Question: Which Greek geometrician determined the value of pi to the 3rd decimal place?

## Show answer

Archimedes.

The Greek geometrician who first determined the value of pi to the third decimal place was Archimedes of Syracuse. Archimedes, one of the most renowned mathematicians and scientists of ancient Greece, made significant contributions to the understanding of pi (π), the ratio of the circumference of a circle to its diameter. His work in this area was pioneering and laid the foundation for future explorations in geometry and mathematics.

Archimedes approached the problem of calculating pi by employing a method known as the “method of exhaustion,” which is an early form of integral calculus. He inscribed and circumscribed polygons around a circle and calculated their perimeters. By using polygons with an increasing number of sides, he was able to create upper and lower bounds for the value of pi. Specifically, Archimedes started with hexagons and then successively doubled the number of sides of the polygons to 12, 24, 48, and finally 96 sides.

Through this method, Archimedes determined that the value of pi lies between 3 1/7 (approximately 3.142857) and 3 10/71 (approximately 3.140845). The average of these two values is approximately 3.14185, which is remarkably close to the actual value of pi (3.14159) when rounded to three decimal places. This approximation was an extraordinary achievement for his time and remained one of the most accurate estimations of pi for many centuries.

Archimedes’ work on pi demonstrated not only his profound understanding of geometry but also his innovative approach to mathematical problems. His method of exhaustion was a precursor to the techniques of calculus developed much later by Isaac Newton and Gottfried Wilhelm Leibniz. Archimedes’ contributions to mathematics, including his work on pi, solidify his legacy as one of the greatest mathematicians in history.

The significance of Archimedes’ calculation of pi extends beyond its immediate application to geometry. It showcases the power of mathematical reasoning and the importance of rigorous methods in achieving precise results. Archimedes’ determination of pi to the third decimal place remains a testament to his ingenuity and the advanced state of Greek mathematics.