Behind the Pi, some forgotten Indian geniuses

What is Pi (π)?

Pi refers to the ratio of a circle’s circumference to its diameter. The concept was popularised in 1988 when physicist Larry Shaw organised the first Pi Day event at the San Francisco Exploratorium. Pi is classified as an irrational number, meaning its decimal form goes on forever without repeating. Because of this unique property, it appears in countless mathematical and physical formulas.

Google’s doodle description notes, “This Doodle celebrates the numerical constant pi (π), highlighting the foundational geometry first used to calculate its limits. Long before modern technology, the Greek mathematician Archimedes popularized an innovative approach.”

A history of Pi

Over the centuries, many mathematicians attempted to calculate the value of pi using different techniques. Notable contributors include Archimedes, Fibonacci, François Viète, Adriaan van Roomen, and Gottfried Wilhelm Leibniz. However, it was Welsh mathematician William Jones who first used the Greek symbol π in 1706 to represent this ratio.

As early as around 250 BC, Archimedes developed a clever method to estimate Pi’s value by placing a circle between two 96-sided polygons. This helped him determine both the upper and lower limits of the constant with impressive accuracy for his time.

The modern celebration of Pi Day began in 1988 – a tradition that continues even today. The occasion gained wider recognition in the United States in 2009, when the House of Representatives passed a non-binding resolution declaring March 14 as National Pi Day.

The Pi and India

Around 800 BCE, Baudhayana — a Vedic priest whose work was driven by the practical need to construct complex sacrificial altars — composed the Sulba Sutras, some of the earliest texts to grapple with the geometry of circles. His constructions imply a value of π as 3.088.

Around 600 BCE, Apastamba refined this work; his Sulbasutra implies an approximation of π as 3.125 through circle-to-square transformations, alongside a remarkably precise approximation of √2 accurate to five decimal places. The next great leap came with Aryabhata (476–550 CE), who employed the value 62,832/20,000 = 3.1416 for π, very close to the actual value of 3.14159. Aryabhata also came to the conclusion that π is irrational — a sophisticated insight not formally proved in Europe until Johann Heinrich Lambert did so in 1761, more than 1,200 years later.

In the 14th century, Mādhava of Sangamagrama (c. 1340–1425) founded the Kerala school of astronomy and mathematics and became the first to use infinite series approximations for a range of trigonometric functions — a decisive step from the finite procedures of ancient mathematics toward the limit-passage to infinity. Using this infinite series method, Madhava evaluated π correctly to 11 decimal places as 3.14159265359 — a precision that would not be matched in Europe for nearly two centuries.

Finally, in 1914, Srinivasa Ramanujan published 17 mathematical formulas to calculate π that were highly efficient and helped compute π faster than any method of the time; these formulas are so foundational that they form the basis for modern computational techniques used by supercomputers today. The Chudnovsky algorithm, directly based on Ramanujan’s formulae, has been used to calculate π to a billion decimal places and beyond, with the record standing at 314 trillion digits as of November 2025.