Every irrational has a unique infinite continued fraction — visualize convergents approaching the target
Every real number has a continued fraction expansion [a₀; a₁, a₂, ...]. Convergents p_n/q_n are the best rational approximations — closer than any fraction with smaller denominator. φ = [1;1,1,1,...] uses only 1s — the slowest-converging CF, making φ the "most irrational" number (hardest to approximate by rationals). This is why phyllotaxis uses golden angles.