Fibonacci Series

The Fibonacci series is a sequence of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1. It has deep connections to many aspects of mathematics, nature, and art.

Definition

The Fibonacci sequence is defined recursively as:

F(0) = 0, F(1) = 1

F(n) = F(n-1) + F(n-2) for n > 1

Visual Representation

The Fibonacci spiral is an approximation of the golden spiral created by drawing circular arcs connecting the opposite corners of squares in the Fibonacci tiling.

Applications

Nature

The Fibonacci sequence is frequently observed in the natural world, from the arrangement of leaves on a stem to the branching of trees and the spiral patterns of various flowers and seeds.

Mathematics and Art

The sequence also holds a special place in art and mathematics, especially in connection with the golden ratio, which artists and architects have employed for centuries to achieve balance and beauty in their works.