On June 7, every visiting researcher in the DIMACS program gave a 10-20 minute introductory project about their summer research. On the right is a link to the slides that Ethan McCarthy and I presented to a group of our peers: 06/07/2011
We were fortunate to inherit a program written by Stephen Weaver, which we used in our presentation, called Orbit Tracer (now found on Ethan McCarthy's website).
On July 5, I began a recreational project studying random number generators. I made a series of graphs to study how the generator would sequences of numbers over time. The compressed file may be downloaded here and seems to indicate an ergodic conclusion. The culmination of this project was a webpage conceived of and created by Ariel "Random" Allon. Before long, his page was found to be erroneous in the face (no pun intended) of the far superior page made by Michael "Fore" Kopinsky.
On July 14, Ethan McCarthy and I delivered our final presentation. The presentation was divided into three sections:
Proven results to count and classify orbits in rectangles, isosceles right triangles, and 30-60-90 triangles,
Unproven conjectures to explain underlying processes in these studied shapes, and methods to study other shapes,
and roadblocks encountered: which shapes' unfoldings do not yield clear formulas to determine the orbits' period.
Throughout the summer, the air conditioner has been bothering me. Though it certainly keeps my room at a comfortable temperature, the air conditioner nonetheless provides the area underneath it with considerable drippage. I left (most of) my tools at home, so I was certainly not planning on fixing the air conditioner myself. Still, I was at Rutgers for the summer on a Math REU, so I chose to analyze the situation mathematically. I happened to have brought a roll of duck (is it duck or duct?) tape with me so, whenever I found that a drop had dripped from the air conditioner onto my desk (and located where the drop landed, I placed a small square of duck tape over the drop. I recently took a picture of the scatter plot that formed on my desk. Through the plot I was able to locate the most likely spot where water fell on my desk and decided to only leave my mediocre quality work in that region.
