File:A Pythagorean tiling View 7.svg
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Summary
| Description |
English: In order to prove the Pythagorean theorem, such a tessellation and its pattern grid can be associated to a set of puzzle pieces, as shown below.
This classical tiling is created from a given right triangle. An Euclidean plane is entirely covered with an infinity of squares, the sizes of which are a and b: the leg lengths of the given triangle. On this drawing, every square element of the tiling, any tile would have a slope equal to the ratio of sizes: a / b = tan 30°, and a square pattern would be repeated horizontally and vertically, without the SVG coding: patternTransform="rotate(75)" (see <pattern id="pg" in the source code). No attribute 'patternTransform' in other versions like this one or that other one. See another page for more informations.Français : Afin de prouver le théorème de Pythagore, un tel pavage quadrillé par ses motifs répétés peut être associé à un jeu de pièces de puzzle, comme ci-dessous ou dans une autre page en français.
Ce pavage classique est créé à partir d’un triangle rectangle donné. Un plan euclidien est entièrement couvert d’une infinité de carrés, dont les dimensions sont a et b : les longueurs des côtés de l’angle droit du triangle donné. Dans ce dessin, tout élément carré du pavage, n’importe quel carreau aurait une pente égale au rapport des dimensions : a / b = tan 30°, et un motif carré serait répété horizontalement et verticalement, sans le codage SVG : patternTransform="rotate(75)" (voir <pattern id="pg" dans le code source). Pas d’attribut 'patternTransform' dans d’autres versions telles que celle-ci ou celle-là. Voir une autre page pour plus d’informations. |
| Date | |
| Source | Own work |
| Author | Baelde |
| Other versions |
Pythagorean theorem A right triangle is given, from which a periodic tiling is created, from which puzzle pieces are constructed.    On three previous images, the hypotenuses of copies of the given triangle are in dashed red. On left, a periodic square in dashed red takes another position relative to the tiling: its center is the one of a small tile. And one of the puzzle pieces is square, its size is the one of a small tile. The four other puzzle pieces have stripes. They can form together a large tile, and they are congruent, because of a rotation a quarter turn around the center of any tile that leaves unchanged the tiling and the grid in dashed red. Therefore the area of a large tile equals four times the area of a striped piece. In case where the initial triangle is isosceles, the midpoint of any segment in dashed red is a common vertex of four tiles with equal sizes: a = b, and each striped piece is still a quarter of a tile, it is an isosceles triangle. Whatever the shape of the initial triangle, the two assemblages of the five puzzle pieces have equal areas: Periodic tilings by squares SVG images coded with a pattern element |
| SVG development |  This /Baelde was created with a text editor. |
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 10:58, 23 December 2012 | | 750 × 600 (798 bytes) | Baelde | adding a grid in order to show a periodicity |
| 15:08, 15 October 2012 |  | 750 × 600 (691 bytes) | Baelde | {{Information |Description ={{en|1=Is evoked a tiling of an Euclidean plane by an infinity of squares of two sizes. Here the ratio of sizes is √{{overline|3}}... |
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