Math + CS = 11

In the words of my geometry teacher, Michael Keyton, Möbius Strips are “interesting creatures.” What makes them interesting are the number of sides and “tops” and “bottoms” that they have, which is only one. Yes, one! They have only one side and only one top (or bottom depending on your view). In our three dimensional world this makes no sence because we never see such a surface. If you were to draw a line down one “side” of it and kept going, you would end up back where you started and upon inspection, you would find that your line is next to both “sides” of the Möbius Strip. Hard to believe? Yes.

What happens if you cut one in half lengthwise? We were discussing this in my vector calculus class yesterday and I was convinced that you would get two strips of paper. How could you not? You’re cutting it in half! Other people claimed that you would still only get one piece, except it would be twice as big. Wait, what?!?! The teacher said that they were correct, that cutting a Möbius Strip down the middle would produce one strip that is twice as big as the first. I did not belive this and had to try it myself by making my own paper Möbius Strip and cutting it down the center. Before I did so, I drew a line down one “side” of it so that I can have a reference to whatever happens after I do cut it. My mind exploded. There was only one strip of paper.

I had to do this again, except paying close attention to what happens. In class, people argued that because the Möbius Strip has only one side, which is infact twice the length of the paper, cutting it down the middle wil produce the second side and will also be twice the length of the paper and thus only one strip will be produced. After cutting the Möbius Strip strip down the cetner again, that is exactly what happens. The new strip also has what appears to be two twists in it.

But wait, there’s more! What happens if I cut it a different way? Maybe instead of down the middle, what if I cut the Möbius Strip near an edge? You get the inner third of the original Möbius Strip which is also a Möbius Strip and a large strip with two twists in it, like with what happens when you cut the original Möbius Strip down the center.

I did this a few more times and went over to the library to get a few books on topology. I will probably won’t get close to getting through them though, but I do plan on checking some more out before break so I can work through them over break. I decided that it would be pretty neat to do a presentation on Möbius Strips for BarCamp (http://www.barcamproc.org) so I will be doing that.

In conclusion, everyone needs t go make Möbius Strips right now. And make a lot of them. It will be awesome, trust me.