So as we created a calculator back to chapter 11, we know how to to display information using the title. However we also know about **Stored Spaces** and **Functions**. We can now use them to add more awesome features to our tiny calculator. First, we can save our result in a file using Stored Spaces:

( space ,// something here) ( $result , @space )'ANS: \(@space)'

Let’s create some functions for our calculator. Do you remember the `!pow(number,power)`

function we wrote together? If you put the `pow.arendelle`

file into the folder where your `calc.arendelle`

file is you can then use it in our calc:

( space ,!pow ( 2 , 7 )) ( $result , @space )'ANS: \(@space)'

And you will see the **ANS: 128** in the title! Something I want to show you are recursive functions:

Do you know the **factorial** operator? It’s like this: When you write `5!`

( *! is the factorial sign* ) you get this:

5! = 5 × 4 × 3 × 2 × 1

And so the factorial of 12 will be:

12! = 12 × 11 × 10 … 3 × 2 × 1

So as you saw `5!`

was `5 × 4 × 3 × 2 × 1`

just like the end of the `12!`

and that’s why we can write this:

12! = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5!

Or even this

12! = 12 × 11!

You see each factorial is connected to it’s preview factorials for example if you want to calculate factorial of 4, you have to do `4 × 3!`

and then you have to calculate `3!`

using `3! × 2!`

till you get to `1!`

which you know it’s `1`

.

In the programming there is a very fun thing called **Recursive Function** which is a function that uses itself! Each math operator like factorial is a function. So as you saw we used factorial to calculate factorial which means we used a function in itself!

Let’s write factorial using recursive technique to see how can you use a function in itself. First create the function `!fact(number)`

and then write this code for it:

< number >{ @number = 1 ,( return , 1 ),( return , @number * !fact( @number - 1 ) )}

You see? We’re calling for function `!fact()`

from the function `!fact()`

! It’s really an amazing possibility we have in programming to call a function from itself!

Exercise Do you know the **Fibonacci sequence**? It’s a sequence of numbers which each number is the sum of it’s two previous number like:

1 1 2 3 5 8 13 21 …

You see `2`

is the sum of `1`

and `1`

, `13`

is the sum of `5`

and `8`

, `5`

is the sum of `2`

and `3`

and so on… Write a recursive function named `!sumOfFibonacci(number)`

that calculate the sum of the `@number`

first members of the sequence like:

!sumOfFibonacci( 4 ) = sum ( 1 , 1 , 2 , 3 ) = 7!sumOfFibonacci( 7 ) = sum ( 1 , 1 , 2 , 3 , 5 , 8 , 13 ) = 33