Continued fraction: x = a₀ + 1/(a₁ + 1/(a₂ + …)). Convergents pₙ/qₙ are the best rational approximations (|x − p/q| < 1/q² only for convergents).
The golden ratio φ = [1;1,1,1,…] has the slowest-converging CF (all 1s), making it the "most irrational" number — important in KAM theory and quasicrystals.
CF of π = [3;7,15,1,292,…]: the partial quotient 292 explains why 355/113 is such a good approximation.