## What is the 1, 1, 2, 3, 5, 8 Sequence Called?

The sequence 1, 1, 2, 3, 5, 8 is known as the **Fibonacci sequence**. This famous sequence is named after the Italian mathematician Leonardo Pisano, better known as **Fibonacci**.

### Understanding the Fibonacci Sequence

The Fibonacci sequence is defined by the following rule:

**The first two numbers in the sequence are 1 and 1.****Each subsequent number is the sum of the two preceding numbers.**

Therefore, to get the next number in the sequence, you simply add the last two numbers together. Here's how the sequence continues:

1, 1, 2, 3, 5, 8, **13**, **21**, **34**, **55**, **89**, ...

### Significance of the Fibonacci Sequence

The Fibonacci sequence appears in nature, art, and mathematics in surprising ways. It is often found in:

**Plant growth patterns:**The arrangement of leaves on a stem, the spirals of a sunflower, and the branching patterns of trees often exhibit Fibonacci numbers.**Animal bodies:**The number of spirals on a snail shell, the arrangement of scales on a pine cone, and the segmentation of a honeybee's body often follow Fibonacci patterns.**Art and architecture:**The proportions of the Great Pyramid of Giza, the paintings of Leonardo da Vinci, and even the layout of the Parthenon are said to incorporate Fibonacci principles.**Computer science:**The Fibonacci sequence is used in algorithms for sorting, searching, and data compression.

### The Golden Ratio

The Fibonacci sequence is closely related to the **Golden Ratio**, often represented by the Greek letter phi (φ). The Golden Ratio is approximately **1.618**. As the Fibonacci sequence progresses, the ratio of consecutive numbers approaches the Golden Ratio.

For example:

- 8 / 5 = 1.6
- 13 / 8 = 1.625
- 21 / 13 = 1.615

The Golden Ratio also appears in nature and art, and its presence often contributes to the perceived beauty and harmony of objects and designs.

### Conclusion

The Fibonacci sequence is a fascinating and pervasive mathematical pattern with applications in various fields. Its simplicity, elegance, and connection to the Golden Ratio make it a subject of continued study and wonder.