This unique and wildly creative book by a Japanese origami master approaches the art of paperfolding from the perspective of mathematical and geometric principles. Jun Maekawa focuses on using rectangular paper to create a wide range of insects, leaves, plants, trees, animals, and fantastic creatures. Models include hummingbirds, dragonflies, peacocks, rabbits, toads, fish, maple leaves, ginkgo leaves, the golden beetle, a praying mantis, a tortoise, silver cranes, and trees. An intriguing blend of art and science, this volume features both simple and complex figures, intended for intermediate-level and serious origamists. This is the first publication outside of Japan for most of these original models. Rather than the square-shaped paper familiar to American folders, all 33 models employ rectangular sheets of paper -- that is, sheets with an aspect ratio of 1:1.41, or 1: √2. Instructions for making rectangular origami paper are included.