Concept
Termination — where it appears
2 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.
The oldest algorithm, drawn as a tiling
Euclid's method for finding a greatest common divisor is usually presented as a loop. It is also a way of tiling a rectangle with squares, and the tiling explains why it works.
A fraction that never closes
Euclid's algorithm throws away everything except the number of squares it peeled at each step. Those counts are a second name for the number it started from — one that terminates exactly when the ratio is a ratio.
Named alongside it
The objects these essays reach for when they reach for this one.
Continued fractionsFibonacciGreatest common divisorIncommensurabilityContinued fraction convergentEuclidean algorithmGolden ratioLamé's theoremPeriodicityRational approximationTiling