File:FB-Fraction continue majorante de racine de 3.png
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Captions
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Geometric figure for the continued fraction of root 3 - the upper approximation
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. Une fraction continue s'exprime comme un assemblage de rectangles.
Pour la séquence MAJORANTE fraction continue de racine de 3 on débute avec un carré adossé à un rectangle 3:1 (ce qui forme un rectangle 3:4). Puis on assemble tour à tour un "carré long" (rectangle au format 2:1) au-dessus, puis un carré sur la droite.
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. A continued fraction is expressed as an assembly of rectangles.
For the UPPER approximation sequence of root of 3 we start with a square backed by a 3:1 rectangle (which forms a 3:4 rectangle). Then we incrementally assemble a "long square" (rectangle in 2:1 ) above, then a square on the right. |
| Date | |
| Source | Own work |
| Author | Frédéric Beatrix |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
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| current | 15:22, 29 November 2022 | | 1,023 × 1,220 (64 KB) | Fred9871 (talk | contribs) | Uploaded own work with UploadWizard |
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