Project: Hyperbolic Racquetball
Faculty supervisor: David Dumas
Graduate mentor: Hai Tran
Student researchers: Horalia Armas, Brandon Reichman
Description: We will build a collection of virtual reality experiences to demonstrate features of multiply-connected spaces and hyperbolic geometry (to students, researchers, or anyone else) using the Oculus Rift VR headset and touch controllers. This application will give the user a “first person experience” of different spaces and geometries by allowing them to play a racquetball-like game with infinitely many copies of themselves, arranged according to a periodic tiling of 3-dimensional Euclidean or hyperbolic space.
Prerequisites: Applicants should have some experience with 3D graphics programming.
Materials and resources:
- Video: Playing ball in the 3-dimensional torus
- Pre-alpha software demo (requires Oculus Rift + Oculus Touch):
Project: 3D Printing Surfaces
Faculty supervisor: Daniel Groves
Graduate mentor: Christopher Perez
Student researchers: Alexander Adrahtas, Joel Finlon, Nicholas James
Description: This project is to explore surfaces in three-dimensional space by 3D-printing models of them. The goal is to start by choosing appropriate equations and end with physical models which would be appropriate for use in multivariable calculus classes. This will involve learning about function graphing software, 3D-modeling software and 3D-printing. Time and student interest permitting, we can investigate such things as curvature, ruled surfaces and other things which touch upon ideas from topology, geometry and algebraic geometry.
Prerequisites: Multivariable calculus would be ideal, though it would be possible to succeed in this project whilst enrolled in Math 210.