Re: [math-fun] beautiful equations and E.T.

The key educational and general intellectual advantage of Euclidean geometry is that so many of its theorems are surprising. For example, it isn't obvious that the angle bisectors of a triangle meet at a point. This is what makes people want to study mathematics or even become mathematicians. 1-1 correspondence of sets as the foundation of elementary arithmetic has no surprises for the school child. Euclid's proof of the infinity of primes is surprising, but it requires an initial interest in primes. The irrationality of sqrt(2) surprised the Greeks, but that was in relation to a prior doctrine of commensurability.