Harmonics
Named by 3 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.
A sum whose terms vanish and whose total does not
Add a half, a third, a quarter, and keep going. The terms shrink to nothing and the total passes every number there is — but so slowly that no computation will ever watch it happen.
The same terms, in a different order, adding to whatever is asked
Flip alternate signs in the harmonic series and it converges. Reorder the terms — add nothing, remove nothing — and it converges to any number chosen in advance. Addition stops being commutative, and the picture shows where it goes.
Named alongside it
The objects these essays reach for when they reach for this one.
ConvergenceDivergenceHarmonic seriesLimitLogarithmAbsolute convergenceAlternating seriesBlock stackingCommutativityConditional convergenceContinuityThe Euler–Mascheroni constant