Mathematics of Flat Origami

Abstract

Abstract. The geometric aspect of origami has been attracting attention for a long time, and has been the subject of research. In recent years, studies using computers have been actively carried out, and the term "computational origami" appeared. Applications of origami related technology to the field of engineering are also actively discussed. In this paper, we summarize the researches on flat-foldability discussed so far in origami mathematics. In addition, we will introduce researches on computational complexity on origami, and origami design methods. We also outline the fields of non-flat origami and rigid origami that are important in application of origami mathematics.