Overview:
What does the spiral arrangement of leaves on a pine cone have in common with the arrangement of florets in a center of a daisy or the spirals of fruit buds on a pineapple? Those spirals can be approximated by a mathematical sequence of numbers known as Fibonacci numbers.
What Is the Fibonacci Sequence?
The Fibonacci Sequence is a definite pattern that can begin with either 0, 1 or 1, 1. The sequence is generated by adding the previous terms, so that 0 +1 equals 1, 1+1 equals 2, 2 + 1 equals 3, 2 + 3 equals 5, 5 + 3 equals 8, 8 + 5 equals 13, 13 + 8 equals 21, 21 + 13 equals 34, 34 + 21 equals 55, and so on. In other words, the sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on, infinitely.
How Do Other Numbers Relate to the Fibonacci Sequence?
Not all numbers are Fibonacci numbers. However, they can be generated by adding Fibonacci numbers. For example, 4 is not a Fibonacci number, but it is the sum of two Fibonacci numbers, 3 + 1. Similarly, 10 is not a Fibonacci number, but it is the sum of 2 Fibonacci numbers, 8 + 2. Sometimes it takes more than 2 Fibonacci numbers. For example, 43 is the sum of 34 + 8 + 1. The number 95 is the sum of 89 + 3 + 1 + 2.
What Is the Golden Ratio?
The Golden Ratio is a mathematical relationship that is closely related to the Fibonacci sequence. The ratio of the first two Fibonacci numbers 1/1 is equal to 1, and the ratio of the second two, 2/1 is equal to 1 + 1/1. The ratio of the third, is 3/2, or 1.5. The ratio of the fourth is 5/3, or 1.66. No matter how many adjacent Fibonacci numbers are compared, the ratio of those numbers is very close to a number that the ancient Greek mathematicians called phi (φ). The number phi has several connections with classical proportions in art, geometry, and architecture.
What Are Other Applications of Fibonacci Numbers?
Fibonacci numbers are also used in applications of computer algorithms. They can be used to compress audio files and generate code. They permeate art, music, and literature. Most recently, Fibonacci numbers have been used to symbolize mathematical relationships in The DaVinci Code, as well as in the TV shows Fringe, Criminal Minds, and Taken.
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