# Pi (Polygons based) Calculator

## Calculates circular constant Pi using the perimeters of regular polygons inscribed in and circumscribed about a circle of diameter 1.

 initial regular polygon tetragon (4) hexagon (6) loop frequency n calculated up to  2 or 3 x 2n -sided polygon 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 The calculation stops when the perimeters of both circumscribed and inscribed regular polygons become equal. The accuracy of π improves by increasing the number of digits for calculation.From ancient times until the 17th century, the approximation of Pi was calculated from the perimeters of the circumscribed and inscribed regular polygons.Pi is calculated from the perimeters of from the initial tetragon or hexagon to the 2 or 3 x 2n-sided circumscribed and inscribed regular polygons. Iterative algorithms　a:perimeter of circumscribed polygon, b:perimeter of inscribed polygon$\normal(1)\ a_0=\left\{{\large{4\atop 2\sqrt{3}}}\right.\ ,\hspace{20}b_0=\left\{{\large{2\sqrt{2}\hspace{20}:square\atop\hspace{20} 3\hspace{30}:hexagon}}\right.\\(2)\ a_{n+1}={\large\frac{2a_n b_n}{a_n+b_n}}\ ,\hspace{20}b_{n+1}=sqrt{a_{n+1}b_n}\\\vspace{5}(3)\ b_n\lt\ \pi\ \lt a_n\\$

Pi (Polygons based)
 [1-1] /1 Disp-Num5103050100200
[1]  2017/05/03 11:26   Male / Under 20 years old / High-school/ University/ Grad student / A little /
Purpose of use
For my mathematical methods b class I have to write a report on pi.

Sending completion

To improve this 'Pi (Polygons based) Calculator', please fill in questionnaire.
Male or Female ?
Age

Occupation

Useful?

Purpose of use?