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The purpose of the study was to establish the relationship between the regular polygon and the circle circumscribing it. The study revealed that the circle is a special polygon if the angle at the centre is reduced to 10^-n where n is the number of decimal places of the angle at the centre of the polygon after finding the sum of areas of the triangles in the regular polygon. It was also discovered that if the angle at the centre of the polygon is reduced to 10-n and has same number of decimal places as π, then the circle circumscribing it would have the same area with the polygon if the two answers are rounded off to (n – 3) decimal places and a polygon with infinite number of sides is a circle. This relationship also proved that π = sin θ (1.8 x 10^n + 2) where n is the number of decimal places of π.

Implication of Reducing the Angle at the Centre to 10-n to the Relationship Between the Regular Polygon and the Circle Circumscribing the Polygon