Rearrangement
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
Euclid proves it without moving anything
The rearrangement proof cuts and slides. Euclid's does neither — it shows that a square and a rectangle are each exactly twice the same triangle, seen from opposite sides, and that is harder to hold in the head for a reason worth understanding.
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.
Absolute convergenceAlternating seriesAltitudeAreaCommutativityConditional convergenceCongruenceConvergenceDissectionDivergenceHarmonic seriesHarmonics