Top ten excuses for not doing Math homework
- I accidentally divided by zero and my paper burst into flames.
- Isaac Newton's birthday.
- I could only get arbitrarily close to my textbook. I couldn't actually reach it.
- I have the proof, but there isn't room to write it in this margin.
- I was watching the World Series and got tied up trying to prove that it converged.
- I have a solar powered calculator and it was cloudy.
- I locked the paper in my trunk but a four-dimensional dog got in and ate it.
- I couldn't figure out whether i am the square of negative one or i is the square root of negative one.
- I took time out to snack on a doughnut and a cup of coffee. I spent the rest of the night trying to figure which one to dunk.
- I could have sworn I put the homework inside a Klein bottle, but this morning I couldn't find it.
Topology refers to a particular mathematical object studied in space.
Two spaces are topologically equivalent if one can be deformed into the other without cutting it apart or gluing pieces of it together. The traditional joke is that the topologist can't tell
the coffee cup she is drinking out of from the doughnut she is eating, since a sufficiently pliable donut could be reshaped to the form of a coffee cup by creating a dimple and progressively enlarging it, while shrinking the hole into a handle.
In mathematics, the Klein bottle is a two-dimensional topological space, for which there is no distinction between the "inside" and the "outside" of the surface. The Klein bottle was first described in 1882 by the German mathematician Felix Klein.
Picture a bottle with a hole in the bottom. Now extend the neck. Curve the neck back on itself, insert it through the side of the bottle (a true Klein bottle in four dimensions would not require this step), and connect it to the hole in the bottom.
Unlike a drinking glass, this object has no "rim" where the surface stops abruptly. Unlike a balloon, a fly can go from the outside to the inside without passing through the surface (so there isn't really an "outside" and "inside").
