Last Week

I haven't posted in a long time, sorry about that. It's dead week, which means that the semester is officially over one week from today. I'm excited for my trip, but I'm also going to miss my friends who are leaving for the states.

Europe is funny, because everything is so close. My friend Todd lives in Denmark right now, and even though he's countries away he doesn't feel distant at all. If I wanted to, I could buy a plane ticket for less than 100 dollars, and in a couple hours I could see him. On the other hand, the US is so big, that unless someone lives in a neighboring state, they might as well be on another planet. And I don't have a rocket ship. Not that I would know how to fly a rocket ship if I had one anyway. The point is, that I may never see a lot of these people again.

I haven't updated since before the putnam exam, so I haven't told anyone how I think I did. I'm pretty sure I got two problems correct, and part of another one. I'm pretty content with my performance for now, but I have big expectations for next year.

Also, my camera is broken. The flash stopped working, and it won't take pictures without the flash. So, I'm sorry for not uploading pictures.

I'm going to get back to preparing for finals, but I'll leave you with a little thing to think about. We proved this in Conjecture and Proof, and it's called the Banach-Tarski Paradox. It uses something called the "axiom of choice", and because its such a strange result, some people believe that the axiom of choice must not be assumed. Most mathematicians accept the axiom, though, but just think that this result just shows how funny math can be.

If you have a sphere, then it IS possible to turn it into two equal copies of itself (which doubles the volume).