Colouring System

You should be familiar with numbers! One or 1 represents a single unit of something. If you have 1 apple then you can eat at most 1 apple. If you have 2 apples you can choose to eat 1 (and thus have another apple to eat later) or you can eat both apples and be left with nothing (or zero - 0 - apples).

These quantities are represented by symbols that we call numbers, 1, 2, 3, 4 and so on. Numbers are a great way to represent quantities of things and we have 10 of them (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9) to represent any quantity we want. We can combine them to represent quantities larger than 10. For example, the number 23 represents 2 tens and 3 ones (or units). So if you have 23 apples you have 2 groups of ten apples and 3 individual apples.

Combining colours outside of the numbering system is like mixing paints. If you mix yellow and blue you get green. So you should not confuse mixing colours with adding quantities. In fact, mixing colours in different situations results in different results. For example there are two ways colours are mixed, the subtractive way (like mixing paints) and the additive way (like mixing lights). In the subtractive way, mixing yellow and blue results in green. In the additive way, mixing yellow and blue results in white. So you should not confuse mixing colours with adding quantities.

Subtracting is called that way, because light is subtracted when you mix paints. For example, if you mix yellow and blue paint, the blue paint absorbs (or subtracts) every colour except blue and the yellow paint absorbs (or subtracts) every colour except yellow. The only colour that is not absorbed (or subtracted) is green, so you see green. The subtractive way is used in painting and printing.

In the additive way, mixing yellow and blue light results in white light. This is because yellow light is made up of red and green light and blue light is made up of blue and green light. When you mix yellow and blue light, you get red, green and blue light which together make white light. In the additive way, yellow is Red + Green. Adding their frequencies, results in yellow. If you also add the frequency of blue, you get white. The additive way is used in computer screens and televisions.

The colouring system used in the Arcade level in Cuprum is a simple one: Instead of representing quantities with symbols (numbers) we represent them with colours. Each colour may represent a different quantity. For example yellow can represent 3, orange can represent 4 and green can represent 7. In this situation, if we were going to add yellow and orange together (3+4) we would get green (7). So yellow + orange = green.

This is a completely different system from the additive and subtractive systems described above. In the colouring system, colours represent quantities and combining them represents adding those quantities together. So if you have yellow (3) and orange (4) you can combine them to get green (7). In this way, colours are used to represent quantities and combining them represents adding those quantities together.

Cuprum makes an effort to use colours that are easy to remember at the start. Because in the Arcade, you need to complete the pythagorean theorem equations, you will find that in some cases: - Yellow represents 3 - Orange represents 4 - Red represents 5

And while Yellow + Orange does not make Red, the Square of Yellow + the Square of Orange makes the Square of Red. This is because 3^2 + 4^2 = 5^2 (9 + 16 = 25).

In order to find more about squaring, go to the Colourful Algebra