Table Problem Revisited

Abstract

We revisit Fenn's table theorem from a differential-topological point of view. We prove a zero-existence theorem on a cylinder, which gives a short proof of the horizontal square-table theorem under Fenn's boundary conditions, and We establish a theorem under more general boundary conditions. We also discuss square tables on saddle surfaces and conjecture that every sufficiently small square table can be placed horizontally on a saddle surface. We further conjecture that any prescribed rectangular table can be placed horizontally on a Fenn graph.