File:Sqrt2 is irrational.svg

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Summary

DescriptionSqrt2 is irrational.svg	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

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File history

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	Date/Time	Dimensions	User	Comment
current	18:10, 17 November 2020	240 × 325 (3 KB)	Proz	better position for B'
	23:09, 15 January 2013	240 × 325 (3 KB)	Proz	lighter code (no more bug ?)
	13:20, 15 May 2011	240 × 325 (14 KB)	Proz	revert
	13:01, 15 May 2011	240 × 325 (3 KB)	Proz	lighter code
	20:54, 1 September 2008	240 × 325 (14 KB)	Proz	{{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