What Color is 16?

The curious question, "What colour is 16?" is one that often crops up in discussions about the intersection of maths and art. It might seem counterintuitive to associate a number with a colour, as we typically think of numbers as abstract concepts. However, there's a fascinating mathematical approach that can help us answer this question.

In this exploration, we'll delve into two main topics: the concept of 'number-colour associations' and how they emerge from mathematical structures, and the specific application of this concept to the number 16.

The Concept of Number-Colour Associations

Number-colour associations, or chromatic geometry, is a branch of recreational mathematics that assigns colours to numbers based on their prime factorisation. This idea was popularised by M.C. Escher in his 1947 woodcut 'Crystal'.

In this system, prime numbers are assigned a specific colour, and composite numbers (those with more than two factors) are assigned colours by combining the colours of their prime factors. For instance, 4, which is 2x2, would be blue (2) mixed with blue, creating a darker shade of blue.

Colouring Primes

Prime numbers, being the building blocks of all other numbers, have a special place in this colour system. Each prime number is assigned a unique colour. For example, 2 is white, 3 is yellow, 5 is red, and 7 is green.

This primes-first approach allows us to establish a base palette for our number-colour system. From here, we can generate the colours of composite numbers by mixing these primes.

Colouring Composites

Composite numbers, being products of prime numbers, inherit their colours. For instance, 6, which is 2x3, would be white (2) mixed with yellow (3), resulting in a pale cream colour.

As you can see, this colouring system follows a simple yet logical pattern that reflects the mathematical structure of numbers. Now, let's apply this to our question: what colour is 16?

The Colour of 16

To find the colour of 16, we first need to understand its prime factorisation. The number 16 is a square of 4, which in turn is 2 squared, meaning 16 = 2^4. So, 16 is composed entirely of the prime number 2.

According to the rules of our chromatic geometry system, we look at the colour assigned to the prime number 2. In this system, 2 is white. Therefore, 16, being composed entirely of 2s, is also white.

Expanding the Palette

You might wonder about more complex numbers. As the system stands, numbers higher than 16 start to mix more colours, leading to a broader and more vibrant palette. For example, 18 (2x3^2) would be a mix of white and yellow, creating a light yellow.

This system continues indefinitely, allowing us to colour all positive integers. It's a beautiful example of how mathematics and art can intersect and enrich one another.

So, there you have it. The colour 16 is white. This exploration not only provides an answer to a curious question but also sheds light on the fascinating world of chromatic geometry and the beauty that can arise from the intersection of maths and art.