chocolate oranges

Every year around this time, I open up a chocolate orange and begin to wonder the same thing. As I remove wedges of the chocolate treat, is there any point at which the surface area of the partially-eaten chocolate orange is greater than the surface area of the intact orange? In other words, given a piece of foil that just covers the full orange (with no foil left over), will removing wedges render the foil insufficient to cover the remaining orange?

some sums

Had trouble falling asleep last night, so I began adding up numbers in my head. "Discovered" this interesting property of integers, though I'm sure it already exists more formally in the mathematics world:

Let n be a positive integer. Let S be the sum of all integers from 1 to n, inclusive.

If n is odd, then S is a multiple of n. However, the same property does not exist for even numbers.

It will take me some time to try to even wrap my head around this, and who knows if I even have the ability to do so. But pretty cool nonetheless. And a bit frightening that this is what goes through my head in the wee hours of the morning...