[HN Gopher] Australian mathematician discovers applied geometry ...
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Australian mathematician discovers applied geometry on 3,700-year-
old tablet
Author : angrygoat
Score : 53 points
Date : 2021-08-04 15:19 UTC (7 hours ago)
(HTM) web link (www.theguardian.com)
(TXT) w3m dump (www.theguardian.com)
| johnnyApplePRNG wrote:
| This was "discovered" some time ago :
| https://en.wikipedia.org/wiki/Plimpton_322
| Jtsummers wrote:
| This is a second tablet, not Plimpton 322 (the article
| references both).
| dotcommand wrote:
| Hasn't this been known for decades now?
|
| 'According to (Hayashi 2005, p. 363), the Sulba Sutras contain
| "the earliest extant verbal expression of the Pythagorean Theorem
| in the world, although it had already been known to the Old
| Babylonians.'
|
| https://en.wikipedia.org/wiki/Indian_mathematics
|
| I remember being taught that pythagoras probably got his math
| from the indians who possibly got it from mesopotamia.
| Wistar wrote:
| I am amazed he was able to find a compatible charger.
| cf100clunk wrote:
| Although this archeological find relates to Pythagorean Triples,
| my take is that one of the most basic concepts in carpentry, the
| "3-4-5" rule for finding right angles, which is described by
| Euclid and is certainly related to the Pythagorean theorum, now
| would logically seem to have been used much earlier. The 3-4-5
| rule holds that a right angle is deduced by marking 3 equal units
| on the x axis, then drawing a wide arc of 4 of the same units
| somewhat orthogonally (appearing to go both plus and minus) from
| point 0 of the x axis, then marking the point from the top of the
| x axis to the point on the arc at which the gap is exactly 5 of
| the same units. The result is a right angle. By using a plumb bob
| to create a vertical x axis in the first place, the resulting y
| axis is thus horizontal. The 3-4-5 rule is and was essential in
| structural work, so I'm suggesting that meaningful contributions
| to architecture and other pursuits were made using the 3-4-5 rule
| long before the use of trigonometry as we know it from
| Pythagorus, so any move of the Pythagorean Triples timeframe
| would thus apply to the timeframe of the 3-4-5 rule. I hope
| someone will correct any errors/delusions in my summary.
| generationP wrote:
| Actual source: [Mansfield, D. F. (2020). _Perpendicular Lines and
| Diagonal Triples in Old Babylonian Surveying_. Journal of
| Cuneiform Studies, 72, 87-99. doi:10.1086 /709309](https://sci-
| hub.se/http://dx.doi.org/10.1086/709309). The "Si." is short for
| [Sippar](https://en.wikipedia.org/wiki/Sippar).
|
| From a quick skim, this seems to indeed bolster Wildberger's
| theory about the Babylonians' use of Pythagorean triples
| (actually the theory predates Wildberger, but he is its main
| proponent). This theory claims that the triples were used as a
| proto-trigonometric table, a ready-made set of rational-sided
| right-angled triangles, as irrationals were not expressible in
| Babylonian numerals. (Of course, Wildberger draws motivation for
| his "rational trigonometry" from this, although it is a
| mathematical theory that needs no historic motivation.) In
| contrast, the more mainstream theory is that the Pythagorean
| triples were a product of "scribal training" or mathematical
| puzzle-solving (like the Japanese sangakus). This mainstream
| theory, despite sounding like a cop-out, still has a lot speaking
| for it (see [Eleanor Robson, _Neither Sherlock Holmes nor
| Babylon: a reassessment of Plimpton 322_ , Historia Mathematica,
| Volume 28, Issue 3, August 2001, Pages 167-206](https://ora.ox.ac
| .uk/objects/uuid:e3d8eedb-e745-45b3-8612-71...), particularly pp.
| 183--185, for some rather convincing context). But the two can in
| fact be combined: who said puzzles cannot be built out of applied
| problems? (Many a math contest problem arose this way.)
| lalos wrote:
| Great talk for those interested in clay tablets and technology:
| https://www.youtube.com/watch?v=s_fkpZSnz2I
|
| In my opinion, I would bet that those old civilizations had more
| technology that we give them credit for. The only thing they
| lacked was to have a long lasting medium to share that knowledge.
| Whimsical stories or songs could've been a way to share advances.
| We're lucky to have one civilization picking clay tablets as a
| medium and luckier that those survived (some even by accident -
| fires destroying houses but cooking those tablets and burying
| them), who knows maybe we were writing on leather for centuries
| before that have all disintegrated by now (we hunted, we had
| access to paint, we naturally don't want to waste scarce
| resources).
| wdb wrote:
| Such a great story teller. Always on the look out if he does a
| talk at the BM :)
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