Angle trisection with origami and proving its correctness using Gröbner basis

Abstract

In this paper, trisection of an angle performed by origami is explained in detail, as well as the correctness of obtained construction. Two different correctness conjectures, one based on trigonometry identities for triple angle and another, based on triangle congruence are formulated. All geometric constraints appearing in premises and conclusion of the conjecture are formulated as polynomials over the set of appropriately chosen variables, and the correctness conjectures are proved using Gröbner basis method. For performing calculations over polynomials obtained, the computer tool Singular is used.