Concept
Imaginary unit
2 essays name this object, across one field. What follows is each of them, and 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