I don't know why but when I was studying some famous aspects of maths, I developed an appetite. I'm sure you'll understand what I mean when I tell you about them. First I'll start with The Ham Sandwich Theorem.

The Ham Sandwich Theorem

---

This is actually real. This is also the actual name, it isn't just a nickname. Anywho, the theorem says that if you cut the three components of a ham sandwich along a plane then each piece will be cut in half. The three pieces are the two slices of bread and the ham. What you have to appreciate is this isn't just applied to your normal ham sandwich. Mathematicians are on about a ham sandwich which may be any shape at all. Each piece doesn't even need to be connected. However, each shape must have a well defined volume. So in the 3rd dimension, three shapes can be bisected via a plane. This was proved in 1938. This was also further generalised into 'in the nth dimension, n shapes can be bisected.' This was proved in 1942 by Arthur Stone and John Tukey.

Now I quite fancy a sausage.

The Sausage Conjecture

---

Conjecture is the mathematical term for a guess.

Suppose that in the 2nd dimension you are packing circles. You want to use the least amount of material possible so you line all the circles and surround them.

Now imagine that you want the smallest area. You would arrange it into a hexagon as it has the smallest area possible. But in the third dimension, a sausage shape has the smallest. This happens for 56 spheres after which, it becomes a more obscure shape.
In 1975 Laszlo Fejes Toth formulated the sausage conjecture. This states that in five or more dimensions the smallest area is always a sausage shape. In 1998 Toth was proven right by Ulrich Betke, Martin Henk and Jorg Willis. This was that for any number of dimensions greater than or equal to 42, a sausage shape is the smallest area. To date, this is the best we know of.

I wrote this blog because I find it interesting that food can crop up in mathematical theorems/hypothesises.
Bye for now.