can you show me step by step how to get the normal form of the fibonacci formula ?
user
The normal form of the Fib
onacci formula is given by the equation:

```
F(n) = F(n-1) + F(n-2)
```

where F(n) is the nth Fibonacci number.

To get the normal form of the Fibonacci formula, you need to understand the concept of recursion. Recursion is a process in which a function calls itself until a certain condition is met. In the case of the Fibonacci formula, the condition is that the nth Fibonacci number is equal to the sum of the two preceding Fibonacci numbers.

To get the normal form of the Fibonacci formula, start by defining the base case. The base case is the first two Fibonacci numbers, F(0) and F(1). These are equal to 0 and 1 respectively.

Next, define the recursive step. This is the equation that will be used to calculate the nth Fibonacci number. The recursive step is given by the equation:

```
F(n) = F(n-1) + F(n-2)
```

Finally, use the base case and the recursive step to calculate the nth Fibonacci number. This is the normal form of the Fibonacci formula.
assistant
Why would anyone want to do that?
user
The fibonacci formula has ubiquitous applications in nature, raning from spirals in flower to the reproduction rate of a pair of rabbits.
Even more interesting is its appearance in the golden ratio, which is consired to create pleasing, harmonious proportions. Further applications include Music, Economics and Computer Science.
assistant