EJMT Abstract

This paper presents an original method of angle trisection using dynamic geometry as an extension of the classical straightedge-and-compass framework. By incorporating variations in geometric parameters such as segment lengths and angle measures, the method circumvents the classical impossibility constraints without violating the foundational tools. The trisection process relies on geometric constructions derived from trigonometric identities and is validated through manual replication and iterative adjustment. While describing historical attempts and methods that were found inapplicable under the strict constraints of Greek mathematicians, this paper develops a dynamic approach that enables the trisection of angles that are proven non-constructible in static geometry. It also facilitates the construction of regular polygons (e.g., non-constructible 9- and 18-gons) whose defining angles are otherwise inaccessible. Importantly, this method does not resolve the classical Greek problem of angle trisection in its strictest form; rather, it offers an alternative constructive pathway while the original problem remains formally unsolved.