# Geometrical Theorems on Perimeter Relationship of a Circle and Regular Polygons

by Open Science Repository Mathematics
(June 2014)

#### Abstract

Perimeter of a circle and inscribed and circumscribed regular polygons has a mathematical relationship. The objectives are to show how a perimeter of a circle and of inscribed and circumscribed regular polygons is interrelating, and to show the relationship of radius length with side length of a regular of the same perimeter. All these relationship is derived from the previous formulas for perimeter of regular polygons and of a circle. There are three theorems provided in this research, GEBRIEL’S and ELILTA’S theorem describe the relationship between circumference of a circle and its inscribed and circumscribed regular polygons respectively, each relation has its own constant given in the tables. JAR theorem describes a relation between a radius length of a circle and side length of regular polygons of the same circumference. The first two theorems helps easily to calculate the needed length of perimeter to inscribed or circumscribed any regular polygon to a circle. JAR theorem helps to calculate circumference of a circle and regular polygons in easy way. All these theorems have further advantage over the previous formulas for calculating perimeter of regular polygons, because no need to use any trigonometry ratios (sine, cosine and tan). These theorems are helpful for high school and above level students and also for those which are interested in engineering and designing of different house hold equipment.

Keywords: perimeter, circle, inscribed regular polygons, circumscribed regular polygons, radius and side length.

#### Full text

Geometrical Theorems on Perimeter Relationship of a Circle and Regular Polygons