[yottalove]

Read and understand the thirteen books of the Elements by Euclid, preferably in the original Greek. This ought to be sufficient for a fundamental understanding of the mathematical method, its power and application--all generated from a handful of axioms and postulates which in turn can be re-visioned to form entirely distinct but consistent systems.

[LolWolf]

There are better presentations of geometry than the Elements :) (Plus, the original constructions, without algebra, are rather tricky and don't generalize well!)

If we're interested in the mathematical method and its power, a good start might be to, well, go with more exploration-based approaches, where students have to learn things in order to solve a "real"(-ish) problem. Of course, the training required and attention to students would rocket and is likely infeasible, but hey, if Euclid's elements in the original Greek are on the table, this doesn't look too bad !

[ARandomerDude]

> better presentations

> more exploration-based approaches

Do you know of any that you'd recommend?

[bslorence]

The main thing Euclid did for me was to enkindle a love for math as such. Geometry done that way is just so ... beautiful.

Unfortunately I didn't have this experience until I was an undergraduate. For the prior 12 years of formal schooling, math mostly felt like repetitive drudgery with occasional flashes of excitement when I would learn a new technique.

[Koshkin]

Here's a beautiful rendition of the original text alongside with an English translation:

https://farside.ph.utexas.edu/Books/Euclid/Elements.pdf

[pkaye]

Back in the 80s, we learned the Euclid axioms and postulates in geometry class which was around 8th grade. Not sure what is taught these days.

Edit: I think that was the first class where we learned about proofs and we solved so many that I really get the hang of it.

[AnimalMuppet]

"For California Public Schools". I'm pretty sure that most high school kids are not going to be reading Euclid in the original Greek...

[andrepd]

/s ?