Approximation Day – 22/7 for π

22 July (22/7) is Pi Approximation Day because 22/7 ≈ 3.142857, which is 0.04% above π ≈ 3.141593. This approximation was known to Archimedes (circa 250 BC). He proved 3 + 10/71 < π < 3 + 1/7, giving 22/7 as the upper bound. 22/7 is the best rational approximation with denominator ≤ 7. Better approximations include 355/113 (from Zu Chongzhi, 5th century), correct to 7 decimal places. But 22/7 remains the most famous fractional approximation.