La secuencia de Fibonacci es una de las series matemáticas más interesantes de la ciencia por su presencia absoluta en multitud de elementos de la vida y la naturaleza. Además de tener propiedades especiales, existe en la geometría, en el álgebra y en la teoría de los números, además de otros campos de las ciencias exactas. Pero lo más curioso de esta serie es su constante en la naturaleza, en las plantas y animales y en otras disciplinas humanas como la arquitectura o el arte.
La vida de Fibonacci
Fibonacci se llamaba en realidad Leonardo Pisano y nació en Pisa alrededor de 1170. Su padre, Guglielmo dei Bonacci, era un rico mercader pisano y representante del gremio comerciante de la República de Pisa en el área de Bugía en Cabilia (Argelia hoy en día).
Después de 1192, llevó a su hijo a trabajar con él ya que quería que aprendiera el oficio. Así empezaron los estudios de Leonardo bajo la guía de un maestro musulmán que le enseñó técnicas de cálculo, especialmente las relacionadas con los números indoárabes, que aún no se habían introducido en Europa.
La educación de Fibonacci comenzó, de esta manera, en Bugía y continuó después en Egipto, Siria y Grecia. Estos lugares formaban parte de las rutas comerciales de Guglielmo, que mantuvieron a Fibonacci en constante movimiento hasta regresar a Pisa a partir de 1200. Durante los siguientes 25 años, Fibonacci se dedicó a escribir manuscritos matemáticos introduciendo conceptos que jamás habían llegado a Europa.
La reputación de Leonardo como matemático se hizo tan grande que el emperador Federico II solicitó una audiencia mientras estaba en Pisa en 1225, para otorgar el título de Discretus et sapiens magister. Este reconocimiento significa maestro juicioso y sabio, y premiaba el progreso que hizo Fibonacci en las matemáticas. Su trabajo en esta ciencia continuó por muchos años hasta su muerte, que tuvo lugar después de 1240, presumiblemente en Pisa.
La reproducción de los conejos y el descubrimiento de la secuencia
Fibonacci registró en su publicación Liber Abaci o Libro del Cálculo su estudio sobre los números indoárabes, que más tarde suplantarían a los números romanos utilizados hasta entonces. El oficio de su padre lo llevó a aplicar sus conocimientos matemáticos al comercio, incluyendo análisis de relación entre precio y producto, cálculo de beneficios o conversión de divisas.
Su trabajo supuso una gran influencia en autores posteriores, especialmente su investigación en la reproducción secuencial de los conejos. Planteó la siguiente cuestión:
¿Cuántos pares de conejos nacerán en un año, a partir de un solo par, si cada mes cada par da a luz un nuevo par que se vuelve reproductivo a partir del segundo mes?
La solución a este problema es la famosa secuencia de Fibonacci: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89… Se trata de una serie de números en la que cada cifra es la suma de las dos anteriores: 0, 1, 1 (1+0), 2 (1+1), 3 (1+2), 5 (2+3), 8 (3+5), 13 (5+8), y así consecutivamente hasta el infinito.
Cuando Fibonacci ilustró esta secuencia como una solución a un problema de «matemática recreativa», no le dio particular importancia. Pero en 1877, el matemático Édouard Lucas publicó varios estudios importantes sobre la serie y la bautizó Secuencia de Fibonacci en honor al autor.
Más tarde se descubrieron numerosas e inesperadas propiedades de la secuencia a partir de nuevas investigaciones que otros matemáticos desarrollaron. En 1963 se publicó una revista dedicada exclusivamente a la serie, The Fibonacci Quarterly, El Fibonacci Trimestral.
La secuencia de Fibonacci en la naturaleza
Observando la geometría de las plantas, flores o frutos, es fácil reconocer la presencia de estructuras, patrones de crecimiento y formas recurrentes. La secuencia de Fibonacci juega un papel vital en la filotaxis, que estudia la disposición de las hojas, ramas, flores o semillas en las plantas, con el objetivo de encontrar la existencia de pautas regulares.
Los diversos arreglos de elementos naturales siguen regularidades matemáticas sorprendentes. D’arcy Thompson, un biólogo, matematico y profesor escocés, observó que el reino vegetal tiene una curiosa preferencia por números particulares y por ciertas geometrías espirales. Estos números y geometrías están estrechamente relacionados.
Podemos encontrar fácilmente estos patrones en margaritas, girasoles, coliflores o en el brócoli.
Kepler notó que en muchos tipos de árboles, las hojas están alineadas en un patrón que incluye dos números de Fibonacci. A partir de cualquier hoja, después de una, dos, tres o cinco vueltas de la espiral, siempre hay una hoja alineada con la primera. Según la especie, será la segunda, la tercera, la quinta, la octava o la decimotercera hoja. De nuevo, la frecuencia matemática.
La secuencia de Fibonacci es un patrón numérico omnipresente y quizás el más intrigante de las matemáticas. Lejos de ser solo una curiosidad o una simple coincidencia, esta serie incluso inspira a muchos arquitectos y artistas para elaborar sus creaciones buscando la perfección de la naturaleza.
El universo entero se encuentra plagado de esta frecuencia de números, ¿en dónde más lo puedes identificar tú?
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