# Maths basics

## Everything about numbers

In this chapter, we'll regard numbers as 1D vectors. This way, we can reuse the knowledge to abstract things to the second and third dimension.

*(TODO: add a nice scale diagram with examples here)*

### The length of a number:

```
abs(x)
```

Lengths are always positive, so the length of a number is the absolute value of the number.

- the number
`1`

has a length of`1`

. - the number
`-2`

has a length of`2`

.

### The direction of a number:

```
sign(x)
```

There are two directions when moving on a number scale. Left (`-1`

) and right (`1`

). The formular for getting the direction of the number is `x / abs(x)`

. In the world of vectors, this would be called "normalized" vector.

- the direction of the number
`5`

is`1`

- the direction of the number
`-2`

is`-1`

- the direction of
`0`

is not defined

### The distance between two numbers:

```
abs(b - a)
```

The distance between two numbers can be calculated by subtracting the numbers and measuring the length between the two.

- The distance between
`-1`

and`1`

is`2`

### Interpolation between numbers

#### Linear Interpolation

Linear interpolation is used to transition between 2 values.

The function for interpolating between 2 values looks like this, taking 2 values `a`

and `b`

and a third parameter `x = [0..1]`

.

```
mix(a, b, x) = a * x + b * (1 - x)
```