Senior Thesis

Department of Mathematics
Harvey Mudd College

Adam Bliss

Harvey Mudd College Mathematics 2003

Thesis: Covering Numbers of the Cubes (PDF)

Thesis Advisor: Prof. Francis Su
Second Reader: Prof. Henry Krieger

Covering Numbers of the Cubes

How many triangles does it take to make a square? The answer is simple: two. This problem has a direct analogue in dimensions three and higher, but the answers are much harder to find. We provide new lower bounds in dimensions 4 through 13, an asymptotic lower bound which is inferior to the best-known bound in high dimensions, and some new ideas which produce good upper bounds in both low and high dimensions.