Geometric Constructions of Regular Polygons and Applications to Trigonometry

TL;DR

This paper explores geometric constructions of regular polygons like pentagons and decagons, linking them to trigonometry and demonstrating educational applications involving specific angles such as 18°, 36°, and 72°.

Contribution

It introduces geometric methods for constructing regular polygons and calculating key trigonometric ratios, expanding trigonometry education through practical applications.

Findings

Constructed regular pentagon and decagon geometrically.

Calculated trigonometric ratios for key angles.

Connected polygon constructions to icosahedron geometry.

Abstract

In this paper, constructions of regular pentagon and decagon, and the calculation of the main trigonometric ratios of the corresponding central angles are approached. In this way, for didactic purposes, it is intended to show the reader that it is possible to broaden the study of Trigonometry by addressing new applications and exercises, for example, with angles 18{\deg}, 36{\deg} and 72{\deg}. It is also considered constructions of other regular polygons and a relation to a construction of the regular icosahedron.