The Fibonacci sequence begins with 1, 1. From there on, each term is the sum of the previous two terms. The first few terms of the sequence are:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, …

The Fibonacci sequence appears often in nature. The sequence is found in the spiral patterns of pine cones and flowers. The number of spirals traced one way will usually be a Fibonacci number. The number of spirals traced the other way will be an *adjacent* Fibonacci number. Count the spirals in this pine cone:

### and in this flower:

#### The ratios of adjacent terms of the fibonacci sequence are also interesting.

## 1 / 1 = 1## 1 / 2 = .5## 2 / 3 = .666667## 3 / 5 = .6## 5 / 8 = .625## 8 / 13 = .615385## 13 / 21 = .619047## 21 / 34 = .617647## 34 / 55 = .618182## 55 / 89 = .617977## 89 / 144 = .618056## 144 / 233 = .618025## 233 / 377 = .618037## 377 / 610 = .618033## …## approaching | ## 1 / 1 = 1## 2 / 1 = 2## 3 / 2 = 1.5## 5 / 3 = 1.666667## 8 / 5 = 1.6## 13 / 8 = 1.625## 21 / 13 = 1.615385## 34 / 21 = 1.619047## 55 / 34 = 1.617647## 89 / 55 = 1.618182## 144 / 89 = 1.617977## 233 / 144 = 1.618056## 377 / 233 = 1.618025## 610 / 377 = 1.618037## …## approaching |