File:Academ scale ratio square root of 2.svg
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English: 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. This drawing shows the direct similarity that enlarges the triangle BCA into EFA. Another drawing with the same notations shows the direct similarity with center A, that shrinks EFA into ATB.
Français : L’un des deux carrés classiques est l’image de l’autre carré par plusieurs similitudes. Chacune d’entre elles a un rapport égal à to √2 ou à son inverse, à cause du rapport 2 ou 0,5 entre les aires des deux carrés. Comme toute similitude qui n’est pas une isométrie, chaque similitude qui transforme l’un en l’autre carré a un point invariant unique, appelé son centre. Le centre de certaines similitudes est un sommet commun aux carrés. Par exemple, le point A est évidemment le centre de la similitude indirecte qui réduit le triangle EFA en BTA. Ce dessin montre la similitude directe qui agrandit le triangle BCA en EFA. Un autre dessin avec les mêmes notations montre la similitude directe de centre A, qui réduit EFA en ATB. |
| 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 | 10:39, 18 September 2011 | | 625 × 500 (3 KB) | Baelde (talk | contribs) | No numbers on the triangles, but + is written before 45 degrees (anti-clockwise turning), the classical {{Nowrap|1=formula <var>a</var><sup>2</sup> + <var>b</var><sup>2</sup> = <var>c</var><sup>2</sup> }} holds with |
| 10:22, 23 May 2010 |  | 450 × 360 (2 KB) | Baelde (talk | contribs) | {{Information |Description={{en|1=A similarity of which the centre is C and the angle 45 degrees (where counterclockwise turning, or anti-clockwise turning is positive) transforms the square ABTC into EFBC, and the isosceles right triangle |
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