22.5 o. Thus, the pattern of the wallpaper is repeated horizontally and vertically.
Eleven arrows depict two pairs of translations. Each pair contains translations through equal distances in perpendicular directions. Each pair generates the group of all translations that leave unchanged either the first tiling only, or the second tiling and the whole wallpaper. Countless rotations are also members of the group of all isometries that transform a Pythagorean tiling into itself. For more informations, see the article "Wallpaper group", about a classification of groups of transformations that leave unchanged a wallpaper. See also other images:• "A pattern Two explanatory grids" • "A wallpaper pattern Overlaid patterns" Français : Deux dessins de pavages semblables sont superposés. Un article en anglais appelle "pavage de Pythagore" un tel pavage périodique par des carrés de deux tailles différentes, où n’importe quel carreau, de n’importe quel côté, jouxte exactement un carré d’une autre taille. Le pavage de carreaux rouges est agrandi à l’échelle √2 : racine carrée de deux. Ses couleurs sont modifiées, ainsi que son orientation, de façon que n’importe quel carré du second pavage ait le même centre qu’un carré rouge. Et l’on voit l’ensemble des carreaux avec la même pente, égale au rapport des dimensions d’un petit carreau à un grand carreau d’un même pavage : √2 – 1 = tan 22.5 o. Ainsi, le motif du papier peint se répète horizontalement et verticalement.
Onze flèches représentent deux paires de translations. Chaque paire contient des translations sur des distances égales dans des directions perpendiculaires. Chaque paire engendre le groupe de toutes les translations qui laissent inchangé soit le premier pavage seulement, soit le second pavage et tout le papier peint. D’innombrables rotations appartiennent aussi au groupe de toutes les isométries qui transforment un pavage de Pythagore en lui-même. Pour plus d’informations, consultez l’article en anglais "Wallpaper group", sur une classification des groupes de transformations qui laissent inchangé un papier peint. Voir aussi d’autres images:• "A pattern Two explanatory grids" • "A wallpaper pattern Overlaid patterns" |
| Date | |
| Source | Own work |
| Author | Baelde |
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| SVG development |  This /Baelde was created with a text editor. |
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| current | 14:01, 21 January 2013 | | 600 × 600 (1 KB) | Baelde (talk | contribs) | User created page with UploadWizard |
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