Saturday, March 24, 2012

the golden number

Cálculo del valor del número áureo
Dos números a y b están en proporción áurea si se cumple: \frac{a+b}a=\frac ab
Si al número menor (b) le asignamos el valor 1, la igualdad será: \frac{a + 1}{a} = a
multiplicando ambos miembros por a, obtenemos:  a + 1 = a^2 \;
reordenamos:  a^2 - a - 1 = 0 \;
La solución positiva de la ecuación de segundo grado es:  \frac{1+\sqrt{5}}{2}=1\textrm{'}6180339887\ldots que es el valor del número áureo, equivalente a la relación a/b.
An example of the golden ratio in architecture is the rosette of the Cathedral of Santa Maria de Palma de Mallorca in Spain, also known as the Eye of Gothic construction being Gothic, has been cited as the world's largest Gothic in reference and allusion to the dimensions of the glass surface. Measured between 12.8 and 13.8 meters in diameter and has nearly 100 square meters. It is composed of 1,236 crystals. It was built in 1370 and was subsequently stained glass windows were added in the sixteenth century. Other features of this huge rosette are the perfect Star of David made ​​up of 24 triangles that its tracery drawn on it and its peculiar location being situated on the main sanctuary and not the feet as usual. Throughout history, the rose has had to be replaced on several occasions, the last time by the fall of a bomb in the palace of La Almudaina during the civil war.

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