Concept
Cosine
3 essays name this object, across 3 fields. What follows is each of them, and the objects they name alongside it.
Two squares, four triangles, and no algebra
The Pythagorean theorem is usually met as a formula to be memorised. It is much better met as a rearrangement that can be checked by eye.
A sine wave is a circle seen from the side
Sine is introduced as a ratio in a right triangle, which is true and explains nothing about why its graph is a wave. There is a better picture.
The dot product is a shadow
Multiply the matching coordinates and add them up. That rule explains nothing, and it hides the fact that the answer is a length — how far one arrow reaches along another, times how long that other one is.
Named alongside it
The objects these essays reach for when they reach for this one.
AreaDerivativeDissectionDot productHypotenuseIncommensurabilityInner productLaw of cosinesMatrixOrthogonalityPeriodicityPi