Transcript [Talk]
Rachel Barnett
BC
Babylon
∏ = 3 ⅛ = 3.125
C
A
B
E
D
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
India
∏ = 4(9785/11136)² = 3.08832…
Indian Sulvasutras
Also ∏ = √10 = 3.16227…
Bible
∏=3
In the Bible:
M.D. Stern ∏ = 333/106 = 3.141509
Ancient Greece
Plato ∏ = √2 + √3 = 3.146….
Algebra did not interest them
Archimedes
3 10/71 < ∏ < 3 1/7
or
3.14085 < ∏ < 3.142858
Accurate to two decimal places
AD
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
China – Tsu Chhung-Chih
3.1415926 < ∏ < 3.145927
Held the world record for 300 years
Accurate to 7 decimal places!
Europe – François Viète
∏ = 2/(√ ½ * √ (½ + ½ √ ½ ) * √ [ ½ + (½
+ ½ √ ½] * …….
Variorum de Rebus Mathematicis
Arctan formulae - 1706
∏ = 16 arctan 1/5 – 4 arctan 1/239
Last Paper and Pencil
approximation
William Shanks
First calculated first 315 digits
Then 530 digits….
Then 707 digits
Then was found to be wrong…
Computer Days
∏ is figured with programs
Started in the 1940’s
ENIAC
Other Approximations to ∏
Sources
∏ Unleashed – Joerg Arndt and
Christoph Haenel
A History of ∏ - Petr Beckmann