Updated: May 31, 2022
The value of pi was first calculated 4000 years ago. The ancient Babylonians and the Egyptians calculated an approximate value of pi by actual physical measurements of the circumference or the area or a circle, and they estimated that pi had a value close to 3.
About 1500 years later, the Greek mathematician Archimedes first used mathematics to estimate pi and showed that its value lies between 22/7 and 223/71. The way he reasoned was as follows. He noted that a regular polygon circumscribed around a circle would have a perimeter larger than the circumference of the circle, while a regular polygon inscribed in the circle would have a smaller perimeter. He then observed that as one increased the number of sides of the polygon, the two perimeters close in on the circumference of the circle. Finally, he used Pythagoras's theorem to find the perimeters of the polygons and thus got upper and lower bounds for the value of pi. Using a hexagon, a 12-sided polygon, a 24-sided polygon, a 48-sided polygon, and then a 96-sided polygon,
he proved that 223/71 < pi < 22/7. In this article, we discuss the basic ideas behind his derivation. (In fact, we provide an improved lower bound.)
During the 5th century CE, the Indian mathematician Aryabhata calculated a value of "pi" that was accurate for up to 3 decimal digits. Zu Chongzhi, a Chinese mathematician and astronomer, calculated an approximate value of pi using a 24576-gon, about 7centuries after Archimedes. His estimated value, 355/113, is approximately equal to 3.14159292. The Greek letter "pi" was 1st introduced by William Jones in 1706. It was derived from the 1st letter of the Greek word 'perimetros,' meaning Circumference.