Concept
Fixed point
2 essays name this object, across one field. What follows is each of them, and 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.
Nothing on a sphere can be combed flat
Point an arrow along the surface at every place on a sphere, continuously, and somewhere an arrow has to vanish. On a doughnut it can be done. The difference between the two is a number that was already known from counting corners.
Named alongside it
The objects these essays reach for when they reach for this one.
ContinuityNonconstructiveBoundaryBrouwerEuler characteristicGenusIndexIntermediate value theoremOrientationRetractionTopological invariantVector field