File:Sqrt2 is irrational.svg
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Summary
| Description |
English: geometric proof for the irrationality of the square root of 2: If the isosceles right triangle ABC had integer side lengths (AB = q = BC and AC = p = q√2), so had the isosceles right triangle A'B'C. Since q < p < 2q, the side lengths of A'B'C are strictly smaller than those of ABC, i.e. p-q < q and 2q-p < p. Repeating this construction sufficiently often, an infinitely descending sequence of positive integer side lengths could be obtained, which is impossible.
Français : Une preuve géométrique de l'irrationalité de la racine carrée de 2: Si le triangle ABC est isocèle rectangle avec ses côtés de longueurs entières, alors c'est aussi le cas du triangle A'B'C, qui est de dimensions plus petites. |
| Date | 01/09/2008 |
| Source | modifications with inkscape and a text editor from Image:Irrationality of sqrt2.svg |
| Author | self creation |
| Other versions | Image:Irrationality of sqrt2.svg, Image:Right isosceles triangle with integer sides.svg |
This vector image was created with a text editor.
Licensing
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I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 23:40, 17 November 2020 | | 240 × 325 (3 KB) | wikimediacommons>Proz | better position for B' |
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