Defining the Fibonacci Sequence
The Fibonacci sequence is a famous series of numbers in which each number is the sum of the two preceding ones. It traditionally starts with 0 and 1. The sequence therefore begins: 0, 1, 1, 2, 3, 5, 8, 13, 21, and continues indefinitely.
Section 2: The Mathematical Rule
The sequence is defined by a simple mathematical recurrence relation: F(n) = F(n-1) + F(n-2), where F(n) is the term number 'n'. The initial values are set as F(0) = 0 and F(1) = 1. To find any number in the sequence, you simply add the two numbers that came before it.
Section 3: A Practical Example in Nature
A classic example of the Fibonacci sequence in nature is the number of petals on many flowers. For instance, lilies and irises often have 3 petals, buttercups have 5, delphiniums have 8, and marigolds can have 13 petals—all of which are consecutive Fibonacci numbers.
Section 4: Why Is It Important?
The Fibonacci sequence is important because it appears unexpectedly often in nature, art, and science, describing patterns of growth and structure. It is closely related to the Golden Ratio (approximately 1.618), a proportion found in architecture, art, and natural forms, demonstrating a fundamental mathematical principle in the world around us.