Concept
Gibbs' phenomenon
The overshoot near a jump in a Fourier partial sum, which narrows as terms are added and never shortens.
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
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.
The staircase that is not the diagonal
A staircase can be made to follow a quarter circle as closely as anyone likes. Its length is 2 at every stage and the arc's length is 1.5708, and no amount of refinement closes the gap — which is a fact about length rather than about staircases.
Named alongside it
The objects these essays reach for when they reach for this one.
ContinuityConvergenceApproximationArc lengthCounterexampleDerivativeHarmonicsLimitOrthogonalityPeriodicityPiRiemann sum