Hor:ratio is a device I came up with to work with rectangular aspect ratios and proportional subdivisions. It has become an indispensable part of my kit, useful for analyzing compositions, copying works of art, creating thumbnails, etc. When they get worn out I just print out a new batch, trim, score, and fold to make a handy pocket reference and proportional protractor.
If you are interested in the geometrical aspects of artistic composition or curious about the arcane world of root rectangles, diatessarons, and hemiolions, you can get your own Hor:ratio and instruction booklet right here at www.matthewmattingly.com under the Hor:ratio tab. Free, no registration or personal information required. I would appreciate any feedback.