We show that if the unit square is covered by n rectangles, then at least one must have perimeter at least 4(2 m+1)/(n+m(m+1)), where m is the largest integer whose square is at most n. This result is exact for n of the form m(m+1) (or m2).
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics