The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. It is named after the Italian mathematician Leonardo of Pisa, also known as Fibonacci, who introduced the sequence to the Western world in his book "Liber Abaci" in the 13th century. The sequence is often denoted as Fn, with the first two numbers typically being 0 and 1, although some variations start with 1 and 1 or 1 and 2. The first few values in the sequence are:
- 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...
The Fibonacci sequence can be defined by the following recurrence relation:
- F0 = 0
- F1 = 1
- Fn = Fn-1 + Fn-2 (for n > 1)
The sequence has various interesting properties and applications in mathematics, nature, and finance. For example, it is closely related to the golden ratio, a proportion approximately equal to 1.618, which appears in many natural and man-made objects.
