When the ancient Greek philosopher Pythagoras first suggested that the Earth was round in 500 BC, his claim was dismissed as unreasonable. Decades later, Greek philosopher Aristotle proved Pythagoras correct when he concluded that the Earth was spherical by observing celestial bodies from different locations across the planet. Ancient mathematicians and self-proclaimed astronomers also tried to prove Aristotle wrong, but eventually concurred that Earth was indeed spherical. About 2,000 years ago, long after the Earth was proved to be round, Eratosthenes of Cyrene, a Greek polymath, poet, astronomer, mathematician, librarian, and geographer, sought to establish the planet's circumference.
Measuring the Earth
Eratosthenes is considered the inventor geography, particularly because he developed the system of latitudinal and longitudinal lines to map the world. He calculated the Earth’s tilt with remarkable accuracy, but also inaccurately measured the distance between Earth and the Moon. Eratosthenes' most recognized milestone was his impressive calculation of the Earth’s circumference. While determining how to calculate the size of the Earth, Eratosthenes became aware of a well in Syene (modern-day Aswan, Egypt) where the sun illuminated the water at the bottom, but not the walls of the well, during the summer solstice, indicating that the Sun was directly overhead. Syene is located at a latitude of 24°05′ North, near the Tropic of Cancer, which is the most northerly latitude when the Sun is directly overhead.
Eratosthenes placed a vertical pole in Alexandria and another in Syene during the summer solstice, and noticed that the pole in Alexandria cast a shadow at noon, meaning that the Sun was not directly above the pole, but slightly to the south. After determining the distance between the two cities and accounting for the Earth’s curvature, Eratosthenes determined the angle of the shadow from the vertical pole to be 7.12°, which represented about one-fiftieth of the circumference of a circle. The distance between the two cities was about 5,000 stadia (500 mi), and Eratosthenes concluded that if one-fiftieth of the circumference was 5,000 stadia, then the full circle was 250,000 stadia (25,000 mi) or 40,000 km. Roughly 2,000 years later, modern equipment calculated the Earth's circumference to be 24,901.461 mi at the equator and 24,859.734 mi at the poles.
Errors and Estimates
Eratosthenes correctly developed a formula for calculating the Earth’s circumference, but his estimate included multiple errors. For example, the ancient Greek unit of measuring length, “stadion”, was based on the circumference of the average Greek stadium, but sports stadiums in Greece had a length of 607 ft while those in Egypt were 517 ft. Eratosthenes also assumed that the Sun was shining parallel to both cities, but the rays in both locations were actually slightly inclined. However, despite numerous errors, Eratosthenes' calculation was only off by 0.16%.