How a Ham Sandwich Helps You Understand Mathematics (and the Universe)

Mathematics is an abstract method to describe topics such as quantity, structure, and even space, which sometimes presents quite an obstacle for everyday folks to understand. To make things easier to grasp, mathematicians like to describe their ideas using terms that are relatable to daily life. 

The Ham Sandwich Theorem (also known as the Pancake Theorem) is a perfect example. It states that for a sandwich, consisting of a slice of ham and two slices of bread, there's always an angle that allows one to cut all three pieces in half in a single shot, wherever any piece of the sandwich may be.

To put it in a more mathematically precise way, in a Euclidean N dimensional space (ours is 3), any N compact objects (3 in our situation) can be equally bisected (cut in half) by a (N-1)-dimensional hyperplane (2-dimensional plane in our scenario). Now you see why mathematicians have to call this Ham Sandwich theorem (for the sake that more people can understand). 

What's more fascinating, two mathematicians at the Georgia Institute of Technology dug deep into this theorem and found something that is both astronomical and mind-bending. According to their paper in 2011, the calculation led them to conclude that "at any given instant of time, there is one planet, one moon and one asteroid in our solar system and a single plane touching all three that exactly bisects the total planetary mass, the total lunar mass, and the total asteroidal mass of the solar system."

Source: Seeker via Youtube