Curvature
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
The triangle that a globe gets wrong
On a sphere, a right triangle with legs of fifty and sixty degrees has a hypotenuse of seventy-two, not seventy-eight. The theorem is not approximately true there — it is false, and what replaces it says exactly how much room the surface has.
Seven hundred and twenty degrees of gap
Unfold the faces around any corner of a solid and they do not close up. The gap left over is different at every corner and on every solid, and the gaps always add to two full turns.
Named alongside it
The objects these essays reach for when they reach for this one.
Angle defectDihedral angleEuler characteristicGauss bonnetGeodesicHyperbolic geometryParallel postulatePlatonic solidsPolyhedronPythagorean theoremSpherical excessSpherical geometry