UROP Openings

Have a UROP opening you would like to submit?

Please fill out the form.

Submit your UROP opening

Tetrahedra


Term:

IAP

Department:

18: Mathematics

Faculty Supervisor:

Bjorn Poonen

Faculty email:

poonen@math.mit.edu

Apply by:

December 11, 2020 at 5pm

Contact:

Bjorn Poonen: poonen@math.mit.edu

Project Description

This will be a large group UROP, run 100% remotely. The goal will be to solve certain problems surrounding the preprint https://math.mit.edu/~poonen/papers/space_vectors.pdf More specifically, students will, in collaboration with others, study tetrahedra that are scissors-congruent to a cube but whose dihedral angles are not necessarily multiples of pi, and try to determine which tetrahedra can tile space (a problem that goes back to Aristotle), and explore higher-dimensional analogues. The administrative details are still being worked out; I expect that participating students may be eligible to earn a small number of units, but not funding. If you are interested in participating, please fill out the form at https://forms.gle/5Q9Fd31aB8tyTMhZ8 preferably by Fri Dec 11 at 5pm.

Pre-requisites

Minimum prerequisite: 18.701, or linear algebra+18.703, or comparable, to be completed by the end of December 2020. Classes like 18.702 and beyond are helpful.