1. Rachel Barnett

2.  BC

3. Babylon  ∏ = 3 ⅛ = 3.125 AB C D E

4. Egypt  ∏ = 4(8/9)² = 3.16049…  Problem number 50 Rhind Papyrus  A = (d – d/9)² = (8d/9)²  Compared with formula A = ∏ d²/4

5. India  ∏ = 4(9785/11136)² = 3.08832…  Indian Sulvasutras  Also ∏ = √10 = 3.16227…

6. Bible  ∏ = 3  In the Bible:  M.D. Stern ∏ = 333/106 = 3.141509

7. Ancient Greece  Plato ∏ = √2 + √3 = 3.146….  Algebra did not interest them

8. Archimedes  3 10/71 < ∏ < 3 1/7 or  3.14085 < ∏ < 3.142858  Accurate to two decimal places

9.  AD

10. China – Liu Hui  ∏ = (314 + 4/25)/10² = 3.1416  Archimedes method with lower bound used Polygon with 192 sides!  Upper bound with double the number of sides

11. China – Tsu Chhung-Chih  3.1415926 < ∏ < 3.145927  Held the world record for 300 years  Accurate to 7 decimal places!

12. Europe – François Viète  ∏ = 2/(√ ½ * √ (½ + ½ √ ½ ) * √ [ ½ + (½ + ½ √ ½] * …….  Variorum de Rebus Mathematicis

13. Arctan formulae - 1706  ∏ = 16 arctan 1/5 – 4 arctan 1/239

14. Last Paper and Pencil  approximation  William Shanks  First calculated first 315 digits  Then 530 digits….  Then 707 digits  Then was found to be wrong…

15. Computer Days  ∏ is figured with programs  Started in the 1940’s  ENIAC

16. Other Approximations to ∏

17. Sources  ∏ Unleashed – Joerg Arndt and Christoph Haenel  A History of ∏ - Petr Beckmann