Intermediate value theorem
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
Something always stays put
Stir a cup of coffee however violently and let it settle. Some molecule is exactly where it started. Crumple a map and drop it on the region it depicts, and one point lies over the place it names.
One line that halves them both
Two shapes lying anywhere on a page, of any sizes and any shapes at all. There is always a single straight line that cuts both of them into two equal halves at once — and finding it needs no cleverness, only the observation that a quantity which reverses sign has to pass through zero.
Named alongside it
The objects these essays reach for when they reach for this one.
BrouwerContinuityFixed pointNonconstructiveAntipodal pairBisectionBoundaryDegreeExistence proofFair divisionOrbitRetraction