The first calculation of π (pi) is attributed to Archimedes of Syracuse.
While the Egyptians had a formula that gave an approximate value for pi of 3.1605, Archimedes was the first to rigorously calculate it. He achieved this between 287 and 212 BC.
Understanding Pi
Pi (π) is a mathematical constant representing the ratio of a circle's circumference to its diameter. It's an irrational number, meaning its decimal representation goes on infinitely without repeating.
Early Approximations of Pi
Before Archimedes, there were attempts to approximate pi.
- Egyptians: As mentioned, they used a value around 3.1605, which they applied to calculate the area of circles.
- Babylonians: They used an approximation of 3 1/8 or 3.125.
Archimedes' Method
Archimedes did not calculate pi as a single number but rather found upper and lower bounds for it. His method involved:
- Inscribing a polygon: He placed a polygon inside a circle.
- Circumscribing a polygon: He placed another polygon outside the circle.
- Increasing the sides: By increasing the number of sides of both polygons, he got closer to the actual value of pi.
- Bounds Calculation: Through this method, he determined that pi was between 3 1/7 and 3 10/71 or approximately 3.142 and 3.140.
Why is Archimedes Considered the Creator of pi's calculation?
- Rigorous Calculation: Unlike earlier approximations, Archimedes provided a rigorous mathematical method to calculate pi with definite upper and lower bounds.
- Mathematical Breakthrough: His method was revolutionary for its time and laid the groundwork for future calculations.
- Historical Significance: Archimedes' work is a key development in the history of mathematics, and his method became a crucial foundation for the concept of pi.
| Mathematician | Approximation or Calculation | Time Period |
|---|---|---|
| Egyptians | Approximate value of 3.1605 | Ancient Egypt |
| Archimedes of Syracuse | Calculated first accurate value of π using bounds | 287–212 BC |
While previous civilizations used estimations of pi, it is widely accepted that Archimedes of Syracuse was the first to calculate pi using a rigorous mathematical method.
