Research Projects

This project took place Summer 2023 after my graduation from CSUF. Dr. Murphy and I characterize the Archimedean solids among the convex uniform polyhedra by circumscribing with regular tetrahedra. We produce a construction for the Archimedean solids resulting from specific truncations applied to the tetrahedron. The main mathematics is mostly basic geometry and trig but I made use of Grasshopper (a computational geometry tool), python, and several 3D modeling programs while exploring this problem.  

Preprint - https://arxiv.org/abs/2404.15142
Publication - https://doi.org/10.1007/s13366-026-00842-0

With additional result in CSUF's Dimensions journal: https://www.fullerton.edu/nsmssc/_resources/pdfs/2024_dimensions.pdf

Here we explore an esoteric programming language from Conway. In the original paper Conway provides a program that generates the digits of Pi using Wallis' product. We alter his code and produce a program for the digits of sqrt(2). K. Kaushik was the primary "programmer" for this project while I assisted by creating the diagrams shown as well as assisted in the background research needed to understand the original code.

Publication - https://doi.org/10.33232/BIMS.0095.23.34

We generalize several formulae involving Chebyshev type orthogonal polynomials to the matrix value case. The two cases considered involve different weight functions and involved using Birkhoff decomposition and quasideterminants.