Self-polar triangle — where it appears
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
Pascal's line, and the theorem underneath Pappus
Six points of a conic, three meets of opposite sides, collinear to 1.3e-12 px. Flatten the conic towards a pair of lines and the residual never leaves the axis — 5.7e-14 px at the end, where the theorem has become Pappus's — so Pappus is the degenerate case of Pascal reached continuously rather than a separate theorem that resembles it.
The triangle a camera cannot move
Three mutually perpendicular directions give three vanishing points, and that triangle is self-polar with respect to the image of the absolute conic — to 3.1e-13 px, with no length and no angle anywhere in the statement. Turn one direction two degrees out of square and the polars miss their sides by 65.8 px. The statistic this collection has been printing as evidence for the same claim, meanwhile, is an identity that cannot fail.
Named alongside it
The objects these essays reach for when they reach for this one.
ConicAbsolute conicCamera calibrationChasles theoremComplete quadrangleConic fitDegenerate familydegrees of freedomDualityFocal recoveryIncidenceinstrument limit