File:11.21 Fraction continue - V2.png
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Captions
Captions
Geometric representation of the continued fraction of \sqrt{2}
Summary
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| Description |
Français : Les fractions continues sont considérées comme un objet arithmétique des mathématiques. Il est pourtant relativement aisé d'en faire une simple expression géométrique si l'on représente une fraction y/x par un rectangle de hauteur y et de largeur x. Alors la pente de sa diagonale est y/x. Ainsi, une fraction continue peut s'exprimer géométriquement comme un assemblage de rectangles. Pour la fraction continue de \sqrt{2} on débute avec un "carré long" horizontal (rectangle au format 1:2), puis on ajoute un carré long vertical (format 2:1) au-dessus de même largeur, puis un carré long horizontal à droite, puis à nouveau un carré long vertical au-dessus et ainsi de suite.
English: Continued fractions are considered an arithmetic object of mathematics. However, it is relatively easy to make a simple geometric expression of it if we represent a fraction y/x by a rectangle of height y and width x. Then the slope of its diagonal is y/x. Thus, a continued fraction can be expressed geometrically as an assembly of rectangles. For the continued fraction of \sqrt{2} we start with a horizontal "long square" (rectangle in 1:2 proportion), then we add a vertical long square (2:1) above with the same width, then a long horizontal square on the right, then again a long vertical square above and so on. |
| Date | |
| Source | Own work |
| Author | Frédéric BEATRIX |
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| current | 19:19, 28 November 2022 | | 1,023 × 1,220 (74 KB) | Fred9871 (talk | contribs) | Uploaded own work with UploadWizard |
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