light Flying eaves These upward-curving roofs let in daylight while keeping rain out. You can calculate the amount of daylight for a given roof shape using trigonometry.
morsels Categorical orientations The pan and ace orientations are optimal in a certain mathematically rigorous sense.
morsels Convex shadows Any convex 3D object will have a silhouette of a certain area. Averaged over all viewing angles, the size of the silhouette is exactly a quarter of the object's surface area. Why? By dimensional analysis, the size of the silhouette must be proportional to
morsels Commuting polynomial chains Find a sequence of polynomials, one for each degree, that all commute? There are essentially only two possibilities.
morsels Cheap numbers The buttons on your postfix-notation calculator each come with a cost. You can push any operator (plus, minus, times, floored division, modulo, and copy) onto the stack for a cost of one. You can also push any integer (say, in a fixed range 1.
morsels Loop counting If there's a unique two-step path between every pair of nodes in a directed graph, then every node has \(k\) neighbors and the graph has \(k\) loops, where \(k^2\) is the number of nodes in the graph. A graph where there's exactly one
morsels M'aide! One afternoon, you call all your friends to come visit you. If they all depart their houses at once, travel in straight lines towards you, and are uniformly distributed throughout the surrounding area, how many people should you expect to arrive as time goes
