File:11.19 Fraction continue - Phi.png
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Captions
Captions
Geometric expression of the continued fraction of the golden ratio
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 fraction continue du nombre d'or on débute avec un deux carrés, puis on ajoute un carré au-dessus de même largeur, puis un carré à droite de même hauteur que l'ensemble, puis à nouveau un carré au-dessus et ainsi de suite. Cette construction donne les nombres de la suite de Fibonacci.
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 continued fraction of the golden number we start with a two squares, then we add a square above of the same width, then a square on the right of the same height as the whole, then again a square above and so on right now. This construction gives the numbers of the Fibonacci sequence. |
| Date | |
| Source | Own work |
| Author | Frédéric Beatrix |
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