×

Folds - the basis of origami. (English) Zbl 0876.00017

Summary: The physical and mathematical aspects of folds, which characterize the shape of artifacts made of a shin sheet of paper, are studied. The present aim is to clarify the reason why shapes of origami works are generally characterized by ragged surfaces consisting of convex and concave surfaces divided by sharp edges. The following conclusions are obtained: first, the ragged surface consisting of complex sharp folds is the natural characteristic deformation of a thin sheet of paper; second, the area of the spherical image for a complex of folds, which is the integral curvature of the domain, must vanish; third, the above condition is satisfied only by compensation of positive and negative areas of spherical images corresponding to convex and concave areas on the origami surfaces.

MSC:

00A69 General applied mathematics
51-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry
PDFBibTeX XMLCite