The Fibonacci sequence is a famous mathematical series in which each number is the sum of the two preceding ones, starting from 0 and 1.

Key Characteristics:

1. Starting values: The sequence starts with 0 and 1.
2. Recursive rule: After the first two numbers (0 and 1), each subsequent number is the sum of the two preceding numbers: F(n)=F(n−1)+F(n−2)
3. Growth pattern: The Fibonacci sequence grows exponentially, and the ratio between consecutive Fibonacci numbers approaches the golden ratio (approximately 1.618) as the sequence progresses.

Applications:

1. Mathematics: Fibonacci numbers appear in many areas of mathematics, such as number theory, combinatorics, and geometry.
2. Nature: The sequence is often observed in nature, such as in the arrangement of leaves, flowers, or the spirals in shells.
3. Art and Architecture: The golden ratio derived from Fibonacci numbers has been applied in art and architecture for aesthetically pleasing proportions.