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Topic: Most theorems in Euclidean geometry are IFF theorems.
Replies: 11   Last Post: Sep 13, 2013 1:32 PM

 Messages: [ Previous | Next ]
 lite.on.beta@gmail.com Posts: 134 Registered: 2/21/06
Re: Most theorems in Euclidean geometry are IFF theorems.
Posted: Sep 5, 2013 4:57 AM

On Wednesday, September 4, 2013 11:54:46 PM UTC-4, Lite Beta wrote:
> On Wednesday, September 4, 2013 8:07:15 AM UTC-4, G. A. Edgar wrote:
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> > In article <Pine.NEB.4.64.1309032118001.16146@panix1.panix.com>,
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> > William Elliot <marsh@panix.com> wrote:
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> > > On Tue, 3 Sep 2013, Lite Beta wrote:
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> > > > Is there a reason why most theorems in Euclidean geometry are IFF theorems?
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> > > They are? My impresion what that most were constructive.
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> > Do you mean, most are constructions? For example, Book I Proposition 1
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> > is: construction of an equilateral triangle.
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> Oops. excluding constructions, which I think are just "there exists" theorems.
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> 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.

Ignore that post of mine. I haven't made my point clear (because I don't have a well formed point yet). I just spit out "rigidity" from my gut ..........