Research Posters

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.  The paper is available here: https://arxiv.org/abs/2404.15142
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.

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.