Cone — where it appears
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
The cone that reads the floor
A conical mirror standing on a design turns it into a picture, and the map it performs is exact, one-to-one, and not a projectivity — a homography fitted to four of the marks returns those four to 7e-13 mm and puts the rest 2480 mm away, on a design 369 mm wide. The reason is that the cone turns the annulus inside out: the middle of the picture comes from the far edge of the floor and the rim from the near one.
The floors that unroll
A ridged floor curves visibly and can be laid flat without stretching anything — 7.4e-9 of strain across the patch. A dished floor curves less and cannot be laid flat by any means whatever. The difference is one number, Gaussian curvature, and it is the number Gauss proved no bending can change: 0 for the ridge, 0.0144 per square metre for the dish, and no cleverness in the flattening touches it.
Named alongside it
The objects these essays reach for when they reach for this one.
DevelopableAnamorphosisArc lengthArea scaleCentral collineationcentre of projectionConformalCylinderGaussian curvatureHomographyInvertibilityIsometry