How do I get an integer from a polygon equation, which usually returns fractions?Known: edge lengthUnknown: number of edgesRadius should increase of decrease to an interval to ensure number of edges in Polygon is divisible by 1E.g. edge length is 100mm, number of edges unknown, radius is 6m. How do I find the closest radius to 6m which gives an integer, divisible by 1, for a realistic number of edges.Previous QuestionIf a regular polygon has a fixed edge length, can I know how many edges it has by knowing the length from corner to its center?and it's answerthe radius of the polygon, and it has the formula r = s 2 sin ⁡ ( 180 ° n ) where s is the side length of the polygon and n is the number of sides. So given r and s, you can simply solve the above equation for n.It's worth pointing out that when you solve for n there's no guarantee that it will turn out to be an integer, and hence correspond to a regular polygonI have no math background, not even enough to know which tags to attach. How do I solve for these intervals of radii?

Question

How do I get an integer from a polygon equation, which usually returns fractions?Known: edge lengthUnknown: number of edgesRadius should increase of decrease to an interval to ensure number of edges in Polygon is divisible by 1E.g. edge length is 100mm, number of edges unknown, radius is 6m. How do I find the closest radius to 6m which gives an integer, divisible by 1, for a realistic number of edges.Previous QuestionIf a regular polygon has a fixed edge length, can I know how many edges it has by knowing the length from corner to its center?and it&#039;s answerthe radius of the polygon, and it has the formula  r  =      s          2      sin      ⁡              (                              180                          °                                n                )            where s is the side length of the polygon and n is the number of sides. So given r and s, you can simply solve the above equation for n.It&#039;s worth pointing out that when you solve for n there&#039;s no guarantee that it will turn out to be an integer, and hence correspond to a regular polygonI have no math background, not even enough to know which tags to attach. How do I solve for these intervals of radii?

Layne Murillo · Accepted Answer

Step 1Rearrange your formula for r in terms of n   n  =      π          arcsin      ⁡              (                  s                      2            r                          )              ≈            2      π      r        s      for   r  ≫  s and insert the desired values.Step 2For your example   n  ≈  2  π            6       m              0.1       m        ≈  377 is very close                    n                    376                    377                    378                            r         in m                    5.9843                    6.0002                    6.0161

If a regular polygon has a fixed edge length, can I know how many edges it has by knowing the length from corner to its center?

Answered question

Answer & Explanation

New Questions in Integral Calculus