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Ancient Geometry


Subdeacon Joe

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YBC 7289
 A Babylonian clay tablet contains an accurate sexagesimal approximation of the square root of 2, which is the length of the diameter of a unit square. This number is given as the equivalent of six decimal places, which indicates that it is the greatest mathematical accuracy known in the ancient world. It is believed that this tablet was the work of a student in southern Mesopotamia.  The Two Rivers in the period between 1800 and 1600 BC This tablet shows "the greatest known mathematical accuracy obtained anywhere in the ancient world. The same sexagesimal approximation was later used by the Greek mathematician Claudius Ptolemy in his book Almagest. Ptolemy did not explain where it came from."  This approximation is that this tablet precedes the birth of Claudius Ptolemy by 1900 years.

 

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The burning of the Library at Alexandria in the ancient world was arguably, the greatest loss of knowledge in history.  We are just now discovering how smart some of those civilizations were 2,000 years ago.

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If they could get to 6 decimal places they could go farther, but they were writing on a clay tablet with a wooden stylus and said 'ah good enough'

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4 hours ago, Badlands Bob #61228 said:

  We are just now discovering how smart some of those civilizations were 2,000 years ago.

 

I dunno. I learned Euclidian geometry in junior high about 1961. And a couple years later that Eratosthenes calculated the circumference of the Earth in about 200 BC. He was correct to within a couple hundred miles! Don't think the mathematical knowledge was ever 'lost'.

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35 minutes ago, Red Gauntlet , SASS 60619 said:

 

... Eratosthenes calculated the circumference of the Earth in about 200 BC. He was correct to within a couple hundred miles!

He was right to that degree. Other's made calculations which showed a much smaller planet.

 

We no longer hear about the smaller calculations because they were wrong. But Columbus thought those smaller results were correct, sailing west would get one to the East Indies.

 

I was at some point taught Columbus proved the Earth was round, but this was simply not a question at the time; the Earth was round and this was an accepted truth. The disagreement was only as to size.

 

Had the New World not been in the way, Columbus and his crews and ships would have perished on the journey, the ships could not hold up to the distant journey had the entire expanse been ocean. There is some evidence he was given the ships and crews of convicts just to get rid of him (and them, and the nearly worn-out ships).

 

Columbus returning was an unexpected surprise, and his "discovery" became a state secret for a while. While Spain realized what he discovered, and even sent him out again, there is no evidence that Columbus ever realized he had not reached the East Indies. Having never been there before, he had no reason to question his own beliefs, including his belief the Earth was small.

 

And now here we are, and we no longer recognize the mathematicians with the wrong size of the Earth, even though their error ended up being historically more significant than the correct result.

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Columbus indeed thought the world was about 10,000 miles in circumference, and he promulgated this view hard. A goodly number of contemporary scholars, however, knew he was wrong. But he persuaded himself, and, fortunately, Ferdinand and Isabella.

 

There's a detailed discussion of the point in the first volume of Samuel Eliot Morison's "The European Discovery of America." A really good account of the whole subject.

 

As JK says, everybody knew the world was round, except maybe peasants on the continental steppes. Maritime folks saw hulls and then masts vanish over the horizon on a daily basis.

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