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the-band-a-count-leaves

The divergence axis from 20° to 180°, with the angles consistent with each reported pair marked on it. 2/3 allows 38.8° of it; 34/55 allows 0.118°, which at this scale is thinner than the line drawn for it. The golden angle is marked because every one of these bands contains it.
What each report rules outThe divergence axis from 20° to 180°, with the angles consistent with each reported pair marked on it. 2/3 allows 38.8° of it; 34/55 allows 0.118°, which at this scale is thinner than the line drawn for it. The golden angle is marked because every one of these bands contains it.20°60°100°137.5°180°137.51°2/338.8°5/85.5°13/210.811°34/550.118°every band contains the golden angle — what changes is how much else it containsdivergence swept 20°–180° · edges bisected38.8° down to 0.118°

Drawn at its defaults, in the survey this site has not done. It takes no options at all, so every essay calling it gets this exact drawing.

Called by 6 essays

the blast radius of changing it

The pattern itself

Counting the spirals

Almost every claim about phyllotaxis is a claim about how many spirals run through a pattern, and the count is almost never done. It can be done from the points alone, by machinery that is never told what angle built them — and then a count of 34 is evidence rather than a restatement.

The pattern itself

Recovering the angle from the counts

Build a head at a stated divergence angle, forget the angle, and get it back from the spiral counts alone. Four angles, worst error twelve thousandths of a degree — and the only thing that crossed between the two halves was a list of coordinates.

The claims, measured

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.

The claims, measured

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.

The claims, measured

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.

The claims, measured

The test a plant could settle

Every other open question in this collection is priced in tens of specimens, and one of them in a hundred and sixty. This one is priced in internodes on a single stem, and the number is fifty-six — because it is a statistic of one sequence rather than a share of a population.

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