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The irrational number π (pi)

The number π is defined as the ratio of the circumference of a circle to its diameter. This geometric definition does not immediately transform into numerical information. For thousands of years, people have been chasing π. The following table gives a partial history of numerical approximations to π.

Era Approximation Who/Where
2000 BCE 3\(\dfrac{1}{8}\) Mesopotania
1200 BCE 3 China
550 BCE 3 Old Testament
263 BCE 3.1459 China
250 BCE Between 3\(\dfrac{10}{71}\) and 3\(\dfrac{1}{7}\) Archimedes (Greece)
150 BCE 3.1416 Ptolemy (Egypt)
800 To 14 decimal places Al'Khwarizmi (Persia)
1600 To 17 places Van Ceulen (Holland)
1706 To 100 decimal places Machin (England)
1853 To 500 decimal places Shanks (England)
1949 To 2000 decimal places An early computer
1997 To 51 billion decimal places Kanada (Japan)

James Gregory (1638–75) produced one of the first mathematical formulas for the calculation of \(\pi\). This is:

\(\dfrac{\pi}{4}=1\ – \dfrac{1}{3}+\dfrac{1}{5}\ – \dfrac{1}{7}+\dfrac{1}{9}\ – \dfrac{1}{11}+\ \ldots\)

Obviously, π has fascinated people for thousands of years. It has given rise to many interesting formulas.