Concept
Imaginary unit
A square root of minus one, multiplication by which turns the plane through a quarter turn. Adjoining it to the reals gives a field in which every polynomial has a root, which is what the fundamental theorem of algebra says.
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
Multiplying is turning
Complex numbers are introduced as an algebraic dodge for square roots of negatives. They are better understood as the arithmetic of rotation, at which point every rule stops needing to be remembered.
Completing the square, by completing a square
The step everybody is taught as an algebraic trick is a literal instruction about a literal square. There is a corner missing, its size is forced, and paying for it is the whole method.
Named alongside it
The objects these essays reach for when they reach for this one.
Algebra tilesAreaArgumentCompleting the squareComplex exponentialDissectionModulusPiQuadratic polynomialsRootsRoots of unitySquare numbers