Dividing an Angle into 3 or n Equal Parts Using Euclidean Tools - Origami Parabola Method

This paper presents a novel classical geometric method for dividing an arbitrary angle into three or n equal parts using only an unmarked straightedge and compass. Challenging the long-held belief in the impossibility of general angle trisection with classical tools, the method combines principles from origami-based proportioning and parabola geometry into a practical, executable construction. The approach introduces an adaptive scaling process using a base unit length *d*, followed by a deterministic sequence of arcs and circles to derive the precise dividing line. Comprehensive validation is provided through an interactive GeoGebra model, demonstrating exact alignment between the classical construction and analytical results. The method is fully generalizable for any integer *n*, applicable to both even and odd divisions, and is supported by an innovative straightedge design for enhanced practical utility in educational and technical applications. Keywords: Angle Trisection, Geometric Construction, Compass and Straightedge, Origami, Parabola, Adaptive Scaling, GeoGebra Model, Generalized Division. Interactive Demo:🔗 https://saeedaliali.github.io/angle-division-origami-parabola/