The values of Pi through time

A Math Forum Project

Table of Contents:

Famous Problems Home

The Bridges of Konigsberg
· Euler's Solution
· Solution, problem 1
· Solution, problem 2
· Solution, problem 4
· Solution, problem 5

The Value of Pi
· A Chronological Table of Values
· Squaring the Circle

Prime Numbers
· Finding Prime Numbers

Famous Paradoxes
· Zeno's Paradox
· Cantor's Infinities
· Cantor's Infinities, Page 2

The Problem of Points
· Pascal's Generalization
· Summary and Problems
· Solution, Problem 1
· Solution, Problem 2

Proof of the Pythagorean Theorem

Proof that e is Irrational

Book Reviews

References

Links

Person/People Year Value
Babylonians ~2000 B.C. 3 1/8
Egyptians ~2000 B.C. (16/9)^2= 3.1605
Chinese ~1200 B.C. 3
Old Testament ~550 B.C. 3
Archimedes ~300 B.C. proves 3 10/71<Pi<3 1/7
uses 211875/67441=3.14163
Ptolemy ~200 A.D. 377/120=3.14166...
Chung Huing ~300 A.D. sqrt(10)=3.16...
Wang Fau 263 A.D. 157/50=3.14
Tsu Chung-Chi ~500 A.D. proves 3.1415926<Pi<3.1415929
Aryabhatta ~500 3.1416
Brahmagupta ~600 sqrt(10)
Fibonacci 1220 3.141818
Ludolph van Ceulen 1596 Calculates Pi to 35 decimal places
Machin 1706 100 decimal places
Lambert 1766 Proves Pi is irrational
Richter 1855 500 decimal places
Lindeman 1882 Proves Pi is transcendental
Ferguson 1947 808 decimal places
Pegasus Computer 1957 7,840 decimal places
IBM 7090 1961 100,000 decimal places
CDC 6600 1967 500,000 decimal places

So what happened between 1220 and 1596? Well, in the late 15th century European mathematicians (benefiting from the greater intellectual freedom that came with the end of the Middle Ages) figured out how to express Pi exactly as an infinite product. This facilitated the computation of much better approximations. As time passed, mathematicians made the expressions for Pi as an infinite product or sum more concise, and computational methods improved as well.

For example: François Viète (1540-1603) determined that:

John Wallis (1616-1703) showed that:

While Euler (1707-1783) derived his famous formula:

Today Pi is known to more than 10 billion decimal places.

to Finding the Value of Pi
to Java Applet on Squaring the Circle

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August, 1998