UROP Research Mentor Project Submission Portal: Submission #1117

Overall Research Project Description Imagine placing four electrons on the sphere of radius 1 (a common beast in a Calculus class). They will repel each other, and therefore move along the sphere. They will stop moving when they reach an "equilibrium state"; mathematically speaking, when their potential energy is minimized. Unfortunately, the word "minimized" has different meanings in pure math vs the real life. In reality, this stable state can be reached at a critical point of the potential energy (the difference between a critical point, a local minimum and a global minimum is a common Calculus 3 problem).

For the project, I propose to collect numerical evidence for the following conjecture: unless the four electrons were placed in a very unfortunate locations, they will reach the stable state at the global minimum of the potential energy. Specifically, they will arrange themselves in the vertices of a regular pyramid.