Undergraduate Math Club Seminar

Under what conditions can we balance a rectangular mathematical table by rotating it about its central axis. We show that for a "nice" enough ground (Lipschitz as a function from R2 → R) and a table with long enough legs, we can cleverly apply IVT to prove the above claim. I also discuss briefly under what conditions differently shaped tables can be balanced via a similar method, and give practical applications for balancing real tables.