We prove that n cops can capture (that is, some cop can get less than unit distance from) a robber in a continuous square region with side length less than sqrt(5)n and hence that [n/sqrt(5)]+1 cops can capture a robber in a square with side length n. We extend these results to three dimensions, proving that 0.34869...n^2+O(n) cops can capture a robber in an nxnxn cube and that a robber can forever evade fewer than 0.02168...n^2+O(n) cops in that cube.