Department of Mathematics Harvey Mudd College 


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 bestknown bound in high dimensions, and some new ideas which produce good upper bounds in both low and high dimensions. 
