Thursday, July 16, 2015

The Lamp Champ

A fourteen-crossing torus
We started off class today by learning about Conway's notation, which is another way to write down knots that is completely different from Dowker notation. Conway sequences come from the twists that are performed when the knot is made, rather than the finished knot. Unfortunately, they can only be used for rational knots (knots made by twisting and reflecting), which not all knots are. They are very useful for determining if two rational knots are the same, though, because if the knots are the same, the continued fractions of the Conway sequences are equal.

Some sort of 3D knot program which is too advanced for us to
do, but was found while playing with the KnotPlot program
Right before lunch, we went outside to take class pictures. After the standard one where all of us were lined up, we decided to make a human knot and take a picture from above, which was fun. At lunch, I sat with Hummd, Arnold, Katherine, and two boys from my Knot Theory class, Liam and Raymond. Near the end, one of the proctors who was walking around the dining hall ran up to me and said, very excitedly, "Oh my gosh, your bracelet is like magic!!" She looked at it for about twenty seconds to figure out that it had arrowhead patterns and not just chevrons. That was interesting. I like having a magical bracelet.

After lunch, we went back to the computer lab to make torus knots. After we figured out the assignment (how many components a given torus has; the greatest common divisor of the number of loops and the number of cycles), she told us to just play with the program for the last hour.

In the TA session, my TA, Jeff, talked a little more about continued fractions. While typing this, I realized that continued fractions are impossible to write in a blog post, so the rest of this paragraph is going to be pictures.

Isn't this awesome?!

On a different topic, the clue for the lamp today was "I sit under a chair." At first I was thinking that it would be a chair somewhere, but then realized that there were way too many chairs and no way to narrow it down, if that were so. So I started thinking about a chairperson, like on a board of directors. The next step down from a chairman (the person who "sits under the chair(man)") is a president or vice-president. The first place I looked was in the Hank lobby, and as it happened there was a portrait of a previous vice-president of the Vanderbilt Board of Trustees. There was a chair beneath it, and I must have spent at least five minutes looking around and underneath it, and in between the cushions, but no luck. Then I recruited Miranda, a girl from my proctor group, to help me, and we went outside. I had noticed on my walk to class that there was a statue of the chairwoman of the Board of Trustees on Hank lawn, so we went there first. We looked underneath it, and around all the blocks of marble in front of it, and then finally I looked down the back of the base, and in between the bushes and the marble base was nestled the pink lamp. (It was nice to find it so quickly, but I'd actually been planning to spend most of my free time looking for it, since it's fun. Instead, I talked to Hummd and Katherine for an hour.) When I walked over to give it to Linzie, the proctor, he said, "Now you're 2-0 against literally everyone in the program." Miranda started calling me "the lamp champ" in our proctor group's group messaging chat, and the name seems to be sticking.

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