PhyllotaxisHow a sunflower packs its seeds. Each seed is dropped a fixed turn past the last one; when that turn is the “golden angle” (137.5°) the seeds never line up and fill the head with no gaps. Nudge the angle a hair and the spiral arms snap to Fibonacci counts — 34 turning one way, 55 the other.Wilhelm Hofmeister saw in 1868 that each bud forms as far as it can from the last. A century later Helmut Vogel reduced the whole flower to one line — seed n at angle n × 137.5° and radius √n — and the tight packing that plants took eons to evolve fell straight out of number theory: the golden angle is the hardest of all angles to approximate with a fraction, so the seeds never fall into rows.