THE HISTORY OF PI

THE PYRAMID AT GIZA

• Perimeter: 1760 cubits
• Height: 280 cubits
• Ratio: 1760/280 = 2π
• Some think that Egyptians knew about π
• Most believe that ratio is just a coincidence

EARLIEST WRITINGS

• Babylon
• Clay tablet
• π = 25/8
• 1900-1800 B.C.

EARLIEST WRITINGS

• Egypt
• Rhind Papyrus
• Formula for area of a circle
• π = (16/9)^2 or 256/81
• 1650 B.C.

INDIA

• 600 B.C.
• Shulba Sutris (mathematical content)
• π = (9785/5568)^2
• 150 B.C.
• π = √(10)

RELIGIOUS WRITINGS

• Hebrew Bible
• Pool in Temple of Solomon
• Diameter: 10 cubits
• Circumference: 30 cubits
• Verses imply π is about 3 if circular

RELIGIOUS WRITINGS

• Mishnat ha-Middot
• Rabbi Nehemiah
• 150 A.D.
• π = 22/7

Archimedes

• Greek mathematician in 250 B.C.
• First recorded algorithm for calculating pi
• Calculate perimeter of two polygons
• Circle was in between the two polygons
• Discovered that π was between 223/17 and 22/7

Ptolemy

• Greek-Roman scientist in 150 A.D.
• Almagest
• π = 3.1416

ANCIENT CHINA

• π = 3.1547 (1 A.D.)
• π = √(10) (100 A.D.)
• π = 142/45 (3rd century A.D.)

Liu Hui

• Polygon-based algorithm with 3,072-sided polygon
• Obtained a value of π = 3.1416
• Then invented faster method of calculating π
• Obtained a value of π = 3.14
• 265 A.D.

ZU CHONGzhi

• 480 A.D.
• π = 355/113 (Milü)
• Hui's algorithm applied to 12,288-sided polygon
• Most accurate approximation for 800 years

Infinite Series

• 16th and 17th centuries
• Infinite series: Sum of infinite sequence
• Allow to compute π to a greater precision

THE GREEK LETTER

• William Jones (earliest use)
• 1706
• Leonhard Euher (popularized)
• 1736

MODERN QUEST

• Computers
• Revolutinized the search for digits
• Discovered 1 million digits in 1973