Chronology of Calculating Pi

Some significant highlights in calculating the value of π:

1650 B.C.

Ahmes, the ancient Egyptian scribe, implies that π = ²⁵⁶/₈₁ = 3.1605.

250 B.C.

Archimedes determines that 3 ¹⁰/₇₁ < π 3 ¹/₇. The average of these two values is 3.1418, correct to 3 decimal places.

ca. 200 A.D.

Claudius Ptolemy uses π = ³⁷⁷/₁₂₀ = 3.14166..., correct to four decimal places.

450 A.D.

In China, Tsu Ch'ung-chih establishes the value of ³⁵⁵/₁₁₃, which is π to six decimal places. This fraction is the smallest fraction that approximates π so well. In the West, this approximation was not discovered as an approximation to π for another millennium.

1220 A.D.

Fibonacci uses π = ⁸⁶⁴/₂₇₅ = 3.141818...

1593 A.D.

Adriaen Romanus finds pi to 15 decimal places.

1596 A.D.

Ludolph Van Ceulen calculates pi to 32 decimal places. In 1610, he continued his calculation to three more decimal places, making 35 in total.

1706 A.D.

John Machin calculates pi to 100 decimal places.

1874 A.D.

William Shanks publishes his calculation of pi to 707 decimal places.

1947 A.D.

D. F. Ferguson calculates 808 decimal places of pi. In doing so, he discovers that Shanks' calculation was wrong from the 527^th place onwards. Ferguson used a desk calculator.

1949 A.D.

ENIAC, an early computer, computes 2,037 decimal places of pi in a little under three days.

1961 A.D.

Daniel Shanks and John Wrench use an IBM 7090 computer to compute 100,200 decimal places. The calculation took 8.72 hours.

1973 A.D.

Jean Guillord and M. Bouyer use a CDC 7600 to compute 1 million decimal places in 23.3 hours.

1983 A.D.

Y. Tamura and Y. Kanada use a HITAC M-280H to compute 16 million digits in under thirty hours.

1989 A.D.

David and Gregory Chudnovsky find 480 million digits, and, later in the year, 1 billion digits. They would calculate over 8 billion digits in 1996.

1997 A.D.

Kanada and Takahashi calculate 51.5 billion digits on a Hitachi SR2201 in just over 29 hours.

Much of this material was obtained from the book The Joy of π by David Blatner (see my bibliography page).