File:Sqrt2 is irrational.svg
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Size of this PNG preview of this SVG file: 240 × 325 pixels. Other resolutions: 177 × 240 pixels | 354 × 480 pixels | 567 × 768 pixels | 756 × 1,024 pixels | 1,512 × 2,048 pixels.
Original file (SVG file, nominally 240 × 325 pixels, file size: 3 KB)
Captions
Captions
Geometric proof the square root of 2 is irrational
Summary
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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 | 18:10, 17 November 2020 | | 240 × 325 (3 KB) | Proz (talk | contribs) | better position for B' |
| 23:09, 15 January 2013 |  | 240 × 325 (3 KB) | Proz (talk | contribs) | lighter code (no more bug ?) | |
| 13:20, 15 May 2011 |  | 240 × 325 (14 KB) | Proz (talk | contribs) | revert | |
| 13:01, 15 May 2011 |  | 240 × 325 (3 KB) | Proz (talk | contribs) | lighter code | |
| 20:54, 1 September 2008 |  | 240 × 325 (14 KB) | Proz (talk | contribs) | {{Information |Description={{en|1=geometric proof for the irrationality of the square root of 2.}} {{fr|1=Une preuve géoémtrique de l'irrationalité de la racine carrée de 2.}} |Source=modifications with inkscape from [[:Image:Irrationality of sqrt2.sv |
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