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Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
231–240 of 248 posts
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#232Every group who ever managed to build a building with a rectangular foundation figured out the relation between the side lengths and the diagonal. The Egyptians used Pythagorean triples to measure right angles way before the birth of Pythagoras. But that's not a theorem, just an observation. It becomes a theorem when you prove (i.e. explain why) this relationship always holds, based on more evident things. The Babylo…
I took a course at the university of Buffalo in the early 80s about pre-roman examples of Pythagorean geometry in henge monuments and early structures. Basically the class was watching slide shows of the professors vacations across Europe and his photos of old ruins. Then he'd show us a line drawing of the structure and pick out what at times seemed random points that created 3-4-5 triangles. He'd exclaim 'see? They knew about the Pythagorean theorem before Pythagoras!' Our only graded assignment was to write a paper where we "discovered" a similar example. I picked a picture of some random ancient church and "found" the right triangle in it's foundation. I got an A. Definitely just an "observation" no theorum involved.
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#233Earlier quoted context omitted.
I think that's hyperbolic. It seems like a natural digression. I think you're just being negative. Put another way, this discussion certainly has more than an infinitesimal relation to the original link.
This seems like a pointless back and forth; you all aren't going to be able to square the circle here.
All math is derivative anyway.
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#234Contributions to the body of knowledge is not and never ever been monopolized by any particular nation or civilization but if you read most modern textbooks you're forgiven to think that it was all started with Greek civilization and then nothing of significance happened until Renaissance movement in the 14th CE (conveniently skipping the contributions of the Roman (namely Rome and Byzantine) and Muslim empires (namely Rashidun, Umayyad, Abassid, Andalusian Spanish, Ottoman)). A popular Monty Python sketch of "What have the Roman's done to us" perfectly summarized this ridiculous sentiment.[1]
The fact that many contributions from other older civilizations for examples Indus Valley (Indian) where the original cuneiform alphabet was started and Phoenician (Arabic) where most of the modern alphabets (Latin, Greek, Arabic, Sanskrit) originated. The former Indus Valley script has not even been successfully deciphered yet until today (Nobel price in waiting for the ones who will deciphered them), perhaps they are some older proofs that are just waiting to be discovered upon the understanding of the Indus Valley scripts and languages.
But the nonsensical narrative of whom has the monopoly of contributions to knowledge will carry on until the end of time but the reality is that we are just standing on the shoulders of giants [2].
[1] What have the Roman's done to us:
[2]Standing on the shoulders of giants:
https://en.m.wikipedia.org/wiki/Standing_on_the_shoulders_of...
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#235Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#236Earlier quoted context omitted.
> The relationship between math and spirituality was very strong back then! On Seymour Cray: Another favorite pastime was digging a tunnel under his home; he attributed the secret of his success to "visits by elves" while he worked in the tunnel: "While I'm digging in the tunnel, the elves will often come to me with solutions to my problem." [0] [0] https://en.wikipedia.org/wiki/Seymour_Cray
I'm actually curious if "digging in the tunnel" is a euphemism for using psychedelics, which would have been severely frowned upon at the time. The elves are known for their wisdom in helping you see the world and solve problems in unique ways. https://maps.org/2004/08/08/nobel-prize-genius-crick-was-hig... > FRANCIS CRICK, the Nobel Prize-winning father of modern genetics, was under the influence of LSD when he firs…
I got another one - Kary Mullis, PCR inventor, revolutionized genetics and biochemistry:
„In it, he recounts his late-night encounter with a glowing raccoon that spoke to him, addressing him as "doctor" -- a raccoon that may or may not have been an alien. He tells of passing out after inhaling too much nitrous oxide and later learning that he'd been saved from a fatal overdose by a woman who traveled to him on an "astral plane."“ [0]
[0] https://www.washingtonpost.com/archive/lifestyle/1998/11/03/...
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#237Earlier quoted context omitted.
Why do you choose b=x/60 for the first iteration? That isn't obvious to me, but 60 must be an obvious choice to be chosen.
You can choose any integer > 1 For example if you choose 2 you will get the binary expansion.
And if you choose b=x/10, x/100, x/1000 ... then each iteration will add the exact decimal point.
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#238Earlier quoted context omitted.
I don’t know of any ancient sources claiming that Pythagoras killed Hippasus. Seems unlikely to me! In any case, Hippasus was a fascinating figure: “Aristoxenus (Fr. 90 Wehrli = DK I 109. 31 ff.) reports that Hippasus prepared four bronze disks of equal diameters, whose thicknesses were in the given ratios, and it is true that, if free hanging disks of equal diameter are struck, the sound produced by, e.g., a disk ha…
I'm pretty confused. How do you think an average 8 year old would feel?
Which is why hands-on learning combined with source material is best practice for children, imo. Taking several disks and demonstrating that the thicknesses double but diameter is the same, letting the kids try hitting them and noting the differences in tone.
Asking the children "why do you think these sound different?" without telling them why first, letting them explore it themselves, gently correcting them along the way. Then pulling out another example and encouraging them to apply the same logic to the new example.
No, instead for the most part, children _still_ get what we all had: memorise these facts without explanation and fill out the blank space on the exam where the memorised words get you points. Most of our entire schooling is just an exercise in memorisation, not in thought and it's sad.
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#239It's interesting that Pythagoras gets credit for a theorem he may not have discovered, especially when there's proof that Babylonians knew it 1000 years earlier. This challenges the idea that ancient Greek mathematicians were always ahead of others.
I think it is the latin based culture that hold the greeks up as the great ones.