File:11.20 Fraction continue - V3.png
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Captions
Captions
Geometric representation of the continued fraction of \sqrt{3}
Summary edit
| 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.
Une fraction continue s'exprime comme un assemblage de rectangles. Pour la suite MINORANTE de racine de 3 on débute avec un "carré long" (rectangle au format 2:1), puis on ajoute tour à tour un carré sur la droite de même hauteur, puis un carré long au-dessus.
English: Continued fractions are considered an arithmetic object of mathematics. However, it is relatively easy to express it with a simple geometric expression : we represent a fraction y/x by a rectangle of height y and width x. Then the slope of its diagonal is y/x.
A continued fraction is therefore a sum of rectangles. For the LOWER approximation of root 3 we start with a "long square" (rectangle in 2:1 format), then we add incrementally a square on the right of the same height, then a long square above. |
| Date | |
| Source | Own work |
| Author | Frédéric Beatrix |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 15:36, 29 November 2022 | | 1,023 × 1,220 (62 KB) | Fred9871 (talk | contribs) | add title on the right - this is the lower sequence of approximation |
| 12:11, 28 November 2022 |  | 1,023 × 1,220 (50 KB) | Fred9871 (talk | contribs) | Uploaded own work with UploadWizard |
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