Calculating Pi

From consideration of 4, 8 and 16 sided regular polygon it is noticeable that a sequence is formed when the number of sides is doubled. The argument for determining the formula for the next, 32 sides, is the same as was used for going from 8 to 16, so I have written this down in a spread sheet up to a regular polygon with 2048 sides, and the value of pi is correct to 5 decimal places. Of course this can be continued but is becoming tedious, so I have stopped at this value

One day I hope to write a program that will automate this, but this is on the back burner for the time being.

Calculation of Pi using 2048 sides

3.141595118 > Perimeter > 3.141591422

Actual value to 9 places of decimal is 3.141592654

So our 2048 side estimate is correct to 5 places.

This is an improvement on the 8 sided polygon which gave

3.31371 > Perimeter > 3.06147