Introduction to Mathematical Origami and Origami Engineering

This paper introduces the basics of origami-based foldable structure designs and gives examples of practical applications using these structures for readers who are not familiar with this research field. First, the mathematics associated with origami-based foldable models, such as the conditions to be flat-foldable around a single vertex (Kawasaki's theorem) and to form a foldable tube like a cylinder, is outlined. Next, referencing these conditions-examples of flat-foldable models, such as foldable winding tubes designed with regular folding patterns and folded along the winding axis of the tube, and circular disks that are wrapped and form polygonal pillars with uneven sides and angles-are demonstrated. Finally, recent application of these foldable models to engineering, as exemplified by studies on vibration isolators and energy absorbers, is discussed.