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 lfloor n/sqrt{5} rfloor + 1 cops can capture a robber in a square with side length n. We extend these results to three dimensions, proving that 0.34869\cdots n^2+O(n) cops can capture a robber in a nxnxn cube and that a robber can forever evade fewer than 0.02168... n^2+O(n) cops in that cube.
We give four elementary examples of recursion that are real-life, non-trivial, more natural than the corresponding iterative approach, and do not involve any sophisticated algorithms, data structures, or mathematical problems. The examples are two forms of writing numbers in words, coalescing page references for an index, and finding unclosed blocks.