Brief History of π
Approximations for the value π were known to the ancient Babylonians, Egyptians, Indians, Greeks, and Chinese. The
earliest records of π date back to the Babylonians (c. 2000 BCE), they referred to π as the fraction 25/8 = 3.125,
out by 0.528%. Roughly around the same time, the Egyptians were using a different fraction 256/81 = 3.160, out by 0.601%.
Indian scriptures contained in the Vedic Shatapatha Brahmana book (c. 800 BCE) referred to π as 339/108 = 3.138̇̇̇̇̇̇̇̇, out
by 0.086%. Approximately five hundred years later (c. 250B CE), Archimedes of Syracuse used inscribed and circumscribed
polygons, and calculated π to be 22/7, out by 0.040%. This easy to remember approximation was still recently in use
for performing rough calculations until the introduction of the modern electronic calculator. Zu Chongzhi a Chinese polymath
(c. 500 CE) some seven hundred years later derived two approximations. The first being the same as the one Archimedes found,
and later the more impressive approximation of 355/113 = 3.14159292, being accurate to seven decimal places, an incredible
feat for the time.
The beginning of the European renaissance (c. 1400 CE), and the introduction of the Hindu-Arabic numeral system by
Fibonacci at around the same time, paved the way for major advances in mathematics in Europe. By the late sixteenth century,
European mathematicians were using infinite series equations to calculate the value of π with greater and greater precision.
Since then, a variety of ingenious methods for approximating π, including the use of prime numbers, and even the use of the
golden ratio have come to pass.