Summary on Latin Squares

This project was quite an adventure from the beginning.  While it was difficult, and ultimately impossible, to find the true formula that I was looking for at the beginning, I learned a lot about the implications of sequences and prime numbers in the grand scheme of mathematics. To recap briefly my project, I began with a numerical analysis of several different sizes of Latin square, including 3×3, 4×4, 5×5, 6×6, and 7×7.   The number of possible Latin squares at each size increased rapidly, and after 7×7 it was much too large to realistically calculate.  I was able to break these numbers down and apply a few different types of tests to these in order to find a pattern leading from one to the next, but the large primes which appeared in the prime factorizations of the numbers prevented any conclusive pattern from appearing. After spending a lot of time working with those numbers, I turned to the second stage of my project.

The second stage was building an app that would allow users to create their own Latin Squares and try to find as many distinct squares as they could. This proved to be difficult even before I actually had to make the app, as acquiring the software I wanted to use was very complicated.  As mentioned in an earlier update, the virtual machine which I attempted to build did not work, and the software wouldn’t run on Windows, so I had to make use of the media center software to make the app.  Not being able to run the software on my own computer poses a problem for display, but if I can find a way to get the app on something portable, it will be on display with the rest of my research at the fair.