The 4 Colour Theorem Explained

Описание: For my video submission, the “4 Colour Theorem Explained”, I highlight some of the underlying principles of Graph Theory and the century old 4 colour problem. I was introduced to this topic when I watched a video by NumberPhile on non-planar graphs. In particular, I found it very interesting to learn how mathematicians found elegant ways of visualising and classifying 2 dimensional graphs.

I begin my video by introducing a hypothetical scenario, where a king has assigned the viewer a task to colour a map with as few colours as possible. I then transition to explaining the theorem at hand and highlight its fundamental components. Finally, I use animations to show how mathematicians were able to prove the theorem using a computer. All along, I place heavy emphasis on visual elements and include many diagrams and equations to support my narration.

The crux of my video is to accentuate how there are certain limits as to how we can draw maps and how mathematicians found a certain set of 1936 reducible configurations for planar maps. I want my video to show viewers how universal math is, and how it has applications in every facet of our daily lives.

This is how I envision math communication, where powerful animations make “Math come alive” and drive understanding. Through my videos, I want to reiterate that math neither is trivial nor uninteresting, but actually fascinating, and rooted in elegant ideas with truly tremendous applications in the real world.

-Submitted for the Strogatz Math Prize. Edit: won second place