Concept
Periodicity
3 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.
A sine wave is a circle seen from the side
Sine is introduced as a ratio in a right triangle, which is true and explains nothing about why its graph is a wave. There is a better picture.
A square wave built entirely out of round ones
Add enough sine waves together and flat tops and vertical cliffs appear from nothing. Almost — there is a 9% overshoot that never goes away, and it is not a bug.
Numbers that wrap
A clock does arithmetic. It has finitely many numbers, addition never leaves it, and multiplication behaves entirely differently depending on one property of the size of the dial.
Named alongside it
The objects these essays reach for when they reach for this one.
PiSineContinuityConvergenceCosineCyclic groupDerivativeFermats little theoremGreatest common divisorGibbs' phenomenonHarmonicsModular arithmetic