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.

proposal Why not put the steering wheel on the other side? When you put the steering wheel on the curb side of the car, the driver can get in and out safely onto the curb. Mail trucks are built like this. Why not all cars?

light Gemstones and light I derive the ideal gemstone shape based on physical principles. Along the way, I uncover connections between gemstones, mirrors, lasers, and glass.

linguistics Colorless green mana sleeps furiously The Magic: The Gathering card game has evolved its own English dialect, complete with new grammar. Here, I describe and codify some of the (implicit) rules.

conic-sections Fitting conics to data Given some empirical data points, find the best-fit hyperbola/parabola/ellipse passing through them. Includes Python code.

pokemon Empirical Pokémon Typing How would you experimentally determine the Pokémon type chart if you didn't already know the types and their interaction strengths?

proposal Social queues My friends and I have developed a helpful strategy for working together. Social queues provide short one-way conversations that enable you to tell someone else that you'd like to talk to them, without interrupting their focus if they're working hard on a problem.

A roadside refueling relay We nearly ran out of gas while driving between states! This usually means walking to the nearest gas station and back. In this article, I devise the optimal cooperative solution.

recreational-mathematics Kinsey arithmetic Converting genders and orientations into numbers allows you to estimate relationship compatibility using arithmetic.

diagrams How to cross the street By optimizing my walk home, I've discovered some beautiful graphs and an unexpected conclusion.

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