Concept
Conic — where it appears
A curve cut from a cone by a plane — a circle, an ellipse, a parabola or a hyperbola, according to the angle of the cut.
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
One cone, four curves
The circle, the ellipse, the parabola and the hyperbola look like four separate objects with four separate equations. They are one object, cut at four angles.
Every triple, on one circle
Draw a line of rational slope through a single point of a circle. Wherever it comes out is a rational point, and clearing the denominators turns it into a Pythagorean triple — so every triple there is comes from one line through one point.
Named alongside it
The objects these essays reach for when they reach for this one.
ProjectionBijectionDandelin spheresDegenerate conicDescentEllipseFocusHyperbolaHypotenuseParabolaParametrisationPrimitive triple