Fibonacci numbers in nature. « Philosophy is written in this huge book that I call universe which has always been opened in front of us but we can’t understand it if we first don’t know its language and its characters. This book is written in the Mathematics language
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that I call universe which has always been opened
in front of us but we can’t understand it
if we first don’t know its language and its characters.
This book is written in the Mathematics language
and the characters are triangles, circles and geometric figures. Without them it is impossible to understand philosophy;
without them it would be like getting lost in a maze».
Galileo Galilei, Il Saggiatore
According to the growth of flowers, the number of most of their petals is a Fibonacci number.
For example lilies have got three petals, buttercups five, chicories 21, daisies could either have 34 or 55; the head of sunflowers is formed by two spirals: one in a direction, the other in the opposite one.
The number of spirals changes between 21 and 34, 34 and 55, 55 and 89, or 89 and 144 seeds.
The same thing happens for pine cones, shells and pineapples
Leonardo of Pisa, also known as Leonardo Fibonacci, was considered the most talented mathematician of the Middle Ages.
Here’s the succession he used for a test on rabbits’ breeding:
f(1) = 1
f(n + 2) = f(n) + f(n + 1)
The numbers he found are called
Fibonacci numbers and they are:
1 1 2 3 5 8 13 21
34 55 89 144 233
377 610 ....................
They have so many applications that
there’s also a Maths magazine, called Fibonacci Quarterly.
If we draw horizontal lines through the axils, we can detect obvious stages of development in the plant. The main stem produces branch shoots at the beginning of each stage. Branch shoots rest during their first two stages, then produce new branch shoots at the beginning of each subsequent stage. The same law applies to all branches.
Furthermore, the number of leaves in any stage will also be a Fibonacci number.
It is a famous game, created by Samuel Loyd in 1878. It consists of a square table, usually in plastic, divided into four rows and four columns, with 15 square tiles, numbered from 1 in random order.
The tiles can scroll horizontally or vertically, but their shift is obviously limited by the existence of a single blank space. The goal of the game is to reorder the tiles after “mixing” them.
the attached game with
the first 15 numbers of