Whorled — where it appears
Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.
The second moment is the measurement
The mean number of sides in a cellular tissue is six, and Euler's formula leaves it no choice — so it takes the same value on a golden-angle head, a whorled head and a set of random points. The mean squared departure from six varies by a factor of eighty across the same three, and almost nobody reports it.
The six are the spirals
Label every contact between two cells in a seed head with the difference between the two nodes' placement indices. The labels are the parastichy numbers — 34, 55, 21, 89 — and the six sides Euler forces turn out to be about two from one family, one and a half from the next, and one each from two more.
The disorder is a staircase
Sweep the second moment of a head's side-count distribution across the divergence angle and it is not a curve. It is flat in stretches with sharp steps between them and narrow deep dips wherever a rational falls — so 0.253 is not the golden angle's number, it is the number of every angle from 137.47° to 137.54°.
Every family but two is a sum
A seed head has six spiral families and everybody reports two. That looks like a convention hiding information and it is the opposite — every family but the two smallest is the sum of two others, so a third count is a prediction rather than a measurement, and a check that catches a wrong pair.
Named alongside it
The objects these essays reach for when they reach for this one.
LatticeMeasurementRational angleDisorderEuler's formulaGolden angleVoronoi cellsCell areaContinued fractionDelaunayLattice offsetPacking