Self similarity — 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.
The Fibonacci ladder
Lower the rise on a cylinder and the parastichy pair climbs — 1 and 2, then 2 and 3, then 3 and 5 — each rung the sum of the two before it. Nothing in the arithmetic mentions Fibonacci, the transitions sit at computable rises, and consecutive ones stand in the ratio 1/φ².
Named alongside it
The objects these essays reach for when they reach for this one.
Continued fractionConvergentsDominant pairFibonacciGnomonic growthφ, the golden ratioGrowth factorLadderLeast squares fitLogarithmic spiralNoiseParastichy