Eratosthenes

Who Measured the World From a Shadow · Geographer & Chief Librarian · c. 276 – c. 194 BC

The chief librarian at Alexandria who measured the circumference of the Earth from the length of a shadow, a reported distance and four assumptions he stated out loud.

Who was Eratosthenes?

Eratosthenes was born at Cyrene, in what is now Libya, around 276 BC, studied at Athens, and was summoned to Alexandria by Ptolemy III to tutor the royal heir and to take charge of the Library — the largest collection of texts in the ancient world. He worked in an unusual number of fields: geography, mathematics, chronology, literary criticism, poetry. His rivals nicknamed him Beta, the second letter, meaning that he was second-best at everything and first at nothing. He seems not to have minded. His best-known result is the size of the Earth. It was reported to him that at Syene, far to the south, a vertical rod casts no shadow at noon on the longest day of the year, and the sun is reflected at the bottom of a well. At Alexandria on the same day a vertical rod does cast a shadow, and the angle it implies is about a fiftieth of a full turn. If the Earth is a sphere, if the sun's rays arrive effectively parallel, and if Syene lies directly south of Alexandria, then the arc between the two cities is a fiftieth of the Earth's whole circuit. The distance between them was reckoned at five thousand stades, so the circumference is two hundred and fifty thousand stades — a figure he later gave as 252,000, which is divisible by sixty and so easier to work with. How good that answer is depends entirely on the length of a stade, which is not securely known; on the most common estimates it is within a few per cent of the true figure. Some of that closeness is luck, because several of his inputs are wrong in ways that partly cancel: Syene is not exactly on the tropic, and it is not due south of Alexandria. He also wrote the Geographica in three books, laying the known world out under a framework of lines running east–west and north–south so that a place could be given a position rather than described by its neighbours; devised the sieve that strains prime numbers out of a list of whole numbers; and compiled a chronology of the world from the fall of Troy. Archimedes, who corresponded with him, addressed the Method to him.

Major achievements

• Measured the circumference of the Earth from a shadow angle and one reported distance
• Stated the assumptions the measurement rests on, rather than presenting the number alone
• Wrote the Geographica, laying the known world under a framework of east–west and north–south lines
• Devised the sieve for finding prime numbers
• Directed the Library of Alexandria under Ptolemy III

Life in brief

• c. 276 BC — Born at Cyrene: In the Greek city on the North African coast.
• c. 245 BC — Summoned to Alexandria: By Ptolemy III, as royal tutor and then chief librarian.
• c. 240 BC — The Earth measured: From the shadow at Alexandria and the well at Syene: 250,000 stades.
• c. 235 BC — The Geographica: Three books laying the known world under a framework of lines.
• c. 194 BC — Died at Alexandria: Reportedly by refusing food after going blind.

Explore the life of Eratosthenes — five chapters

1. Cyrene to Alexandria — The man they called second-best
2. The Shadow and the Well — How to weigh a world you cannot leave
3. How Good Was It, Really? — Two wrong inputs that partly cancelled
4. Lines Across the World — The Geographica, and the invention of a position
5. The Sieve, and the End — A method still taught, and a death still argued about

Read the five-chapter life of Eratosthenes →

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