Chapter 1: The Four Colour Conjecture

The question arises: what is the minimum number of colours required to ensure that no two adjacent regions on a political map share the same colour? The answer is four. While three colours might seem sufficient, eventually, two neighboring areas will inevitably end up with the same hue. However, employing four colours guarantees that any map, regardless of its complexity, can be coloured in such a way that confusion is completely avoided.

The next logical inquiry is how one can substantiate this claim. Proving it is a more complex challenge, and it wasn't until 1976 that a widely accepted proof was achieved. Mathematicians from Urbana, Illinois, employed extensive scenario analysis and computer modelling to reach their conclusion, culminating in a proof that spanned nearly 1,000 pages.

It may seem feasible to visualize a map using only four colours where adjacent areas are the same colour, but attempting it will reveal the impossibility of the task! Regardless of how intricate the shapes may be or how many large regions are adjacent to numerous smaller ones, the rule remains unbroken.

For instance, examining the map of the United States, one can observe that predominantly, only three colours are necessary, with crimson appearing on few occasions. Alternatively, one could have employed orange for Wyoming and blue for Maryland. However, since you cannot utilize "three and a half" colours, the total must be four!

If you're looking for a creative way to keep your children entertained on a rainy Saturday, consider challenging them to prove this theorem through practical application!

The first video, "The Four Color Map Theorem - Numberphile," delves into the intricacies of this theorem and its significance in mathematics.

The second video titled "The Four Colour Theorem" provides further insights and detailed explanations about this intriguing mathematical concept.

For additional engaging articles, visit my collection: Science

For updates and links to other writings, follow me on Twitter @welfordwrites

If you're interested in exploring more content, consider joining Medium to access a wealth of articles from me and other creators. Please note that a small portion of your membership fee will support my work.