Region count
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
Four circles cannot do it
Three overlapping circles cut the plane into exactly the eight regions three sets need. Four circles cut it into fourteen, and sixteen are required — so the diagram everyone draws stops working at four, and the reason is a count.
Which side of the line is inside
A closed curve with no self-crossings divides the plane into an inside and an outside. Nobody doubts it, almost nobody can prove it, and on a curve wound tightly enough nobody can see which side a given point is on either.
Named alongside it
The objects these essays reach for when they reach for this one.
Closed curveArrangementBoundaryConnectednessContinuityConvexityCounterexampleEuler formulaMembership patternNon orientableParitySet operations