Phyllotaxis
the spirals are counted, not admired
Concept

Binomial — where it appears

The count of successes in a fixed number of independent trials, each with the same chance. Here it sizes a survey exactly: how many specimens it takes to tell one Fibonacci share from another, with the cut and the power read off summed terms rather than a normal approximation.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

14 specimens separate 14.7% from 50%. The exact binomial power against sample size, for a one-sided test at 5 per cent. It is a staircase rather than a curve because the decision rule is a whole number of specimens: at 14 the cut sits at 5 and the power is 91.0 per cent. A normal approximation smooths that staircase away and reports a different answer.

How many plants would it take

Fourteen specimens separate the geometry's Fibonacci share from a coin weighted to a half. Four separate it from what a grown history gives. One fir cone measured at three rings settles whether its transitions are spaced as a cone's or an ogive's. The sample sizes are small, and that is the uncomfortable part.

wrong · Sample size How many specimens the census needs, counted at four different pairs, as the closing error spreads. The exact one-sided binomial sample size, at five per cent and ninety per cent power, separating the geometry's Fibonacci share from a census of grown plants, every specimen scored as read. Counted at 13/21: 4, 4, 5, 6, 14 specimens; counted at 21/34: 4, 5, 9, 17, 43 specimens; counted at 34/55: 5, 10, 27, 54, 276 specimens; counted at 55/89: 8, 32, 104, 449, none specimens, at spreads of 1.8°, 3.6°, 5.4°, 7.2°, 10.8°. With every count right the answer is four.

The census wants a low count

Four specimens separate the geometry's Fibonacci share of 14.7 per cent from the ninety per cent a grown history gives — if every count is right. Counted with a closing error spread over 7.2°, the same census needs six specimens counted at 13/21, fifty-four at 34/55 and 449 at 55/89, because the geometry's own pairs are all small enough that no closing error under 11° moves them, while a grown plant counted high loses its Fibonacci reading first. Counted at 55/89 with a spread of 9.83° the census reads plants as less Fibonacci than random angles. The count that pins the divergence best is the one a census should avoid.

wrong · Sample size

Named alongside it

The objects these essays reach for when they reach for this one.

CensusFibonacciSample sizeSurveyDivergence angleHonest limitsIdentifiabilityJugacyLadderMeasurement errorParastichy pairRise

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