A4 and the golden ratio

Today I wandered why A4 is the size it has. OK it's not the golden ratio that is the basic principle but the fact that A0 has a square of 1 m2. The ratio of the sides in the A-series is the square root of 2 and not 1,68033.. It's close but not and ideal format for prints. "Well Pieter, what is the size of your Photoshop prints?" "40,0 cm x 23,8 cm". "But what about the frames, passpartous and floating glass?" Hmm..