Laguerre formula — where it appears
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
An angle is a cross-ratio
A projection destroys angle, which every account of perspective says and this site has measured. It destroys it only in the sense that the picture no longer carries it for free — because an angle is a cross-ratio taken against two particular points, and once those two points are located in a photograph the world's angles can be read off it directly, with no rectification, no camera, and nothing measured but which lines pass through which points.
The two points a picture hides
The stratification rung says a photograph of a plane is projective, becomes affine when the vanishing line is known, and becomes metric with one more fact. The one more fact has a size and a shape: it is two points, complex conjugates on the vanishing line, and a rectification built from those two and nothing else returns every world angle to a tenth of a picodegree and every ratio of lengths to five parts in a quadrillion — and refuses to name a length.
Named alongside it
The objects these essays reach for when they reach for this one.
Circular pointsConicDemonstrationline at infinityMetric rectificationProjective stratificationRectificationSimilarityAbsolute conicConic fitCross ratiodegrees of freedom