Mathematics

Geometry was not my specialty, and I still maintain that most of it is stupid. HOWEVER, since I wrote some pretty good looking term papers for a required geometric analysis course, I'm including this section purely out of pride. Here are the term papers:

• Term paper 1: "Geometry from a Taxicab"
• Term paper 2: "Cyclic Quadrilaterals"

The first term paper is about a norm known colloquially (at least in mathematics) as the "taxicab norm". It is a method of measuring distance which gives results similar to a taxi driving along blocks of a city to reach its destination. In general, it gives greater lengths than if one were to measure a straight line from the origin to the destination. When applying this norm to a general cartesian space, shapes take on odd properties. For instance, a circle using the taxicab norm would insteadlook like a diamond.
The second term paper is about cylic quadrilaterals. These are four-sided figures which can be placed on a circle such that all four of their corners lie on the circle. While interesting, there is very little information in this subject as they are more or less regarded by mathematicians as inconsequential. The paper contains some neat information about these quadrilaterals and their unique properties.

Much of my numerical analysis work involved testing the limits of exactness in the computing systems we used. For instance, when using native C data types such as float, analytical interpolation algorithms would often fail very quickly. Most of the code I wrote for this purpose was in C, but in some cases I did use Python for additional library support and when I felt like using the programming language equivalent of crayons. You can access the programs I wrote on my GitHub page here. The small followup papers I wrote on them are listed below.

• Estimating the Zeta Function using C
• Interpolating functions using the Lagrange method
• Estimating integrals using methods of varying precision
• Estimating differential equations using various methods