doi: **10.7392/openaccess.45011811**

Asmara College of Health Sciences, Asmara, Eritrea

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.

Citation: Dawit, G., & Tesfu, E. (2014). Geometrical Theorems on Perimeter Relationship of a Circle and Regular Polygons. *Open Science Repository Mathematics*, Online(open-access), e45011811. doi:10.7392/openaccess.45011811

Received: May 22, 2014

Published: June 5, 2014

Copyright: © 2014 Dawit, G., & Tesfu, E. Creative Commons Attribution 3.0 Unported License.

Contact: research@open-science-repository.com

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**APA**

Dawit, G., & Tesfu, E. (2014). Geometrical Theorems on Perimeter Relationship of a Circle and Regular Polygons. *Open Science Repository Mathematics*, Online(open-access), e45011811. doi:10.7392/openaccess.45011811

**MLA**

Dawit, Gabriel, and Elilta Tesfu. “Geometrical Theorems on Perimeter Relationship of a Circle and Regular Polygons.” *Open Science Repository Mathematics* Online.open-access (2014): e45011811.

**Chicago**

Dawit, Gabriel, and Elilta Tesfu. “Geometrical Theorems on Perimeter Relationship of a Circle and Regular Polygons.” *Open Science Repository Mathematics* Online, no. open-access (June 05, 2014): e45011811. doi:10.7392/openaccess.45011811.

**Harvard**

Dawit, G. & Tesfu, E., 2014. Geometrical Theorems on Perimeter Relationship of a Circle and Regular Polygons. *Open Science Repository Mathematics*, Online(open-access), p.e45011811.

**Science**

1. G. Dawit, E. Tesfu, Geometrical Theorems on Perimeter Relationship of a Circle and Regular Polygons, *Open Sci. Repos. Math*. **Online**, e45011811 (2014).

**Nature**

1. Dawit, G. & Tesfu, E. Geometrical Theorems on Perimeter Relationship of a Circle and Regular Polygons. *Open Sci. Repos. Math*. **Online**, e45011811 (2014).

Research registered in the DOI resolution system as:** ****10.7392/openaccess.45011811**.

This work is licensed under a Creative Commons Attribution 3.0 Unported License.