How Eratosthenes found the circumference of the Earth

Eratosthenes of Cyrene (b. c. 276 BC, Cyrene, Libya–d. c. 194, Alexandria, Egypt), Greek scientific writer, astronomer, and poet, the first man known to have calculated the Earth’s circumference. At Syene (now Aswan), some 800 km (500 miles) southeast of Alexandria in Egypt, the Sun’s rays fall vertically at noon at the summer solstice. Eratosthenes noted that at Alexandria, at the same date and time, sunlight fell at an angle of about 7 from the vertical. He correctly assumed the Sun’s distance to be very great; its rays therefore are practically parallel when they reach the Earth. Given estimates of the distance between the two cities, he was able to calculate the circumference of the Earth. The exact length of the units (stadia) he used is doubtful, and the accuracy of his result is therefore uncertain; it may have varied by 0.5 to 17 percent from the value accepted by modern astronomers. He also measured the degree of obliquity of the ecliptic (in effect, the tilt of the Earth’s axis) with great accuracy and compiled a star catalog. His mathematical work is known principally from the writings of Pappus of Alexandria.

After study in Alexandria and Athens, Eratosthenes settled in Alexandria about 255 BC and became director of the great library there. He worked out a calendar that included leap years, and he tried to fix the dates of literary and political events since the siege of Troy. His writings include a poem inspired by astronomy, as well as works on the theatre and on ethics. Eratosthenes was afflicted by blindness in his old age, and he is said to have committed suicide by voluntary starvation