Euclidean Cover Bands of the Ancient World

July 17, 2021 10:13 AM

"So the written forms of Greek geometric propositions were not so much something one would learn and copy slavishly as prompts that said: here is something interesting; try it yourself. The Elements was not a dead repository of facts but a support for learning and practice, an invitation to perform for oneself, in the same way that rhetoric textbooks aimed to prepare students for rhetorical performance."
posted by escabeche (9 comments total)

This is so cool.
posted by nebulawindphone at 1:30 PM on July 17, 2021

I have discovered a truly remarkable proof of this theorem which this potsherd is too small to contain…
posted by GenjiandProust at 1:52 PM on July 17, 2021 [8 favorites]

I don't know whether the story of Archimedes being killed by an invading Roman soldier on his native island of Syracuse when Archimedes peremptorially ordered the soldier out of the light Archimedes needed to see the diagram he was drawing in the sand is apocryphal or not (though it certainly has that feel -- and I think I may first have read it in ET Bell's Men of Mathematics ?), but wet sand strikes me as a little more convenient and useful for performances and solitary investigation than potsherds could have been.

But that doesn't diminish in the slightest my amazement that the Greeks got as far as they did with the materials and non-materials at their disposal (no algebra, for goodness sake! no analytic geometry).

I've never gotten straight how long the Pythagoreans were able to keep the existence of the dodecahedron to themselves, but it doesn't surprise me that it was evidently so hard to discover.

What would be a modern equivalent? A secret proof of the Riemann hypothesis, for example, or that P ≠ NP?
posted by jamjam at 3:35 PM on July 17, 2021 [1 favorite]

Very cool. Thanks for posting!
posted by Don.Kinsayder at 6:20 PM on July 17, 2021

Hmmmm. A secret group with a P ≠ NP proof would be a solid base for a thriller.
posted by GenjiandProust at 4:04 AM on July 18, 2021 [1 favorite]

This may be slightly off topic but if you're interested in more Euclidean goodness, check out escabeche's *book* that was just recently released.

Shape - the hidden geometry of information, biology, strategy, democracy and everything else.

I am on page 75, and have to say this is a really fun read. So far I've learned about how many holes there are in a pair of pants, Lincoln and Euclid, the law of anti-averages, that weird formula that has pi in it which is to do somehow with whether a pair of numbers share a factor. It's quite a romp!
posted by storybored at 7:54 AM on July 18, 2021 [3 favorites]

But not so much about Euclid's place in the ancient Near East and Greece because it's not a subject I know well -- too bad Wardhaugh's book wasn't out while I was writing!
posted by escabeche at 8:12 AM on July 18, 2021 [1 favorite]

At my weird little college in Santa Fe we worked through the Elements by presenting them in turn on the blackboard. That meant that one had to memorize the proofs well enough to present them - It was such a delight to see how earlier proofs were used as tools to take on the more complex ones! Still one of my very favorite educational experiences.
posted by Makwa at 7:31 PM on July 18, 2021

weird little college in Santa Fe

M<y father attended St. John's in the 40's, not in Santa Fe. He left rather than read Aquinas, I think.
posted by thelonius at 3:07 AM on July 19, 2021