Trisection
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
The angle that will not divide by three
Halving an angle costs one circle. Cutting it in three means solving a cubic, and for sixty degrees that cubic has no rational root — but plenty of angles do trisect, and which ones is a question with a countable answer.
Three trisectors and a triangle nobody expected
Cut every angle of a triangle into three. The trisectors nearest each side meet in three points, and those three points are always the corners of an equilateral triangle — for every triangle there is, with no exceptions and no reason anybody finds obvious.
Named alongside it
The objects these essays reach for when they reach for this one.
Straightedge and compassAngleConstructible numberConstructionCosineCounterexampleDegree of an extensionEquilateral triangleExhaustive searchInvarianceIrreducible polynomialMorley triangle