euclid

Mostly arithmetic but the patterns were very pretty (think Euclid algorithm generalized).

They're responsible for creating meaningful visualizations of the Euclid Analytics Engine.

And people have been known to read Euclid for fun.

After all, we still use the exact algorithm as Euclid for finding gcds.

I really love Euclid proof of The infinitude of primes.

Basic concepts of summation leading to integration, like what Euclid did in ancient Greece, or differentiation as the slope of a line, can be learned after a college algebra course.

But keep in mind my run with geometry hasn't gone past Euclid (the illustrated version of the Elements edited by Taschen) and I'm still in the dark about other fields (I'm using Professor Gowers' The Princeton Companion to Mathematics for direction).

However, I also read: > Euclid is often erroneously reported to have proved this result by contradiction, beginning with the assumption that the set initially considered contains all prime numbers, or that it contains precisely the n smallest primes, rather than any arbitrary finite set of primes.

I didn't call it "the proof that appears in Euclid's Elements ".

-- Paul Halmos "There is no Royal Road to geometry," -- Euclid, in reply to King Ptolemy's request for an easier way of learning mathematics.

What I couldn't find was an answer to the question "why?" I could see this being an interesting basis for teaching Computer Science in high schools, where a text like this functions in a way similar to Euclid in high school Geometry courses.

"Euclid is said to have replied to King Ptolemy's request for an easier way of learning mathematics that 'there is no royal road to geometry'" Math education could certainly use more fun, and I think most teachers who love the subject and are skilled (if not talented) mathematicians are capable of making it more fun and relevant.

It is a common simplification of Euclid's proof to convert it to a proof by contradiction.

Before that it was only arithmetic and bits and bobs of Euclid's Elements (=Geometry).

This version is not constructive, actually the first example of the wikipedia article on constructive proofs points this out: Euclid's proof is constructive.