revelations about paper sizes (and root 2 rectangles)

today in architecture class we learned about the four important shapes of architecture - the square, the double square, the golden ratio rectangle, and the root-two rectangle.

naturally root-two rectangles captivated me; not only are they just naturally awesome, but they also gave me a bit of insight into paper sizes (now i understand!).

so to explain the basic idea of a root-two rectangle: it is a rectangle with the ratio of 1:1.414 (or, square root of 2), and its diagonal forms the angles of 35 and 55 degrees.  most interestingly, when you cut it in half it yields two similar rectangles.

this is the principle that yields the paper system used in countries that are, well, let's just say, way more practical than the united states.  yes, just like how the metric system makes SO MUCH SENSE, so does this system.  so, the standard A4 page is half the size of an A3 page, which in turn is half the size of an A2 page, which is half the size of an A1 page, which is half the size of the gigantic A0 sheet...i am still fascinated.