This 2D companion unfolds a real number into its continued fraction [a0; a1, a2, ...] and animates the convergents p_n/q_n across three linked views — a number line where the ticks visibly zoom in on the target, an independent Stern-Brocot mediant search that finds the same fractions by binary-searching the tree of all positive rationals, and a log-scale error chart checked against the theoretical 1/(q_n*q_(n+1)) bound — so the "best rational approximation" property is something you can watch happen, not just read.