Orbit — where it appears
Named by 3 essays across 3 fields — 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.
Numbers that wrap
A clock does arithmetic. It has finitely many numbers, addition never leaves it, and multiplication behaves entirely differently depending on one property of the size of the dial.
Necklaces that prove a theorem
Thread five beads in two colours, thirty-two ways. Two of them are all one colour; the other thirty fall into rings of five. That count, and nothing else, is Fermat's little theorem.
Named alongside it
The objects these essays reach for when they reach for this one.
CompositeCyclic groupFermats little theoremModular arithmeticModulusOrderPrimesBoundaryBrouwerContinuityCounting two waysFixed point