Fun fact, 2phi²-5pi/3 is 0.0000802. The ancients certainly knew about phi, because it defines the ratios between segments of a pentagram. They loved pentagrams

Fun fact, 2phi²-5pi/3 is 0.0000802. The ancients certainly knew about phi, because it defines the ratios between segments of a pentagram. They loved pentagrams. They probably would have considered the match above exact, having no independent method to estimate pi. (Phi is (sqrt(5)+1)/2. Phi²=phi+1, 1/phi=phi-1.) A measurement system used by builders in medieval times had units that were related by powers of phi. Nobody knows how far back the convention goes, passed from master to apprentice.