Concept

Identifiability — where it appears

4 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.
137.51°, rise 0.098.5e-14°counted 2/3137.51°, rise 0.032.0e-13°counted 3/5137.51°, rise 0.0122.8e-14°counted 5/899.50°, rise 0.083.0e-13°counted 1/3151.14°, rise 0.071.1e-13°counted 2/399.50°, rise 0.021.1e-13°counted 4/7error in the recovered divergence anglecounts and hop lengths onlyworst 3.0e-13°

Two numbers out of the points

A seed head's divergence angle can be recovered from its spiral counts only to within an interval, because a range of angles gives the same counts. On a stem the counts come with lengths attached, two measurements pin two unknowns, and the lattice comes back to the last digit it was built with.

cylinder · cylinder recovery
-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
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 angleFibonacciLadderRiseSurveySpecimenBinomialCensusConeCounting radiusCylinderInverse problem

All concepts