Concept

Survey — where it appears

7 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.
golden 137.51°55 and 89FibonacciLucas 99.50°47 and 76Lucas151.14°50 and 81neither77.96°37 and 60neithercounted from the pointsone sequence per branch

Fibonacci is a branch, not a law

Fibonacci counts come from one branch of the model. The Lucas branch — which the same rule reaches at a different growth rate — gives 47 and 76, and neither is a Fibonacci number. The sequence is a consequence of an angle rather than a property of plants.

wrong · fibbranch
5/107.9%5 × 1/23/67.9%3 × 1/22/46.1%2 × 1/24/85.5%4 × 1/27/145.2%7 × 1/26/122.8%6 × 1/28/160.1%8 × 1/2share of divergences at this riserise 0.008 · 3600 divergences35.4% share a factor

What "whorled" was hiding

The expansion phase's census put 35% of divergences in a bucket labelled whorled and moved on. Opened, every pair in it is k and 2k — the coarsest rung of the ladder, repeated k times — and reading the census up to jugacy takes the Fibonacci share from 14.7% to 50.1% without describing a single extra plant.

wrong · jugate census
Fibonacci59.6%Lucas20.8%whorled10.7%other8.9%5 distinct pairs over 1200 divergencesrise 0.100Fibonacci 59.6%

How often is it Fibonacci

The claim that plant spirals come in consecutive Fibonacci numbers is stated as a near-universal. Asked of the geometry, the answer collapses with scale — at a coarse rise 67% of divergences give Fibonacci pairs, and at a fine one 15%, with whorled and unnamed pairs taking the rest.

wrong · frequency
-10111.5022.503product of the two counts, log₁₀angles left open, log₁₀ °7 pairs · edges found by bisectionwidth × mn = 221°

What a count is worth

A reported parastichy pair pins the divergence angle to a band 221°/mn wide — so 2 and 3 says almost nothing and 34 and 55 fixes it to a tenth of a degree. Every rung of the ladder is worth a factor of φ², and the counting radius this collection has asked published counts for since its foundation adds ten per cent.

wrong · count value
00.2500.5000.75015101520specimenschance of detecting it14 specimens90%exact binomial · one-sided at α = 0.0514 specimens, cut at 5

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 ladder is spaced as a cone's or an ogive's. The sample sizes are small, and that is the uncomfortable part.

wrong · sample size
plants show consecutive Fibonacci pairs far more…4and more often even than a coin weighted to a half14a conifer cone's rings are spaced as a cone rather…1multijugate patterns are a real minority rather than…34against 14.7%, if the truth is 90%needs: the pair, at a stated rungagainst 14.7%, if the truth is 50%needs: the pair, at a stated rungagainst φ² = 2.62, if the truth is φ^(2/1.88) = 1.67needs: three ring positions, to ±3%against 2%, if the truth is 15%needs: the pair; the whorl's symmetryspecimens neededexact binomial · α = 0.05 · power 0.91 to 34 specimens

The survey this site cannot do

Four phases of asking for a dataset, and it is still not here. What this phase can do instead is specify it — the fields, the sampling, the sizes, and which of this collection's claims each one would settle. Two of the four fields asked for turn out to be worth less than the asking implied, and one was never asked for at all.

wrong · survey spec
error per ringrings neededspread vs bound1%4 of 5 rings1.9% > 1.4%1%5 of 5 rings8.2% > 2.8%2%5 of 5 rings8.2% > 5.7%3%not on this oneunder 8.5%5%not on this oneunder 14.1%8%not on this oneunder 22.6%an ogive · 5 rings available5 rings at 1%

How much of a cone to measure

Two rings cannot show a varying exponent — not with difficulty, but in principle, because one gap determines one exponent with nothing left to disagree. Four or five can, if each is found to within a per cent. At three per cent this specimen cannot be told from a power law however many of its rings are recorded.

cylinder · ring identifiability

Named alongside it

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

Divergence angleFibonacciRiseCensusLadderBranchIdentifiabilityJugacyCounting radiusParastichy pairRotational symmetrySample size

All concepts