This is a fascinating article.

http://www.telegraph.co.uk/sci...history-maths-could/

A 3,700-year-old clay tablet has proven that the Babylonians developed trigonometry 1,500 years before the Greeks and were using a sophisticated method of mathematics which could change how we calculate today.

The tablet, known as Plimpton 332, was discovered in the early 1900s in Southern Iraq by the American archaeologist and diplomat Edgar Banks, who was the inspiration for Indiana Jones.

The true meaning of the tablet has eluded experts until now but new research by the University of New South Wales, Australia, has shown it is the world’s oldest and most accurate trigonometric table, which was probably used by ancient architects to construct temples, palaces and canals.

However unlike today’s trigonometry, Babylonian mathematics used a base 60, or sexagesimal system, rather than the 10 which is used today. Because 60 is far easier to divide by three, experts studying the tablet, found that the calculations are far more accurate.

“Our research reveals that Plimpton 322 describes the shapes of right-angle triangles using a novel kind of trigonometry based on ratios, not angles and circles,” said Dr Daniel Mansfield of the School of Mathematics and Statistics in the UNSW Faculty of Science.

“It is a fascinating mathematical work that demonstrates undoubted genius. The tablet not only contains the world’s oldest trigonometric table; it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry.

“This means it has great relevance for our modern world. Babylonian mathematics may have been out of fashion for more than 3000 years, but it has possible practical applications in surveying, computer graphics and education.

“This is a rare example of the ancient world teaching us something new.”

The Greek astronomer Hipparchus, who lived around 120BC, has long been regarded as the father of trigonometry, with his ‘table of chords’ on a circle considered the oldest trigonometric table.

A trigonometric table allows a user to determine two unknown ratios of a right-angled triangle using just one known ratio. But the tablet is far older than Hipparchus, demonstrating that the Babylonians were already well advanced in complex mathematics far earlier.

The tablet, which is thought to have come from the ancient Sumerian city of Larsa, has been dated to between 1822 and 1762 BC. It is now in the Rare Book and Manuscript Library at Columbia University in New York.

“Plimpton 322 predates Hipparchus by more than 1000 years,” says Dr Wildberger.

“It opens up new possibilities not just for modern mathematics research, but also for mathematics education. With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own.

“A treasure-trove of Babylonian tablets exists, but only a fraction of them have been studied yet. The mathematical world is only waking up to the fact that this ancient but very sophisticated mathematical culture has much to teach us.”

The 15 rows on the tablet describe a sequence of 15 right-angle triangles, which are steadily decreasing in inclination.

The left-hand edge of the tablet is broken but the researchers believe there were originally six columns and that the tablet was meant to be completed with 38 rows.

“Plimpton 322 was a powerful tool that could have been used for surveying fields or making architectural calculations to build palaces, temples or step pyramids,” added Dr Mansfield.

The new study is published in Historia Mathematica, the official journal of the International Commission on the History of Mathematics.

Interesting article. I’ve often wondered what our arithmetic and mathematics would have been like if we’d had 12 fingers rather than 10.

That is very interesting. Using a Base 60 system, they would have little or no need for decimal places. They must of done much of their math in their heads, and gotten very good at it, as writing supplies were nearly non existent.

Cool post! I am so glad I don't have to relearn trig in base 60 though. LOL

Learning to count in base 60 would be a chore. We have kids today who can't learn 26 letters of the alphabet.

flashguy

quote:

Originally posted by sigfreund:
Interesting article. I’ve often wondered what our arithmetic and mathematics would have been like if we’d had 12 fingers rather than 10.

It would have allowed even the most feeble minded man to count to 25.

quote:

Originally posted by flashguy:
Learning to count in base 60 would be a chore. We have kids today who can't learn 26 letters of the alphabet.

flashguy

They could, and would, if you made it worth their while.

The publc school system in the US has eroded to such a complete waste that becoming educated occurs if at all in spite of school, not because of it.

It's not a matter of intelligence for the most part but of values, and want to.

That's certainly interesting.

Did anyone figure out if there's a connection to 60 minutes to an hour?

quote:

Originally posted by Rey HRH:
That's certainly interesting.

Did anyone figure out if there's a connection to 60 minutes to an hour?

I believe so. And 360 degrees in a circle.

flashguy

Reminds me of an episode of Hardcore History where Dan Carlin was talking about the Assyrians and other people who occupied the mid-east before the rise of the Persian Empire. Those people had an oral history that is now lost of scores and scores of ancient civilizations we'll never know anything about.

Fascinating.

quote:

Originally posted by flashguy:

quote:

Originally posted by Rey HRH:
That's certainly interesting.

Did anyone figure out if there's a connection to 60 minutes to an hour?

I believe so. And 360 degrees in a circle.

flashguy

I think it may be the other way around, that they had a 60 based number system, because it made it convenient to do chronological and astronomical calculations.

Consider that 365, the number of whole days there are in a year is close to 360, the number of degrees in a circle. It may be that in their calendar there were 360 days in a year. Similarly, with 24, the hours in a day, that number divides evenly into 360.

This message has been edited. Last edited by: Storm,

quote:

Originally posted by sigfreund:
Interesting article. I’ve often wondered what our arithmetic and mathematics would have been like if we’d had 12 fingers rather than 10.

Well arcs and curves would be easier deal with for one.

Count the segments of you fingers for 12

quote:

Originally posted by sigfreund:
Interesting article. I’ve often wondered what our arithmetic and mathematics would have been like if we’d had 12 fingers rather than 10.

When I read your post I thought, base 60 has been known and ascribed to the ancient world for a long time. 12 base is on the lines of the 60 base systems.

I started looking for a link for you and noticed when I came back that somebody already referred to a clock.

Watches, clocks, sundials and many things in history are not based on fingers and toes systems. Here is a LINK.

I remember in college fiddling with various base systems in calculating things. It was part of the curriculum.

We didn't use base 60 in trig. I guess the real news is proof of how early it was used in trig. It makes sense, though, because base 60 was known to be the basis of their arithmetic.

The Scientific America article linked above tethers the 60 base system back to the Babylonians of 4,000 BC.

It felt weird to calculate in bases. It was like playing a song in 7/8 odd time.

quote:

Originally posted by sigfreund:
Interesting article. I’ve often wondered what our arithmetic and mathematics would have been like if we’d had 12 fingers rather than 10.

Hmmmm. I've only got eight fingers. The two lumpier ones on the outside are my thumbs.

I agree, however, that we have ten digits.

tac

quote:

Originally posted by tacfoley:

quote:

Originally posted by sigfreund:
Interesting article. I’ve often wondered what our arithmetic and mathematics would have been like if we’d had 12 fingers rather than 10.

Hmmmm. I've only got eight fingers. The two lumpier ones on the outside are my thumbs.

I agree, however, that we have ten digits.

tac

All thumbs are fingers, but not all fingers are thumbs.

quote:

Originally posted by scratchy:
It would have allowed even the most feeble minded man to count to 25.

Can you imagine having to learn your multiplication tables up to 60?

There are 10 kinds of people: those that understand binary, and those that don't.