Fibonacci sequence

In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted $F_n$. Many writers begin the sequence with 0 and 1, although some authors start it from 1 and 1 and some (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the sequence begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, .....
— Wikipedia

Fiboancci Spiral

A Fibonacci spiral approximates the golden spiral using quarter-circle arcs inscribed in squares derived from the Fibonacci sequence.

Applications of Fibonacci numbers include computer algorithm:

• Fibonacci search technique - Wikipedia
• Fibonacci heap - Wikipedia

Fibonacci sequence generation in Python

Main idea: each number is the sum of the two preceding ones, input is length of Fibonacci sequence, output Fibonacci sequence. We need to store result of latest calculation (sum of A and B), so we need to use temporary variable.

i = 7
a, b = 0, 1
while i > 0:
  print(a)
  c = a + b
  a = b  # it's important to update a before b
  b = c  # b is changed
  i -= 1

Results:

0
1
1
2
3
5
8

Simplified version

a, b = 0, 1  # multiple assignment, initialize variables
while a <= 21:
    print(a)
    a, b = b, a+b  # tuple stored somewhere in memory, unpacked to a, b