ABSTRACT
First, congruence and similarity are defined. A key table summarise some special rectangles and their properties which are valuable for origami. The special rectangles are: square, silver (1:sqrt(2)), leftover (1:1+sqrt(2)), bronze (1:sqrt(3)), double bronze (2:sqrt(3)), golden, 1:3, 4:5, landscape-portrait rectangles and some others. The first three rectangles have a close relationship with 45 degrees and 22.5 degrees. Bronze rectangles are related to 60 degrees. Methods for folding and cutting from paper are given for the key rectangles. As well as the precise angles given, some classic approximations are described. For example, there are good approximations for making regular polygons having five, seven and thirteen sides. Landscape-portrait rectangles are a novel definition and consist of a rectangle in portrait orientation (standing on the short edge of rectangle) and similar rectangle in landscape orientation (standing on the long edge of the rectangle).
