FIBONACCI SEQUENCE

The Fibonacci Sequence is the series of numbers:

0,1,1,2,3,5,8,13,21,34,55,...

The next number is found by adding up the two numbers before it:

• the 2 is found by adding the two numbers before it (1+1),
• the 3 is found by adding the two numbers before it (1+2),
• the 5 is (2+3),
• and so on.

Example: the next number in the sequence above is 34+55=89

It is very simple!🤠

Here is a longer list:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, ...

Makes A Spiral

When we make squares with those widths, we get a nice spiral:

Fibonacci spirals in Nature

The Rule

The Fibonacci Sequence can be written as a "Rule".

First, the terms are numbered from 0 onwards like this:

n =  0   1  2  3  4  5  6 7 8 9 ... xn = 0  1  1  2  3 5 8  13  21  34  ...

Example: the 8th term is
the 7th term plus the 6th term:

x₈ = x₇ + x₆

So we can write the rule:

The Rule is x_n = x_n−1 + x_n−2

where:

• x_n is term number "n"
• x_n−1 is the previous term (n−1)
• x_n−2 is the term before that (n−2)

Example: term 9 is calculated like this:

x₉ = x₉₋₁ + x₉₋₂

     = x₈ + x₇

     = 21 + 13

     = 34

History

Fibonacci was not the first to know about the sequence, it was known in India hundreds of years before!

About Fibonacci

His real name was Leonardo Pisano Bogollo, and he lived between 1170 and 1250 in Italy.

"Fibonacci" was his nickname, which roughly means "Son of Bonacci".

As well as being famous for the Fibonacci Sequence, he helped spread Hindu-Arabic Numerals (like our present numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9) through Europe in place of Roman Numerals (I, II, III, IV, V, etc).

Fibonacci Day

Fibonacci Day is November 23rd, as it has the digits "1, 1, 2, 3" which is part of the sequence.