2. The letter π The constant is named "π" because it is the first letter of the Greek words: περιφέρεια = periphery περιφέρεια = periphery περίμετρος = perimeter περίμετρος = perimeter

3. Definition In Euclidean plane geometry, π is defined as the ratio of a circle's circumference to its diameter. π = c/d = c/2r

4. Calculating π π can be empirically measured by drawing a large circle, then measuring its diameter and circumference, since the circumference of a circle is always π times its diameter. π can also be calculated using purely mathematical methods

6. Principle of Archimedes' method to approximate π n=5 n=6 n=8

7. ninscribed polygondescribed polygon 32,5980762115,196152423 42,8284271254 52,9389262613,63271264 633,464101615 73,0371861743,371022332 83,0614674593,313708499 93,078181293,275732108 103,0901699443,249196962 113,0990581253,229891422 123,1058285413,215390309 133,1111036363,204212219 143,1152930753,195408641 153,1186753623,188348425 163,1214451523,182597878 173,1237418033,177850751 183,1256671983,173885653 193,1272972153,170539238 203,1286893013,167688806 213,129887593,165240713 223,1309264423,163122468......... Infinit e ππ

9. a few excitements... In 2002 Kanada and fellow researchers at Japan's Information Technology Center set a new record for finding the number of digits of π 1.24 trillion decimal places. This calculation took about 602 hours. Chao Lu of China recited π on 67,890 decimal places on 20 November 2005. Rose Hare is the youngest person to make the Pi World Ranking List (age: 3 years 356 days) Math lovers celebrate March 14 (or "3-14") as Pi Day. The theory of elliptic curves and complex multiplication derives the approximation which is valid to about 30 digits.