The first calculation of π was done by Archimedes of Syracuse.
While the concept of a ratio that is now known as π has been used for centuries, it was Archimedes of Syracuse (287–212 BC), a prominent mathematician of the ancient world, who made the first calculation of its value. He didn't exactly "find" pi in the sense that he discovered a new mathematical constant; instead, he meticulously calculated its approximation using geometric methods.
Archimedes' Calculation Method
Archimedes used polygons inscribed within and circumscribed around a circle to approximate the value of π. Here's a breakdown:
- Inscribed Polygon: He drew a polygon inside the circle, touching the circle at each vertex. The perimeter of this polygon is always *less* than the circumference of the circle.
- Circumscribed Polygon: He drew another polygon outside the circle, touching the circle at each side. The perimeter of this polygon is always *greater* than the circumference of the circle.
- Increasing Sides: Archimedes started with hexagons and kept doubling the number of sides for each polygon. As the number of sides increased, the perimeters of both polygons got closer and closer to the actual circumference of the circle.
By calculating the perimeters of these polygons, Archimedes was able to establish upper and lower limits for π. Through his method, he determined that π falls between 3 1/7 and 3 10/71, an approximation that remains significant in the history of mathematics. This was a groundbreaking achievement because it offered a method to calculate π with high accuracy, given the tools available at the time.
It is important to note that although Archimedes is credited with the first rigorous calculation of π, the concept of the relationship between a circle's circumference and its diameter was known and used by mathematicians long before him. However, Archimedes' contribution was to provide a specific, reasonably accurate method for computing it, moving it beyond just a known concept into a calculated value.
| Mathematician | Contribution |
|---|---|
| Archimedes of Syracuse | First rigorous calculation of π using inscribed and circumscribed polygons. |
