The ISO 216 standard ratio is cos(45°), but American letter paper is 8.5x11 because it uses radians, and 8.5/11 = pi/4.

"ISO Paper Size Golden Spiral", by Randall Munroe, licensed under Creative Commons Attribution-NonCommercial 2.5 License

Alt Text

The ISO 216 standard ratio is cos(45°), but American letter paper is 8.5x11 because it uses radians, and 8.5/11 = pi/4.