ABSTRACT
In the works just cited, except for the books by Franco and by Youngs and Lomeli, little or no effort is made to incorporate both folding and quantitative mathematical analysis of typical origami models. It is our hope that the synergy involved in the introduction of origami as a method of making interesting objects as well as a vehicle for introducing and practically applying geometric, trigonometric, and calculus concepts can be of great pedagogical value. As an illustration of our approach, we describe in this paper the origami and the associated mathematics of folding a simple, but interesting class of isosceles triangular boxes with any vertex angle 9 (0° to 180°) from rectangular paper
of arbitrary length L and width W. It will probably be surprising to students that boxes with any vertex angle can be folded in principle. (Of course, it would be physically impossible to actually fold boxes for certain ranges of the parameters L,W, and 9.)
2 Folding Procedures The first author had originally designed right-apex-angle (45° — 45° — 90°) and equiangular/equilateral (60° — 60° — 60°) pie containers from arbitrary rectangular sheets. It was then noted by the second author that the folding procedure could be generalized so that a box with any arbitrary apex angle 9 could be folded using well-defined landmarks.
