Voronoi cell area — where it appears
Named by 3 essays across one field — each of them below, with the objects they name alongside it.
Packing, measured four ways
The claim is that the golden angle packs best. It is measurable, and the measurement gives three different winners on three criteria — all near 137.5° and none of them it. That does not make the claim wrong; it makes the usual statement of it wrong.
A dip with no outer edge
The disorder of a head dips at every rational divergence, and how wide that dip is has carried a long argument. Reading the width as a level crossing has a resolution problem, and the obvious repair is to integrate instead. The integral reproduces beautifully across head sizes and never settles on a value, because there is nothing out there for it to settle against.
The window is the neighbour
An integral needs a limit, and this one has two conditions on it that pull opposite ways. It has to scale with the dip, so that two head sizes are comparable, and it has to stay clear of the next rational, which is a fixed distance in degrees. Between them there is no stretch where the answer holds still — and the limit that decides it is the crowding.
Named alongside it
The objects these essays reach for when they reach for this one.
Divergence angleRational approximationArtefactConvergentsDiscretisationDisorderHonest limitsMeasurementMeasurement errorNull modelRational angleSampling