File:A wallpaper pattern Overlaid patterns.svg
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English: Several analogous patterns are overlaid in this "wallpaper", four tiling patterns. An article calls "Pythagorean tiling" such a tiling covering entirely the Euclidean plane by squares of two different sizes, where any tile, by any edge, abuts against exactly one tile of another size. Such tilings have necessarily a property of "wallpaper": they are periodic.
Out of two small tiles with violet edges, a tile has an empty surface in bright blue, the other tile shows a central square bearing a tiny circle. Leaving aside the central ornaments and the surface colors, the tilings of which the lines are violet or brown remain unchanged under the same group of translations. This group is generated by two translations through equal distances in perpendicular directions, forming a 45 degrees angle with an edge of the image. See other images for more informations:• "Academ Translations depicted on a wallpaper" • "A pattern Two explanatory grids" See also the article "Wallpaper group", about a classification of groups of isometries that leave unchanged a wallpaper. Français : Plusieurs motifs analogues sont superposés dans ce “papier peint”, quatre motifs de pavage. Un article en anglais appelle "pavage de Pythagore" un tel pavage couvrant entièrement le plan Euclidien par des carrés de deux tailles différentes, où n’importe quel carreau, de n’importe quel côté, est contigu à un carreau exactement d’une autre taille. De tels pavages ont nécessairement une propriété de "papier peint" : ils sont périodiques.
Sur deux petits carreaux aux côtés violets, un carré a une surface vide en bleu clair, l’autre carré montre un carré central portant un petit cercle. Abstraction faite des décorations centrales et des couleurs des surfaces, les pavages tracés en brun et violet restent inchangés par le même groupe de translations. Ce groupe est engendré par deux translations sur des distances égales dans des directions perpendiculaires, formant un angle de 45 degrés avec un bord de l’image. Voir d’autres images pour plus d’informations :• "Academ Translations depicted on a wallpaper" • "A pattern Two explanatory grids" Voir aussi l’article en anglais "Wallpaper group", sur une classification des groupes d’isométries qui laissent inchangé un papier peint. |
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| Source | Own work |
| Author | Baelde |
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| current | 03:24, 29 January 2013 | | 600 × 600 (1 KB) | Baelde (talk | contribs) | User created page with UploadWizard |
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