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

**Authors:** Pawan Kumar Bishwakarma

A regular polygon is a planar geometrical structure with all sides of equal length and all angles of equal magnitude. The ratio of perimeter of any regular polygon to the length of its longest diagonal is a constant term and the ratio converges to the value of as the number of sides of the polygon increases. The result has been shown to be valid by actually calculating the ratio for each polygon by using corresponding formula and geometrical reasoning. A computational calculation of the ratio has also been presented to validate the convergence. The values have been calculated up to 30 significant digits.

**Comments:** 16 Pages.

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### Submission history

[v1] 2017-09-11 16:58:23 (removed)

[v2] 2018-01-06 02:31:12

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