Pi Fully Defined From An Improper Fraction

n ∈ N

Pi ∈ S

S ∈ Q

Example 1

S = 2 * ( 4 * ( n + 1 ) + 3 ) / (10 * n + 4) / 2

n = 1 returns the value 3 + 1/7 , 22/7 or Pi.

Reference the conclusion with that of the article Proof of the True Value of the Pi Ratio.

IT programming via iteration or estimation is what currently propagates the accepted Windows OS, Pi value. The value above is not estimation. It is the true, accurate and precise value of Pi.

© Sydney Matinga 2026