Golden number
With Fibonacci numbers you can calculate the golden ratio as
Explanation
We start with the fibonacci sequence
In a representation you can show squares with sides that correspond to these numbers. This results in rectangles where the ratio between long and short sides develops as 3 : 2, 5 : 3, 8 : 5, ...
1 1 3 8 2 5
If you divide each number in the Fibonacci sequence by its direct predecessor you get
1 / 1 = 1.000 2 / 1 = 2.000 3 / 2 = 1.500 5 / 3 = 1.666 8 / 5 = 1.600 13 / 8 = 1.625 21 / 13 = 1.615 34 / 21 = 1.619 55 / 34 = 1.617 89 / 55 = 1.618 144 / 89 = 1.617 233 / 144 = 1.618 377 / 233 = 1.618
The divisions stabilize so that the number 1.61803398874989… is created.
HistoryLeonardo of Pisa (1180 - 1241), known as Fibonacci, described the sequence that was later named after him. |