## Geometry   ## Convergence of the Ratio of Perimeter of a Regular Polygon to the Length of Its Longest Diagonal as the Number of Sides of Polygon Approaches to ∞

Authors: Pawan Kumar B.K.

Regular polygons are planar geometric structures that are used to a great extent in mathematics, engineering and physics. For all size of a regular polygon, the ratio of perimeter to the longest diagonal length is always constant and converges to the value of π as the number of sides of the polygon approaches to ∞. The purpose of this paper is to introduce Bishwakarma Ratio Formulas through mathematical explanations. The Bishwakarma Ratio Formulae calculate the ratio of perimeter of regular polygon to the longest diagonal length for all possible regular polygons. These ratios are called Bishwakarma Ratios- often denoted by short term BK ratios- as they have been obtained via Bishwakarma Ratio Formulae. The result has been shown to be valid by actually calculating the ratio for each polygon by using corresponding formula and geometrical reasoning. Computational calculations of the ratios have also been presented upto 30 and 50 significant figures to validate the convergence.

### Submission history

[v1] 2017-09-11 16:58:23 (removed)
[v2] 2018-01-06 02:31:12 (removed)
[v3] 2018-12-29 04:20:55