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Old Babylonian Math with HP-25
10-24-2017, 05:27 AM
Post: #1
Old Babylonian Math with HP-25
Tonite I tried to grasp Old Babylonian methods of calculating and dig out - unexpectedly - an HP-25 program doing multiplications of numbers in base 60. The program is -- nai, not from the old Babylonians -- it is mentioned in a paper of Jöran Friberg from 1981. See here on page 316 (page 40 of the PDF). What a finding!

If you are interested in this subject I suggest this paper about Plimpton 322 with some insights from down under, luckily not behind a paywall.

Ciao.....Mike

PS: is there a rotine around for division in base 60? Not calculating decimal and then convert, but for reason of accuracy all completely sexagesimal.
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10-24-2017, 06:44 AM
Post: #2
RE: Old Babylonian Math with HP-25
Very interesting. I'm not aware of any device that can calculate in base-60. The H->H.MS and H.MS->H functions are the closest I know of.


Pauli
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10-24-2017, 06:58 AM (This post was last modified: 10-24-2017 07:03 AM by Mike (Stgt).)
Post: #3
RE: Old Babylonian Math with HP-25
(10-24-2017 06:44 AM)Paul Dale Wrote:  The H->H.MS and H.MS->H functions are the closest I know of.

Thank you for this hint. I hope it helps, not sure yet. I thoght about "Horner Schema" for polynom division: https://matheguru.com/algebra/horner-sch...ision.html
/M.
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10-24-2017, 07:19 AM
Post: #4
RE: Old Babylonian Math with HP-25
thanks for sharing!

Wikis are great, Contribute :)
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10-24-2017, 11:18 AM
Post: #5
RE: Old Babylonian Math with HP-25
(10-24-2017 06:44 AM)Paul Dale Wrote:  I'm not aware of any device that can calculate in base-60.

Well, maybe an IBM 407 could do, or at least, it probably could be twisted to do so. As far as I know it was able to cope with the British way counting coins prior to Decimal Day in 1971 where twelve pence made a shilling, and twenty shillings made a pound, and a half-crown was two shillings and sixpence (what is just half way to sexagesimal math).
Not to forget, the shilling when instructed 1816 was to coin one troy pound (weighing 5760 grains or 373 g) of standard (0.925 fine) silver into 66 shillings (!) -- and ... well ... this 66 is very close to 60, close enough to be sexagesimal. Wait! For easier calculations the Babylonians also took Pi = 3, knowing it is not.

BTW, about Shakespearean allusions and "Twelfth Counters", the IBM 407 Accounting Machine lives farther on as it influenced the design of "spec", a stage within CMS Pipelines, see footnote there.

Ciao.....Mike Wink
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10-24-2017, 12:08 PM
Post: #6
RE: Old Babylonian Math with HP-25
The true mathematical meaning of the Babylonian tablet Plimpton 322.
El verdadero significado matemático de la tablilla babilónica Plimpton 322

http://francis.naukas.com/2017/09/07/el-...mpton-322/

[Image: Dibujo20170906-plimpton-322-babylonian-c...80x398.png]

http://www.hpcalc.org 20 years online
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10-24-2017, 12:24 PM (This post was last modified: 10-24-2017 12:24 PM by pier4r.)
Post: #7
RE: Old Babylonian Math with HP-25
(10-24-2017 12:08 PM)compsystems Wrote:  The true mathematical meaning of the Babylonian tablet Plimpton 322.
El verdadero significado matemático de la tablilla babilónica Plimpton 322

"The true" is quite a claim.

And it is not even claimed by the article (that says that some australian guy proposes that the table is about trigonometry).

So if I were you, I wouldn't use such sentences, they can erode the credibility.

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10-24-2017, 01:31 PM
Post: #8
RE: Old Babylonian Math with HP-25
(10-24-2017 12:08 PM)compsystems Wrote:  El verdadero significado matemático de la tablilla babilónica Plimpton 322

Sorry, in the article you link, the line 11 of P322's transcription show compared to the original differing values for width (45, 0) and diagonal (1, 15, 0). The ', 0' to the right shifts "one up", so both values are multiplied by 60 whereby the resulting ratio stays the same.

Interestingly this line 11 is the only one of P322 that is not 'reduced to the max'. In priciple it shows the well known Pythagorean triple of 3^2 + 4^2 = 5^2 but mulitplied by 15. Therefore the width is 15*3=45 and the diagonal is 15*5=75 decimal. Or 1*60^1 + 15*60^0 -- hence 1,15 sexagesimal.

None of the ohter lines bear a factor on original P322.

Ciao.....Mike
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