The Table Theorem¶
Authors: Roger Fenn
Published: 1970 (Journal Paper)
Source: Bulletin of the London Mathematical Society
Algorithm: The Table Theorem
DOI: 10.1112/blms/2.1.73
Summary¶
Proves the square-table theorem for a continuous nonnegative "hill" f: R^2 -> R that is zero outside a compact convex disk D: for any prescribed square side length, there is a square with center in D on whose four vertices f takes a single value. Later accounts describe this as the problem of balancing a square table on a hill, and follow-up work shows that the convex support condition is essential while several natural strengthenings, such as using only translations or replacing the square by most other polygons, fail.