Eratosthenes and the Size of the Earth

According to popular myth, the Europeans, benighted by religious fervor and faith in the Bible, thought the world was flat until Christopher Columbus proved them all wrong in 1492. In reality, the ancient Greeks already knew that the world was round 2,000 years before Columbus. And one of them, the mathematician Eratosthenes, used an ingenious method to calculate with remarkable accuracy just how large the Earth was.

Eratosthenes was born in the Greek colony of Cyrene, in present-day Libya, in 276 BCE. He traveled to Athens and studied mathematics and geometry, then was invited to Alexandria in Egypt to serve as a tutor to the Pharoah Ptolemy II’s son. He worked at the Library of Alexandria.

Eratosthenes soon immersed himself in a number of topics. One of his discoveries was the “Sieve of Eratosthenes”, a mathematical process which extracts a series of prime numbers. He was also the first to accurately trace the Nile to two separate sources in “Ethiopia”, concluded that the tributaries began at lakes, and that the flooding of the Nile was caused by heavy rains near its source. And he compiled a history of the known world from all of the various narratives he could find in the Library.

Most of Eratosthenes’ work centered around astronomy. He made a star map with over 675 stars, and devised a calendar system that included leap years. Using basic geometry and measurements made during eclipses, he calculated the distance from the Earth to the Sun and Moon. But his most famous accomplishment was to determine the circumference of the Earth. The Greeks already knew that the Earth was round–they could see the tops of faraway ships or mountains appearing over the horizon before the bottom did. But they did not know how big this sphere was.

One day, Eratosthenes was told of a water well at Syene, near present-day Aswan directly south of Alexandria, where on June 21, the summer solstice when the sun is highest in the sky, the sun’s rays happened to shine directly down the well all the way to the bottom, thereby making a straight line from the Sun through the center of the Earth. Eratosthenes realized that with some basic geometry, he could use this information to calculate the size of the Earth. By measuring the angle of a shadow at Alexandria on the same day, he could determine what portion of a circle this angle represented. Since the shadow angle he measured in Alexandria was 7 degrees and 12 minutes, this represented one-fiftieth of a circle, and therefore the circumference of the Earth was 50 times the distance between Alexandria and Syene, which travel caravans had put at 5,000 Greek stadia. Therefore, the Earth was 250,000 stadia in circumference. The accuracy of Eratosthenes’ calculation was necessarily limited by the imprecise measure of the distance between the two spots, and today we have several different possibilities for the size of one Greekstadia, but all of the modern calculations convert Eratosthenes’s figure of 250,000 stadia into about 25,000 miles–less than 100 miles off from the true figure of 24,901 miles.

Later, using a similar method, Eratosthenes used measurements of shadow angles to determine that the sphere of the Earth was tilted at a 23-degree angle relative to the Sun’s rays.

Despite his writings in many areas of study, Eratosthenes was never considered by his fellow Greeks to be a top-notch scholar.  Many of his contemporaries referred to him as “Beta”, after the second letter of the Greek alphabet–because he was always in second-place and never reached the Alpha level. Nevertheless, much of Eratosthenes’s work was remarkably accurate for its time, and is still discussed today.

Eratosthenes died sometime around 195 BCE, at roughly age 80.  According to later stories, he had committed suicide by starving himself to death because, being old and blind, he considered his life to now be useless.

Over a thousand years later, the work of Eratosthenes had a history-making influence. By the time Columbus set sail in 1492, every educated person in Europe knew that the Earth was round and, thanks to Eratosthenes, how big it was. But several years after Eratosthenes had died, another Greek mathematician, Posidonius, had repeated his calculations using new figures, and arrived at a much smaller size for the Earth, putting its circumference at only 18,000 miles. Columbus seized on this figure and concluded that the Earth was actually much smaller than was believed by everyone else, and therefore Japan and China were much closer–and he could reach them by sailing west from Europe. Armed with this conclusion, he convinced Ferdinand and Isabella of Spain to give him three ships, sailed west–and found the New World. Posidonius had been wrong, and so was Columbus–China was another 7,000 miles away, and had he not unexpectedly hit North America, Columbus and his crew would have starved to death on the way there.

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