Concept
Logarithmic spiral — where it appears
2 essays name this object, across one field. What follows is each of them, and the objects they name alongside it.
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.
The nautilus question
A golden spiral grows by 6.854 per turn. Measured nautilus sections give about 3.2. That is a factor of 2.14 — not a rounding error, not an artefact of where the centre is assumed to be, and not close.
Named alongside it
The objects these essays reach for when they reach for this one.
Growth factorBranchClaim testingFibonacciGnomonic growthφ, the golden ratioGolden spiralLeast squares fitMeasurement sensitivityNoiseφ⁴Residual