Concept
Caustic
A curve that every trajectory of a family stays tangent to and never crosses. In a billiard table the caustics bound the regions a path cannot enter, and a table filled with them is one whose motion is completely organised rather than chaotic.
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
A bounce is a fold of the table
Reflect the room instead of the ball and every bounce disappears — the trajectory becomes a straight line through a tiled plane, and questions about what a ball does forever become questions about the slope of that line.
A room that cannot be lit
Mirror the walls of a room and put a lamp inside it. Every point should be lit, since light bounces forever — and there are rooms with a dark spot no ray from the lamp ever reaches.
Named alongside it
The objects these essays reach for when they reach for this one.
BilliardsIntegrabilityPeriodic orbitReflectionConicCounterexampleEquidistributionFocusImpossibilityInvariantIrrational rotationUnfolding