
Babylonians Were Using Geometry Centuries Earlier Than Thought - anigbrowl
http://www.smithsonianmag.com/science-nature/ancient-babylonians-were-using-geometry-centuries-earlier-thought-180957965/?no-ist
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sosuke
I'm so astonished and impressed with this kind of work. When I look at that
tablet all I see are a bunch of triangle impressions like scales. I wonder how
it is read.

[http://thumbs.media.smithsonianmag.com//filer/67/a8/67a8aa02...](http://thumbs.media.smithsonianmag.com//filer/67/a8/67a8aa02-268f-4622-bce1-2588049737f1/tableta.jpg__800x600_q85_crop.jpg)

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ljak
From

[http://www.livescience.com/53518-babylonians-tracked-
jupiter...](http://www.livescience.com/53518-babylonians-tracked-jupiter-with-
fancy-math.html)

> "It's not an actual trapezoid that describes the shape of a field, or some
> configuration of the planets in space," Ossendrijver told Live Science.
> "It's a configuration in a mathematical space. It's a highly abstract
> application."

> "Actually, this particular tablet has ugly handwriting," Ossendrijver said.
> "It's slanted. It's like cursive if it were written very rapidly. It's very
> abbreviated. He left out everything that is not absolutely necessary to
> follow the computation."

You can read the details here:

[http://science.sciencemag.org/content/351/6272/482.full](http://science.sciencemag.org/content/351/6272/482.full)

The supplementary materials give a full transcript of the tablet you linked
(one of several):

[http://science.sciencemag.org/content/sci/suppl/2016/01/27/3...](http://science.sciencemag.org/content/sci/suppl/2016/01/27/351.6272.482.DC1/Ossendrijver.SM.pdf)

> 1 The day when it appears: 0;12, until 1,0 days, 0;9,30.

> 2 0;12 and 0;9,30 is 0;21,30, times 0;30

> 3 is 0;10,45, times 1,0 is 10;45.

> 4 After completing 1,0 days, until 1,0 days 0;1,30.

> 5 0;9,30 and 0;1,30 is 0;11, times 0;30 is 0;5,30.

> 6 0;5,30 times 1,0 days is 5;30. (erasure) 10;45 and 5;30 is

> 7 16;15, the total. From appearance until station the motion is 16;15.

The actual trapezoid is mentioned in another tablet, which is also translated.

To see how the numerals actually work, just look up Babylonian Mathematics.
It's a pretty simple base-60 system.

~~~
anticore
Weird question, but how does one write very rapidly in stone?

~~~
acqq
Clay tablets texts were written in soft clay mass, just pressing the clay with
the wooden stylus produces the marks. Only once it's baked it is durable.

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gene-h
Title is a bit misleading, what they were doing was a lot closer to a
precursor to calculus.

~~~
rubidium
Reminds me a bit of a guy my physics teacher met in the oil fields of alaska.
The guy, who had never finished high school (and much less seen Calculus), had
figured out a way to calculate the volume of a large, tapering tank using his
own shorthand. He had the concept of limits and was essentially doing
calculus.

~~~
sdenton4
As my math phd adviser once told me, 'Those who do not understand homology are
doomed to reinvent it.'

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acqq
The original paper in Science by Mathieu Ossendrijver:

[http://science.sciencemag.org/content/351/6272/482](http://science.sciencemag.org/content/351/6272/482)

"Ancient Babylonian astronomers calculated Jupiter’s position from the area
under a time-velocity graph"

As gene-h noted, it's interesting because it's something close to calculus but
done so early in history.

~~~
leoc
I'm guessing that the mentions of fourteenth-century Europe refer to the work
of the
[https://en.wikipedia.org/wiki/Oxford_Calculators](https://en.wikipedia.org/wiki/Oxford_Calculators)
, an interesting bunch in their own right.

~~~
acqq
Oresme in Paris did it graphically. The calculators apparently produced the
"mean speed theorem". It's written in the full text of the paper:

"The “Oxford calculators” of the 14th century CE, who were centered at Merton
College, Oxford, are credited with formulating the “Mertonian mean speed
theorem” for the distance traveled by a uniformly accelerating body,
corresponding to the modern formula s = t•(v0 + v1)/2, where v0 and v1 are the
initial and final velocities (12, 13). In the same century Nicole Oresme, in
Paris, devised graphical methods that enabled him to prove this relation"

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carlob
The trapezoid rule, also known as Tai's method in the diabetes community.

[http://care.diabetesjournals.org/content/17/2/152.abstract](http://care.diabetesjournals.org/content/17/2/152.abstract)

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orbitingpluto
History of math class... one of the assignments was to find the error in a
Babylonian secant table and also reason out how the computing error happened.
Fun.

