Imagine a rectangular grid of points with spacing (a,b) along the x and y directions, respectively, starting at the origin and filling all four quadrants. Center a rectangular box on the origin. The question is: what is the box of largest area that contains only the single point at the origin? The sides of the box can just touch other points, but no other point can be in its interior. Trying some cases, I find: a) trivially, the largest box whose sides are parallel to x and y has area A = 4ab. b) if the box is tilted so its end touches a point on the line x = a (and, of course, the other end touches the mirror symmetric point at x = -a), the largest area is A = 4ab regardless of tilt. c) if the box is long and skinny so it passes between two of the points located on the line x=a (and corresponding points on x=-a), A=4ab. Well it looks like there's a pattern! Does anyone know of a general theorem? This problem came up in the context of synthetic aperture radar imaging.