File:Academ Repeated translations on tiling.svg
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English: Five arrows represent three translations named The three transformations are members of the group of translations which preserve the tiling of the wallpaper, if we imagine an infinite tiling that fills the entire space.
The action of a given translation may be repeated. The following equality is written within theimage: This other equality is not written: but the drawing shows two points N and (N ), and two successive arrows from N to (N ). The elements of the tiling are right triangles with same shape and size. Two triangular elements with a common side have different colors, gray and blue. If their common side is their larger leg, the two elements together shape an equilateral triangle. A vertex common to twelve elements is the center of a regular hexagon, that translations endlessly repeat to fill the whole plane. A quarter of regular hexagon is drawn in thick transparent lines, and its two successive images In this image we find the same tiling, and the same red arrow to represent In this other image we also find the same violet arrow which representsFrançais : Cinq flèches représentent trois translations nommées Les trois transformations appartiennent au groupe des translations qui conservent le pavage du papier peint, si on imagine un pavage infini qui remplit l’espace en entier.
L’action d’une translation donnée peut se répéter. L’égalité suivante est inscrite dans l’image: Cette autre égalité ne l’est pas : mais le dessin montre deux points N et (N ), et deux flèches successives de N à (N ). Les éléments du pavage sont des triangles rectangles de même forme et même taille. Deux éléments triangulaires qui ont un côté commun sont de couleurs différentes, gris et bleu. Si leur côté commun est leur grand côté de l’angle droit, les deux éléments forment un triangle équilateral. Un sommet commun à douze éléments est le centre d’un hexagone régulier, que des translations répètent à l’infini pour remplir le plan en entier. Un quart d’hexagohne régulier est tracé en trait épais transparent, ainsi que ses deux images successives Dans cette image nous retrouvons le même pavage, et la même flèche rouge Dans cette autre image, nous trouvons aussi la même flèche violette qui représente |
| Date | |
| Source | Own work |
| Author | Yves Baelde |
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I, the copyright holder of this work, hereby publish it under the following license:
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 09:05, 26 March 2013 | | 750 × 600 (3 KB) | Baelde (talk | contribs) | Better SVG code, better image |
| 13:38, 19 June 2012 |  | 625 × 500 (3 KB) | Baelde (talk | contribs) | «stroke-linejoin="bevel"» specified with «fill="none"» | |
| 05:16, 16 August 2011 |  | 625 × 500 (3 KB) | Baelde (talk | contribs) | some modifications, for example to get better arcs around the start points of the arrows through all software, I hope | |
| 13:56, 15 August 2011 |  | 625 × 500 (3 KB) | Baelde (talk | contribs) | {{Information |Description ={{en|1=Five arrows represent three translations named <math style="vertical-align:-20%">\mathit{S,~S}^{\,-\,1}\mathrm{~and~}\mathit{T.}</math> The three transformations are members o |
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