In this experiment, I am adding the inradius (let's call it $A$) and circumradius (let's call it $B$) of different polygons with equal sides each equal $1$ (starting with a square and adding one side each time). The result is $A+B=C$ when side of polygon = 1.

When comparing the $C$ of one polygon with the $C$ of a polygon with one side more, the difference seems to go smaller, as if approaching a version of $\pi$ number with $0.$ before (possibly such as 0.314159265359...).

Can anyone confirm it or elaborate on it?

I can not go over a polygon with 1000 sides in my computation power, and would like to know what to expect while going towards a polygon with infinity sides.

Here are some examples:

4 sided polygon: $0.5 + 0.707106781 = 1.207106781$

5 sided polygon: $0.68819096 + 0.850650808 = 1.5388417680000002$ (Difference of **0.33173498700000015** from previous result)

6 sided polygon: $0.866025404 +1 = 1.866025404$$ (Difference of **0.3271836359999998** from previous result)

7 sided polygon: $1.0382607 + 1.15238244 = 2.1906431399999997$ (Difference of **0.32461773599999977** from previous result)

8 sided polygon: $1.20710678 + 1.30656296 = 2.51366974$ (Difference of **0.3230266000000004** from previous result)

9 sided polygon: $1.37373871 + 1.4619022 = 2.83564091$ (Difference of **0.32197116999999986** from previous result)

10 sided polygon: $1.53884177 + 1.61803399 = 3.15687576$ (Difference of **0.3212348500000002** from previous result)

11 sided polygon: $1.70284362+ 1.77473277 = 3.47757639$ (Difference of **0.3207006299999997** from previous result)

12 sided polygon: $1.8660254+ 1.93185165 = 3.79787705$ (Difference of **0.32030066** from previous result)

13 sided polygon: $2.02857974+ 2.08929073 = 4.11787047$ (Difference of **0.31999341999999986** from previous result)

14 sided polygon: $2.19064313 + 2.2469796 = 4.43762273$ (Difference of **0.31975226000000045** from previous result)

15 sided polygon: $2.35231505+ 2.40486717 = 4.757182220000001$ (Difference of **0.3195594899999996** from previous result)

...

999 sided polygon: $158.995264 + 158.99605 = 317.991314$

1000 sided polygon: $159.154419 + 159.155205 = 318.309624$ (Difference of **0.31830999999999676** from previous result)