Original file (SVG file, nominally 750 × 750 pixels, file size: 716 bytes)
 | This is a file from the Wikimedia Commons. Information from its description page there is shown below. Commons is a freely licensed media file repository. You can help. |
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 the leg lengths of the given triangle: a and b. On this drawing, every square element of the tiling has a slope equal to the ratio of sizes: a / b = tan 22.5°, and a square pattern is indefinitely repeated horizontally and vertically, if we forget patternTransform="rotate(67.5)": see <pattern id="pg" in the source code. See another page for more informations. |
| Date | |
| Source | Own work |
| Author | Baelde |
| Other versions |
    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 can form together another tile, and they are congruent, because of a rotation of a quarter turn around the center of a large tile that transforms at the same time the tiling and the grid in dashed red into themselves. Therefore the area of a large tile equals four times the area of one of these four puzzle pieces. 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 puzzle piece which is a quarter of a tile 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, images coded with a pattern element in SVG |
| SVG development |  This /Baelde was created with a text editor. |
Licensing
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
|
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
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 09:00, 26 September 2012 | | 750 × 750 (716 bytes) | Baelde | {{Information |Description ={{en|1=The image evokes a covering of the entire Euclidean plane with an infinity of squares of two different sizes.}} |Source ={{own}} |Author =Baelde |Date =2012-09-26 |Per... |
File usage
The following 3 pages use this file:
Global file usage
The following other wikis use this file:
- Usage on es.wikipedia.org
- Usage on fr.wikipedia.org
- Usage on ro.wikipedia.org
- Usage on ru.wikipedia.org
- Usage on uk.wikipedia.org
