Revisit of "Geometric Exercise in Paper Folding" from a Viewpoint of Computational Origami

Abstract

We revisit the seminal classical work of T. Sundara Row on the geometry in paper folding published in 1893. After 123 years, the significance of the book remains. This note is intended to provide a short description of Sundara Row’s masterpiece from the viewpoint of the current mathematical theory of origami and show how various geometrical shapes that Sundara Row drew in his book can be produced by a modern tool of computational origami. Furthermore, the tool enables a reader to manipulate, by a simple scripting language, graphics of the produced shapes and the internal algebraic representations, as well as to perform algebraic proofs of the lemmas and theorems that Sundara Row wrote down in his book.