By Randy Alfred 
June 19, 2008 | 12:00 am | Categories: Uncategorized
240 B.C.: Greek astronomer, geographer, mathematician and librarian Eratosthenes calculates the Earth’s circumference. His data was rough, but he wasn’t far off.
Eratosthenes was an all-around guy, a Renaissance man centuries before the Renaissance. Some contemporaries called him Pentathalos, a champion of multiple skills. The breadth of his knowledge made him a natural for the post of librarian of the library of Alexandria, Egypt, the greatest repository of classical knowledge.
His detractors, however, mocked Eratosthenes as a jack-of-all-trades and master of none. They called him Beta, because he came in second in every category.
Envy? Perhaps. He invented the Sieve of Eratosthenes, an algorithm for finding prime numbers still used in modified form today. He sketched the course of the Nile from the sea to Khartoum, and he correctly predicted that the source of the great, life-giving river would be found in great upland lakes.
Eratosthenes knew that at noon on the day of the summer solstice, the sun was observed to be directly overhead at Syene (modern-day Aswan): You could see it from the bottom of a deep well, and a sundial cast no shadow. Yet, to the north at Alexandria, a sundial cast a shadow even at the solstice midday, because the sun was not directly overhead there. Therefore, the Earth must be round — already conventionally believed by the astronomers of his day.
What’s more, if one assumed the sun to be sufficiently far away to be casting parallel rays at Syene and Alexandria, it would be possible to figure out the Earth’s circumference. Eratosthenes computed the shadow in Alexandria to be 1/50 of a full 360-degree circle. He then estimated the distance between the two locations and multiplied by 50 to derive the circumference.
Of course, his measurements were slightly off. Alexandria was not due north of Syene, but 2 degrees of longitude off. Syene was not precisely on the Tropic of Cancer but 39 minutes of latitude north of it. The distance between the cities was an estimate. The Earth is not a perfect sphere, but an oblate spheroid flattened at the poles.
And we don’t know today the exact size of the measurement unit Eratosthenes was using when he came up with the final figure of 252,000 stades. (We know he knew it was just a rough estimate, because he adjusted his initial number of 250,000 upward by 2,000 — or 0.8 percent — to make it divisible by 60 or 360 for easy computation.)
So how big is 252,000 stades? Depending on which classical source you trust, it’s somewhere between 24,663 and 27,967 miles. The accepted figure for equatorial circumference today is 24,902 miles. Pretty darn good for a guy without modern measurement tools.
Eratosthenes went further and computed the tilt of the Earth’s axis to within a degree. He also deduced the length of the year as 365¼ days. He suggested that calendars should have a leap day every fourth year, an idea taken up two centuries later by Julius Caesar.
Grade-school tales aside, it was thus known long before Columbus that the Earth was round and even how big it is, approximately. But it was just not widely known among the masses in 15th-century Europe. One reason is that Eratosthenes’ very own library of Alexandria had been destroyed, and there was no complete backup of its data.
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