Eratosthenes of Cyrene: Biography & Work as a Mathematician

Instructor: Mark Bowles

Mark has taught, designed, and written textbooks for university history courses. He has a Ph.D. in history.

Understand Eratosthenes of Cyrene's life, his work as a mathematician and geographer, and how he became the first person to correctly approximate the circumference of the Earth. Then you can test your knowledge with a quiz.

Eratosthenes the Man

Eratosthenes of Cyrene was a Greek born about 276 BCE and died around 194 BCE. Cyrene is what we would today recognize as Libya, and there he earned a great deal of fame due to his skill in diverse fields of knowledge. This included mathematics, music, geography, astronomy, philosophy, philology (the study of language), and literature. Because of his genius, his friends, among whom was Archimedes, gave him the nickname 'Pentathlos' meaning he was tremendously knowledgeable in every field he studied.

But he also had another name as well, this time given by his critics. They called him 'Beta,' which was the second letter of the Greek alphabet. They suggested that even though he was brilliant on many subjects, he was never the 'best' in any of them, but was instead just 'second place.' Nevertheless, because of his extensive knowledge Ptolemy Euergetes invited him to become the head of the most impressive library of that time, the great Library of Alexandria.

Image of Eratosthenes

Measuring the Earth's Circumference

We often hear stories about sailors during the era of Columbus in the 15th century CE who thought the world was flat, and that ocean voyagers would sail off the edge of the world. Here's a surprising secret: many people had already deduced that the Earth was a sphere, and not flat at all! Eratosthenes was one of the first to do this, and even more remarkable, he correctly approximated its circumference. Keep in mind this was a time when he didn't travel outside Egypt or have communication with distant parts of the world, so he didn't just hop in a boat with a really long tape measure. Instead he achieved this great feat through the power of mathematics and observation, and sticks and shadows.

He started with the following observation: at noon during the summer solstice in an Egyptian city called Syene (or Swenet) the Sun appeared overhead in such a way that a stick perpendicular to the ground cast no shadow. However in Alexandria, at the same time and on the same day, a stick cast a shadow of 7.20 degrees. This was his clue to determining the size of the Earth.

Eratosthenes knew that the distance between Alexandria and Syene was 5000 stades. He also knew that there were 360 degrees in a circle, so he simply divided 360 by 7.2 and found the result was 50. If there were 50 segments around the Earth equal to the distance between Alexandria and Syene, then its circumference was 250,000 stades (50*5000).

We don't know for sure the exact measurement of a stade in the time of Erastosthenes, but scholars estimate it to be 157.5 meters. This means, in modern terminology, that he predicted the Earth was 39,690 kilometers as compared to our measurements today which are an exact 40,009. This is amazingly close, especially with his very basic technology.

How he calculated the circumference of the Earth

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