One of my favorite pastimes is thinking up some random problem, not knowing how I might even approach a solution, and then persevering until I figure it out. Simpler problems (or variations of them) end up in the Math Problems section here, while more difficult problems turn into excellent research topics.
In Spring 2013, I thought up a problem which I was not quite sure how to solve, so I approached one of my professors with it: Given sticks of possible sizes one through six, what is the smallest number of sticks you can have to ensure that you are able to form a perfect square? It turned out to be a rather in-depth question, so I set out to answer it. In the following paper, I define the problem clearly, provide pseudocode for generating results, and share a C++ program which I wrote in order to generate results. My talk on this research received 3rd place at the 2013 AUM Undergraduate Research Symposium.
From June 2012 to May 2013, I worked for Dr. Luis Cueva-Parra as a paid research assistant funded by the U.S. Department of Energy. Our efforts were part of a larger group under the name NePCM (Nano-enhanced Phase Change Materials). The purpose of our team was to explore the physics of nanofluids undergoing phase change and to model it using computer simulations and advanced modeling techniques. Read more >>
This solution to a journal problem was published in Pi Mu Epsilon's Fall 2013 journal:
In Fall 2012, a friend showed me a card trick. Amazed that the process worked every time, I set out to figure out why. After discovering the "trick" to the trick, I set out to generalize it for any size deck. Here is that generalization. My talk on this research received the Patterson Award at the MAA Southeastern Section 2013 Conference.