New Method for Generating a Regular Polygon

Abstract

This paper presents a new method for generating a regular polygon. It is based on the method of limits of Isaac Newton and the method of indivisibles of the Italian mathematician Boenoventura Cavalieri. The traditional way to construct a regular polygon is based on trigonometry, which uses (sin, cos, and radius), respectively. Several vertices and radius characterize it. The new method defines the polygon by the number of vertices and the side length. And it only uses relationships of parallel segments. The new way allows drawing a polygon with a number of vertices stretching to infinity. This is one of the main differences between the two methods, which is significant. In the existing method until now, the number of vertices is limited to a specific value. Through the new way, the number of vertices can grow to infinity. It can be a disadvantage because it requires a lot of computer power. These new polygons can form complex geometric shapes, such as polyhedra (prism, truncated pyramid, and pyramid). Thanks to the new method, the polyhedra are mathematically more accurate than the traditional way, which should extrude the polygons to polyhedra.