So… we are in the business of doing nerdy things (like data science and engineering). Just to brighten your day here’s an extra piece of maths that you didn’t know you needed.
Imagine you wanted to get to Essen (it’s an awesome city), but you had a powerful enemy that didn’t want you to go, and they had the powers to drop you anywhere in another country, say some place in France. How would they choose where in France to put you to make your journey as difficult as possible? Well, they would choose the point in France that is furthest away from Essen. Somewhere in the Pyrenees.
And here we go… Felix Hausdorff dealt with this problem from a theoretical viewpoint about a century ago and invented the corresponding distance metric. It’s called Hausdorff metric and you might have heard about it in a topology class if you ever had the pleasure of taking one.
And here’s the fun bit… As theoretical as this metric sounds, we can actually use it to cluster routes for mining machines. How cool’s that?