On Wednesday, September 4, 2013 8:07:15 AM UTC-4, G. A. Edgar wrote: > In article <Pine.NEB.firstname.lastname@example.org>, > > William Elliot <email@example.com> wrote: > > > > > On Tue, 3 Sep 2013, Lite Beta wrote: > > > > > > > Is there a reason why most theorems in Euclidean geometry are IFF theorems? > > > > > > They are? My impresion what that most were constructive. > > > > > > Do you mean, most are constructions? For example, Book I Proposition 1 > > is: construction of an equilateral triangle. >
Oops. excluding constructions, which I think are just "there exists" theorems.
But there seems to be less important one way implication theorems than two way one. All the big ones also have their converse true, like Thales, Pythagoras, Pons Asinorum, etc. I imagine it to be because of the "rigidity" of geometrical objects.