Original file (SVG file, nominally 600 × 600 pixels, file size: 3 KB)
 | 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 |
One of the two classical squares is the image of the other square under several similarities. Each of them has a ratio equal to √2 or its inverse, because of the ratio 2 or 0.5 between the areas of the squares. As any similarity that is not an isometry, each similarity that transforms one square into the other one has a unique fixed point, called its center. The center of some similarities is a vertex common to the squares. For example, the point A is obviously the center of the indirect similarity that shrinks the triangle EFA into BTA. This drawing shows the direct similarity that shrinks EFA into ATB. Another drawing with the same notations shows the direct similarity with center A, that enlarges the triangle BCA into EFA.
We conceive the direct similarity that transforms AEF into BAT, and B into C, because of four thin red lines. Each of them begins with an arc of 135 degrees that starts from a vertex of ABEF, and finishes by going straight to the image of the start point, and straight toward S. As any direct plane similarity that is not an isometry, the exhibited similarity is the composition of an homothety and a rotation with the same center S. The exhibited homothety has a positive ratio, so its ratio equals the ratio of the similarity: 1/ √2. And the angle of the rotation is + 135 degrees modulo 360 degrees: the angle of the similarity. We can construct the center S of this similarity solely because of its oriented angle + 135 degrees. This point S is the intersection of the two blue quarter-circles. Each of them is drawn inside a square, its center is F or T, and its radius is the dimension of the square: AF or BT. The two legs of the right triangle AEF are drawn in red, and the letters A and F are red. The rotation transforms these red legs into a blue line, and the images of A and F under the rotation are named with blue letters: U and W. The homothety transforms the blue line into a green line: the two legs of the isosceles right triangle BAT. The letters B and T are green. |
| Date | |
| Source | Own work |
| Author | Yves Arthur Baelde |
| 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.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 12:49, 1 March 2022 | | 600 × 600 (3 KB) | Arthur Baelde | better framing, lighter colors and other improvements |
| 10:25, 18 September 2011 |  | 625 × 625 (3 KB) | Baelde | code SVG stroke-linejoin="bevel" in element g | |
| 10:21, 18 September 2011 |  | 625 × 625 (3 KB) | Baelde | {{Information |Description ={{en|1=One of the two classical squares is the image of the other square under several similarities. Each of them |
File usage
Global file usage
The following other wikis use this file:
- Usage on es.wikipedia.org
- Usage on id.wikipedia.org
- Usage on sr.wikipedia.org
- Usage on ta.wikipedia.org
- Usage on vi.wikipedia.org
- Usage on zh.wikipedia.org
