The big idea
Start with 1 and 1. Each new number is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and on. Squares with those sides fit together into a rectangle that keeps its shape as it grows, and dividing each number by the one before it closes in on the golden ratio φ = (1 + √5) ÷ 2 ≈ 1.618. Turn by 360° ÷ φ² ≈ 137.5° for every new seed, and the seeds pack evenly with no spokes or gaps.
Memory trick: “Add the last two to grow the next. Divide the last two to find phi: a little high, then a little low.”
A bit of history: Leonardo of Pisa, later nicknamed Fibonacci, put a puzzle about breeding rabbits in his Liber Abaci (Book of Calculation) of 1202, and the numbers it produces now carry his name. Indian scholars who studied the rhythms of poetry described the same rule earlier: Virahanka (between A.D. 600 and 800), Gopala (before 1135) and Hemachandra (about 1150) used it to count patterns of long and short syllables.
Optional verse: “O LORD, how manifold are thy works! in wisdom hast thou made them all: the earth is full of thy riches.” (Psalm 104:24, KJV)