Mathematical secrets of ancient tablet unlocked after nearly a century of study

["Dave Farber" <farber () gmail com>]

Begin forwarded message:

> From: Dewayne Hendricks <dewayne () warpspeed com>
> Date: August 25, 2017 at 4:18:54 AM EDT
> To: Multiple recipients of Dewayne-Net <dewayne-net () warpspeed com>
> Subject: [Dewayne-Net] Mathematical secrets of ancient tablet unlocked after nearly a century of study
> Reply-To: dewayne-net () warpspeed com
>
> Mathematical secrets of ancient tablet unlocked after nearly a century of study
> Dating from 1,000 years before Pythagoras’s theorem, the Babylonian clay tablet is a trigonometric table more 
> accurate than any today, say researchers
> By Maev Kennedy
> Aug 24 2017
> <https://www.theguardian.com/science/2017/aug/24/mathematical-secrets-of-ancient-tablet-unlocked-after-nearly-a-century-of-study>
>
> At least 1,000 years before the Greek mathematician Pythagoras looked at a right angled triangle and worked out that 
> the square of the longest side is always equal to the sum of the squares of the other two, an unknown Babylonian 
> genius took a clay tablet and a reed pen and marked out not just the same theorem, but a series of trigonometry 
> tables which scientists claim are more accurate than any available today.
>
> The 3,700-year-old broken clay tablet survives in the collections of Columbia University, and scientists now believe 
> they have cracked its secrets.
>
> The team from the University of New South Wales in Sydney believe that the four columns and 15 rows of cuneiform – 
> wedge shaped indentations made in the wet clay – represent the world’s oldest and most accurate working trigonometric 
> table, a working tool which could have been used in surveying, and in calculating how to construct temples, palaces 
> and pyramids.
>
> The fabled sophistication of Babylonian architecture and engineering is borne out by excavation. The Hanging Gardens 
> of Babylon, believed by some archaeologists to have been a planted step pyramid with a complex artificial watering 
> system, was written of by Greek historians as one of the seven wonders of the ancient world. 
>
> Daniel Mansfield, of the university’s school of mathematics and statistics, described the tablet which may unlock 
> some of their methods as “a fascinating mathematical work that demonstrates undoubted genius” – with potential modern 
> application because the base 60 used in calculations by the Babylonians permitted many more accurate fractions than 
> the contemporary base 10.
>
> Mathematicians have been arguing for most of a century about the interpretation of the tablet known as Plimpton 322, 
> ever since the New York publisher George Plimpton bequeathed it to Columbia University in the 1930s as part of a 
> major collection. He bought it from Edgar Banks, a diplomat, antiquities dealer and flamboyant amateur archaeologist 
> said to have inspired the character of Indiana Jones – his feats included climbing Mount Ararat in an unsuccessful 
> attempt to find Noah’s Ark – who had excavated it in southern Iraq in the early 20th century.
>
> Mansfield, who has published his research with his colleague Norman Wildberger in the journal Historia Mathematica, 
> says that while mathematicians understood for decades that the tablet demonstrates that the theorem long predated 
> Pythagoras, there had been no agreement about the intended use of the tablet.
>
> “The huge mystery, until now, was its purpose – why the ancient scribes carried out the complex task of generating 
> and sorting the numbers on the tablet. 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. It is a fascinating 
> mathematical work that demonstrates undoubted genius.
>
> [snip]
>
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> Twitter: https://twitter.com/wa8dzp



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