Australian mathematician discovers applied geometry on 3,700-year-old tablet

https://www.theguardian.com/science/2021/aug/05/australian-mathematician-discovers-applied-geometry-engraved-on-3700-year-old-tablet

by angrygoat • 5 years ago

73 11 5 years ago

theguardian.com

cf100clunk2• 5 years ago

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.

CheezeIt• 5 years ago

Maybe they just used a square (tool) or levels.

Geometrically the simpler and more precise way to make a perpendicular line is to mark two points an equal distance on the left and right, and then from them intersect circles of a larger radius above the line. Drop a perpendicular down to your starting point. That’s much more precise because you don’t need to have a radius 5/4 the size of another one.

But you can lay out rectangles on the ground with proper right angles with fewer workers if you use the Pythagorean theorem instead of trying to get a parallelogram out of ropes with the diagonals equal.

cf100clunk2• 5 years ago

Creating a square tool required some sort of rule or trick: the 3-4-5 rule, your solution, or blind luck. Creating a level meant easily deducing a straight line from the surface of a liquid, which became known as a "spirit level". The 3-4-5 rule was also easy to use with tools such as calipers, protractors, and lengths of cord. Also, from the standpoint of working in enclosed spaces, the 3-4-5 rule takes about half the width of your solution.

lalos• 5 years ago

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• 5 years ago

Such a great story teller. Always on the look out if he does a talk at the BM :)

johnnyApplePRNG• 5 years ago

This was "discovered" some time ago : https://en.wikipedia.org/wiki/Plimpton_322

Jtsummers• 5 years ago

This is a second tablet, not Plimpton 322 (the article references both).

dotcommand• 5 years ago

Hasn't this been known for decades now?

'According to (Hayashi 2005, p. 363), the Śulba Sūtras 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.

random314• 5 years ago

The sulabha sutras are from 550BC and these discoveries are over 1000 years older.

Pythagorean triplets have been discovered in Babylon in this time period before, but only as a list of triplets.

Here we see its use in land surveys i.e. being applied in the marketplace.

Another aspect of the sulabha sutra is that the statement can be interpreted as being applied only to isosceles right angle triangles. If this is true, the sutras don't really state the Pythagoras theorem because the isosceles 45 degree hypotenuse case is trivial.

From geographical constraints it is unlikely Pythagoras obtained it from India. Pythagoras is however known to have stated multiple times that the greatest center of learning is in Egypt (Alexandria??) and one must travel there. So one possible transmission route is Babylon->Egypt->Greece. But all of this is wild speculation.

Wistar• 5 years ago

I am amazed he was able to find a compatible charger.

generationP• 5 years ago

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.)

Australian mathematician discovers applied geometry on 3,700-year-old tablet

Related Stories