Mathematisms

An Intuitive Explanation of Monsky's Theorem

1. Introduction

Let’s set the scene. I (16M) am a huge fan of Minecraft. As such, since my birthday is coming up, I obviously want to get a Minecraft themed birthday party - this will include a pig pinata, Minecraft themed utensils, and obviously, a Minecraft cake.

Minecraft Cake

A wonderful Minecraft cake.

When it comes time to cut the cake, I’ve only got a couple of - relatively self explanatory - rules. Obviously, I want every cut of the cake to be a triangle (for the sake of tradition), and I want every single cut to have an equal area, to avoid situations like this.

Slightly Less Cake

He got slightly less cake.

I invited six people other than me to my birthday party. How should I cut the cake?

At a first glance, it seems like there has to be a solution. I mean, there’s an infinite variety of ways to cut a cake into \(7\) triangles - surely one of them is such that all the triangles have equal area, right?

In fact, I encourage you to give this problem a shot! Try to split a...

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