Approximation of Points on Higher Dimensional Spheres

Max Trimmer ’27

Faculty Mentor: Dr. Cha

What is the broader impact of your summer research? That is, why should the world care about your work?

While physical space might only be 3D, plenty of data sets and mathematical models are higher dimensional. Knowing about the geometry of higher dimensional spaces gives us tools that could help analyzing these datasets and models. It gives information on the distribution of Pythagorean triples, which provides insight into the geometry of higher dimensional space. It also gives a way to approximate irrational points in higher dimensional space.

What has summer research taught you about yourself and the field that you researched and/or studied?

I learned that I work well independently, and that I work better when I split my time up instead of trying to do everything all at once. I also learned that I am capable of living independently and cooking for myself. I learned valuable organizational skills. I also learned how to use SageMath for mathematical computation. I learned how to find and read mathematical literature as well. I also learned plenty of background knowledge about geometry and number theory.

What advice would you give to students considering a future research opportunity similar to the one you participated in?

Make sure you take care of yourself. Take breaks when necessary. Get organized. Make sure you love what you do.