Operation set
Named by 3 essays across one field — each of them below, with the objects they name alongside it.
What two points can build
A compass and a straightedge are not a craft. They are two operations on a set of points, applied over and over, and writing them that way turns "can this be drawn?" into a question with an answer.
The cube that will not double
Doubling a cube needs an edge in the ratio of the cube root of two. That number satisfies an equation of degree three, three does not divide any power of two, and the oldest open problem in geometry closes in a line.
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.
Named alongside it
The objects these essays reach for when they reach for this one.
Constructible numberStraightedge and compassDegree of an extensionIrreducible polynomialRational root theoremCircleClosureCosineDoubling the cubeField extensionGeometric meanIncidence