"The paper dimension standard used in essentially all countries using the metric system, specified in the metric system, and with constants chosen to fit nicely

"The paper dimension standard used in essentially all countries using the metric system, specified in the metric system, and with constants chosen to fit nicely with that system" is a bit long. An A0 sheet has an area of 1m². For the ratio in general, see https://en.wikipedia.org/wiki/Square_root_of_2 https://en.wikipedia.org/wiki/Square_root_of_2