The numerical value 3.1415926 can be used to approximate pi.
Pi (π) is an irrational number, meaning its decimal representation neither terminates nor repeats. Therefore, we often use approximations for calculations. Several numerical values can approximate pi, with varying degrees of accuracy.
Here are some examples of approximations of pi:
- 3.14: A common and easily remembered approximation.
- 22/7 (approximately 3.142857): A fractional approximation that's slightly more accurate than 3.14.
- 3.14159: A more precise approximation, accurate to five decimal places.
- 355/113 (approximately 3.1415929): A remarkably accurate fractional approximation.
Zu Chongzhi's Contribution
The reference text highlights the historical achievement of Zu Chongzhi, who calculated π to be between 3.1415926 and 3.1415927. This calculation was accurate to seven decimal places. He also provided two other approximations: 22/7 and 355/113, but his decimal result provides a more precise numerical approximation for practical use.
Choosing an Approximation
The choice of which approximation to use depends on the level of accuracy needed for a particular application. For many everyday calculations, 3.14 is sufficient. For more precise calculations, a value like 3.14159 or even Zu Chongzhi's more accurate bounds would be preferable.
