Australian Geometry Test Too Difficult?

[Paul Dale]

I would say that given theorems are acceptable in a proof as well as axioms.

I've gone through the process of beginning with the Peano's set theory axioms and constructing the complex numbers (and beyond). However, I'd never start proving anything from these axioms.

Likewise, I'd never start from Euclid's axioms of geometry when attempting a proof. The list of knowledge required I gave above includes none of these axioms, however they all derive from them so a purely axiomatic approach is possible.


As a positive contribution, I'll reference a recent theorem in geometry that was proven in the late 1800s: Morley's theorem. This one stunned me when I first saw it.


Pauli