# Gabriel’s Theorems on Area of a Circle and Regular Polygons

by Open Science Repository Mathematics
(November 2013)

#### Abstract

Area of a circle and regular polygon i.e. including inscribed and circumscribed regular polygons are interrelated to each other. The objective is to show how the area of a circle and regular polygons is interrelating. Depend on this; these entire theorems can give an infinite ways to calculate area of a circle and other new ways for regular polygons. The methodology used is the previous known formulas for a circle and regular polygons, to derive new relation formulas. The results obtained are in relationship of a circle with regular polygons of the same perimeter, its inscribed and circumscribed regular polygons. These theorems (results) have overcome some limitations of previous existed formulas; now no need to calculate radius for a circle if only circumference is given and no use of trigonometry (sine, tangent and cosine) for regular polygons in addition to these it also brings us to a simple new way for calculating area of a sector and segment which are present in inscribed regular polygons. Therefore here are new ways for calculating area of a circle, regular polygons, segment and sector.

Keywords: area, circle, regular polygons, inscribed regular polygons, circumscribed regular polygons.

#### Full text

Gabriel’s Theorems on Area of a Circle and Regular Polygons