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
