Today in Knot Theory we went back to link invariants. We first learned one called the unknotting number--the minimum number of changes to crossings that it's necessary to make to turn a knot into the unknot. We also learned one called bridge number. The bridge number is the minimum number of maximal overpasses (basically, but not exactly, any strand that crosses over others) that a knot can be drawn with. She tried to have us show the diagram in which the bridge number of a particular five-crossing knot was 2, but no one could. Then she assigned us to show that any rational knot could be drawn as a 2-bridge knot, but no one made much progress on that either. Apparently we will be going back into it on Monday, and she'll explain the solution to us all.
Since today was the last day of Arete (each Arete class is only a week long), there was a showcase performance and each class that had something to perform did so. For the juggling performance, I demonstrated two-person passing juggling with someone else in the class, and also performed with the poi. (I think poi are just really fun to swing around, even if they hurt a lot if you mess up and they hit you.)
|The theme of the dance was "glowing"|
This evening there was also a dance which everyone was required to attend. I was there for about five minutes before the strobe lights and ear-drum-bursting music gave me a headache (plus, who wants to be in a closed room with lots of hot, sweaty teenagers for any amount of time?). Luckily, there was a game room off of a different hallway where the atmosphere was more sane. I spent the majority of my time in there, making friendship bracelets and teaching other people how to make friendship bracelets because apparently not everyone knows. I had sort of assumed that friendship bracelets were just something you learned to make at around seven or eight, but I suppose not. Raymond, a boy in my Knot Theory class, was one of the ones I taught. He said it reminded him of the knots we draw in class. Interestingly, friendship bracelets aren't actually knots (mathematically, anyway), because the ends of the strings aren't connected, so they can be untied without breaking the string. (Theoretically. Who would go to the trouble of unraveling a friendship bracelet, I don't know.)
Something annoying that happened today was that someone screwed up the lamp search. The clue was "I'm hanging out with Calvin's best friend," and it was by Hobbs building. Someone found it during lunch; however, during lunch you're not supposed to leave the dining hall, so it didn't count and they didn't get any points. Nonetheless, it had already been found from its hiding place, so no one else was able to look for it either.