240 BC

Events in 240 BC 3

• 240 BC Eratosthenes measures the Earth First accurate calculation of Earth's circumference Around 240 BC, Eratosthenes of Cyrene, chief librarian at Alexandria, calculated the circumference of the Earth by measuring the difference in the angle of the sun's shadow between Alexandria and Syene (modern Aswan) at noon on the summer solstice. His result of approximately 252,000 stadia is remarkably close to the modern value of 40,075 km — an error of less than 2%. It was the first scientific measurement of the size of a planet.
• 240 BC Measurement of a Circle — pi calculated 3 10/71 < π < 3 1/7 — the most precise value for 1,500 years In his Measurement of a Circle, Archimedes calculated pi by inscribing and circumscribing regular polygons around a circle with up to 96 sides, and computing their perimeters. He proved that pi lies between 3 10/71 (≈3.1408) and 3 1/7 (≈3.1429) — the most precise calculation of pi achieved for over 1,500 years. His upper bound of 22/7 remained in widespread use until electronic calculators made arbitrary precision trivial. The method of exhaustion he used anticipates integral calculus.
• 240 BC The Sand Reckoner Counting grains of sand in the universe — and inventing a number system to do it In The Sand Reckoner, addressed to King Gelo (son of Hiero II), Archimedes set himself the challenge of expressing the number of grains of sand that would fill the entire universe. The Greek number system had no way to express such enormous quantities, so Archimedes invented a new system based on powers of the myriad (10,000), effectively creating the concept of scientific notation. His final estimate was 10^63 grains — remarkably, using Aristarchus's heliocentric model of the universe as the basis for his size estimate. The work also shows Archimedes understood the concept of positional notation two millennia before it became standard.