Tag: cool studies

Cutting a pizza – it’s easy as pi

A bunch of mathematicians (no doubt uni students) have attempted to solve the dilemma of distributing pizza slices evenly to people who have made equal contributions to the pizza buying cause. This article explains.

The problem that bothered them was this. Suppose the harried waiter cuts the pizza off-centre, but with all the edge-to-edge cuts crossing at a single point, and with the same angle between adjacent cuts. The off-centre cuts mean the slices will not all be the same size, so if two people take turns to take neighbouring slices, will they get equal shares by the time they have gone right round the pizza – and if not, who will get more?

It’s complex. Apparently. If you have two diners, and the pizza is cut an even number of times, the trick is to take alternate pieces.

It has been known since the 1960s that when N is even and greater than 2, an answer to the first question is for Gray and White to choose alternate slices about the point P of concurrency.

The conclusion – from the paper that’ll cost you $20 to buy – was this:

It was conjectured by Stan Wagon and others, that for N=3,7,11,15,…, whoever gets the center gets the most pizza, while for N=5,9,13,17,…, whoever gets the center gets the least. We prove this Pizza Conjecture by first showing its equivalence to a (pretty wild) trigonometric inequality. This inequality is proved with the aid of a theorem that counts lattice paths. Our main theorem is sufficiently general that, as a bonus, results concerning the equiangular slicing of other dishes are obtained.

One can only assume all this would be easier with one of these plates.

How zombies work

In the latest bit of cool, but mostly frivolous, science – a Harvard Psychiatrist has explained how zombies work. Now we’ve got mathematical modeling of the zombie outbreak and an understanding of their headspace.

The Frontal Lobe

This part of the brain is involved with “executive functioning” – enabling us to think carefully and solve problems in an abstract way. Clearly, there’s not much going on there if you have the misfortune of being afflicted with living deadness. But we do know that zombies can see us and sense us. Schlozman concludes that zombies possess just enough frontal lobe activity to “listen” to the thalamus, through which sensory input is processed.

But the frontal lobe function most relevant to understanding zombie behavior is the control of “impulsivity”-the general term for when you do something and, if you had two more seconds, you might not have done it. For instance, if in a fit of rage you have the sudden urge to punch your boss in the face, the frontal lobe intervenes and allows you to consider why that might be a bad idea.

The Oatmeal has a nice graphical warning about the coming zombie apocalypse. It’ll be eye-opening. But it might contain some words you’ll find offensive – so be warned.