File:A tri-colored Pythagorean tiling View 6.svg

From Wikimedia Commons, the free media repository
Jump to navigation Jump to search

Original file (SVG file, nominally 600 × 600 pixels, file size: 846 bytes)

Captions

Captions

Add a one-line explanation of what this file represents

Summary

[edit]
Description
English: It is possible to associate such tilings with some proofs of the  Pythagorean theorem,  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(60)"  (see   <pattern id="pg"  in the source code).  No attribute  'patternTransform'  in other versions like this one or that other one.  How many methodical arrangements of colours of tiling elements, here is a mathematical topic.

See another page for more informations.
 
Français : Il est possible d’associer de tels pavages à certaines preuves du  théorème de Pythagore,  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(60)"  (voir   <pattern id="pg"  dans le code source).  Pas d’attribut  'patternTransform'  dans d’autres versions telles que celle-ci ou celle-là.  Combien de dispostions méthodiques de couleurs pour tous les éléments carrés, voilà un problème mathématique.

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:
 a 2 + b 2  =  c 2.    Hence  the  Pythagorean  theorem.

 Periodic tilings by squares 

    SVG images coded with a pattern element
SVG development
InfoField
 
The SVG code is valid.
 
This /Baelde was created with a text editor.

Licensing

[edit]
Arthur Baelde, the copyright holder of this work, hereby publishes it under the following licenses:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
Attribution: Arthur Baelde
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.
GNU head 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.
You may select the license of your choice.

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current05:10, 19 October 2012Thumbnail for version as of 05:10, 19 October 2012600 × 600 (846 bytes)Baelde (talk | contribs){{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 [[w:Square root of 3|is square...

You cannot overwrite this file.

Metadata

This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.

Retrieved from "https://commons.wikimedia.org/w/index.php?title=File:A_tri-colored_Pythagorean_tiling_View_6.svg&oldid=779027507"