On the WURSTKATASTROPHE and hairy spherical cows
For the non-German speaking people: The word in the title literally translates to SAUSAGE CATASTROPHE.
You may ask yourself "huh?" and you would be right to do so.
Today I was browsing Wikipedia for some maths stuff. Then the magic of Wiki happened and I clicked one of the many links flying around. I landed on the page for half-integers. These are somehow related to the problem of packing 4-dimensional spheres as tightly as possible (the least amount of space wasted). I read something about that stuff before, so I searched for links leading me to the German page about packing a finite amount of spheres. https://de.wikipedia.org/wiki/Theorie_der_endlichen_Kugelpackungen
This is where the WURSTKATASTROPHE comes into play. If you would like to pack a number of spheres (say, oranges or so) with as little wasted space as possible, what would you do?
Well, the theory of finite sphere packing will tell you, that the form of a sausage would be best (you line them up), BUT this will only work until the WURSTKATASTROPHE takes place. Starting with 55 spheres, the sausage form won't be the best anymore, instead some sort of clustering would fit better. Man, what a disaster!
But don't despair, for there is the WURSTVERMUTUNG (literally sausage conjecture). If you were to live in a higher dimensional plane (starting with 5D), the sausage form would always be best. Sadly, this isn't proved yet.
There are some kinda weird things in maths. I will now explain the second part of the title.
Let's start with the weird thing. The hairy ball theorem ( https://en.wikipedia.org/wiki/Hairy_ball_theorem) . It states (paraphrased), that if you had a ball full of hair, you wouldn't be able to comb it in such a way, that no hair would stand up. In other words: There would always be a cowlick.
What can you do with that. Well, you can model some realistic real life scenarious. Let's assume you had a perfectly spherical cow (https://en.wikipedia.org/wiki/Spherical_cow), just as you can see running around on the fields. You are asked by friends to show it to them, since they like cows. Of course you want to show its best side! So you comb it, but oh noes! Your cow will get a cowlick and there is nothing you can do about that!
Knowing the maths could have prevented you from doing all the pointless work!
It's fun reading about weird mathy things and there are quite a few :)