Serie de Fibonacci en Java

Es interesante ver cómo mediante la lógica se puede reproducir esta serie,en un programa computacional:

public class Fibonacci
{
    public static void main(String args[])
    {
        int a=0;
        int b=1;
        int serie=0;
        System.out.print((a+b)+"\t");
        for (int i=0;i<7;i++)
        {
            serie=a+b;
            a=b;
            b=serie;
            System.out.print(serie+"\t");
        }
    }
}

La sucesión de Fibonacci

La sucesión de Fibonacci es una secuencia de números enteros descubierta por matemáticos hindúes hacia el año 1135 y descrita por primera vez en europa gracias a Fibonacci (Leonardo de Pisa). La sucesión se describe de la forma siguiente:

F(0) = 0;
F(1) = 1;
F(n) = F(n-1) + F(n-2)

Lo que da la recurrencia siguiente:

0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597

Aparte de que esta sucesión tiene varias propiedades interesantes, como que se puede formar cualquier número natural mediante la suma de términos de la sucesión, sin que ninguno se repita, lo más curioso de esta sucesión es su presencia en la naturaleza. La sucesión de Fibonacci está muy ligado a la vida y estos hechos lo demuestran:

Los machos de una colmena de abejas tienen un árbol genealógico que cumple con esta sucesión. El hecho es que los zánganos, el macho de la abeja, no tiene padre (1), pero sí que tiene una madre (1, 1), dos abuelos, que son los padres de la reina (1, 1, 2), tres bisabuelos, ya que el padre de la reina no tiene padre (1, 1, 2, 3), cinco tatarabuelos (1, 1, 2, 3, 5), ocho tataratatarabuelos (1, 1, 2, 3, 5, 8) y así sucesivamente, cumpliendo con la sucesión de Fibonacci.

En la mano humana también se encuentra esta recurrencia, la longitud del metacarpo es la suma de las dos falanges proximales y la longitud de la primera falange es la suma de las dos falanges distales.

El número de pétalos de una flor es generalmente un término de Fibonacci. Hay flores con 2 pétalos, 3, 5, 8, 13, 21, 34, pero muy rara vez es un número que no esté en esta sucesión.

En la relación entre la altura de un ser humano y la altura de su ombligo.

En las espirales de los girasoles.

En las espirales de las piñas.

La relación entre la altura de la cadera y la altura de la rodilla.

Número áureo

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Real concepto de arte

Según la Real Academia Española la definición de arte es la siguiente: 


"Conjunto de preceptos y reglas necesarios para hacer bien algo."


En la actualidad las personas tienden a definir arte simplemente como un conjunto de técnicas que tienen el fin de expresar algún mensaje o sentimiento. Sin embargo arte va mucho más allá de esa vana definición, incluso, es erróneo el concepto de que mediante una obra se da un solo  mensaje, ya que cada persona interpreta diferente.


A pesar de que muchas veces despreciamos el arte y pensamos que es un pasatiempo para algunos, pero nada importante; deberíamos saber que el arte es el valor de cambio más caro que existe, para comprobar esta afirmación basta con conocer que el banco del Vaticano es el más poderoso, pues posee obras de suma importancia.


Para conocer realmente el significado de arte debemos tener claro los siguientes conceptos: