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This paper explains how to obtain the number Φ, using a square with side length equal to a, the right triangle with sides a/2 and a, and a circle with radius equal to the hypotenuse of this right triangle. In particular, from a square whose side length is equal to a, we will show how to obtain a segment b in such a way that the value of a/b is the...
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... using squares with side length equal to each term of the sequence, as it shows Fig. (2). The growth ratio is Φ, that is, the golden ratio. This Fibonacci spiral, it is found in the spiral structure of the shell of some mollusks, such as the nautilus as it shows Fig. (3), and also in Leonardo da Vinci's masterpieces, as for instance it is shown in Fig. (4). Mathematicians like Edouard Lucas [24] and Kepler studied this sequence, and the Scottish mathematician Robert Simson found in 1753 (later than Leonardo da Vinci's masterpieces) that the relationship between two successive Fibonacci numbers approaches the golden ratio Φ when n tends to ...
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This paper explains how to obtain the number Φ, using a square with side length equal to a, the right triangle with sides a/2 and a, and a circle with radius equal to the hypotenuse of this right triangle. In particular, from a square whose side length is equal to a, we will show how to obtain a segment b in such a way that the value of a/b is the...
