Residual — where it appears
Growth as a rule
A logarithmic spiral is not a shape somebody admired. It is what a thing grows into when it adds material at its opening without changing shape, its one parameter is how much it grows per turn, and that parameter can be recovered from any drawn curve to the last digit.
Fitting the exponent
Assuming the exponent is three and reporting the error tells you how wrong the data is. Fitting the exponent and reporting what it comes out as tells you what the network is doing — and the machinery has to be shown returning something other than three, or it is not a fit.
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.
What one exponent reports
Fit a single shape exponent to an organ that has four of them and it returns a real quantity — the harmonic mean of what its individual steps report. Harmonic means sit below arithmetic ones, so the fit understates, systematically, in a known direction, and invisibly.
Named alongside it
The objects these essays reach for when they reach for this one.
CylinderFibonacciRiseBranchConeDa Vinci's ruleDiscriminationDivergence angleExponent fittingFittingGnomonic growthGrowth factor