# Numbers

by Lea Rosema

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.

### The length of a number

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``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

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``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

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``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

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#### Linear Interpolation

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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)``