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Fascinating account of how the great Greek mathematician Eratosthenes figured the circumference of the Earth
His estimate was 28,000 miles - about 15% higher than the actual figure of 24,901 miles
Yet remarkably accurate for its time - circa ~200 BCE
His estimate was 28,000 miles - about 15% higher than the actual figure of 24,901 miles
Yet remarkably accurate for its time - circa ~200 BCE
Eratosthenes was the chief librarian of the Library of Alexandria
He was told by someone that at Syene (modern Aswan), the sun casts no shadow at noon on June 21st (as it lies v close to Tropic of Cancer)
In his native Alexandria, the sun did cast a shadow even on Jun 21st
He was told by someone that at Syene (modern Aswan), the sun casts no shadow at noon on June 21st (as it lies v close to Tropic of Cancer)
In his native Alexandria, the sun did cast a shadow even on Jun 21st
He measured the length of the shadow of an obelisk at noon in Alexandria.
Using basic trigonometry, estimated the angle of the Sun to be 7 degrees 14' from overhead.
As there is no shadow at Aswan, the angle should be 0 there.
Using basic trigonometry, estimated the angle of the Sun to be 7 degrees 14' from overhead.
As there is no shadow at Aswan, the angle should be 0 there.
Then he estimated the distance between Aswan and Alexandria to be roughly 5000 stadia - each stadium amounting to 607 feet.
Circumference of earth was then 50 times 5000 stadia = 250K stadia
As 360 degrees / 7 degrees 14' is 50
Circumference of earth was then 50 times 5000 stadia = 250K stadia
As 360 degrees / 7 degrees 14' is 50
This gave him his estimate of 28.7K miles - very nearly correct.
The error creeping in because of the erroneous assumption that Aswan is exactly at the Tropic of Cancer and possibly some error in estimating the distance between Aswan and Alexandria!
The error creeping in because of the erroneous assumption that Aswan is exactly at the Tropic of Cancer and possibly some error in estimating the distance between Aswan and Alexandria!
But sadly enough Eratosthenes's remarkable breakthrough was sort of neglected by Ptolemy some 300 years later (2nd cen AD)
Ptolemy was a great Greek polymath of Alexandria - perhaps the most influential geographer of all time
Ptolemy was a great Greek polymath of Alexandria - perhaps the most influential geographer of all time
He chose not to be guided by Eratosthenes's circumference of 28.7K, and the assessment that each "degree" is about 70 miles
Rather he was guided by the other Greek polymath Posidonius (1st cen BCE) that 1 degree is 50 miles!
Hence estimating circumference to be 18K miles
Rather he was guided by the other Greek polymath Posidonius (1st cen BCE) that 1 degree is 50 miles!
Hence estimating circumference to be 18K miles
So while Eratosthenes's estimate was 15% higher, Ptolemy's inferior estimate was 28% lower!
This had consequences. Eventually leading to the discovery of America 1400 yrs later!
This had consequences. Eventually leading to the discovery of America 1400 yrs later!
Columbus, like most learned men of his age, followed Ptolemy. Not Eratosthenes.
Ptolemy was after all the greatest authority on geography from the ancient world
Hence he was convinced he could reach India by sailing west, as he had underestimated the size of the earth
Ptolemy was after all the greatest authority on geography from the ancient world
Hence he was convinced he could reach India by sailing west, as he had underestimated the size of the earth
Many learned men cautioned Columbus
But Columbus was confident he could reach India. Instead he fell way short, and reached a hitherto largely unknown continent. (Caribbean)
Had Columbus followed Eratosthenes, he may have never gathered courage for his venture
But Columbus was confident he could reach India. Instead he fell way short, and reached a hitherto largely unknown continent. (Caribbean)
Had Columbus followed Eratosthenes, he may have never gathered courage for his venture
This is a classic example from history of how a "geographical mis-estimate" popularized by Ptolemy proved to be a blessing in disguise triggering geographic exploration
Reference : The Discoverers, Daniel Boorstin
