RCA
Posts:
11
Registered:
11/26/05


Re: Euclids postulates and nonEuclidean geometry
Posted:
Mar 7, 2006 8:03 PM


Thanks all for your great responses. My key takeaway from all your responses are:
My interest is logical and not historical  most of the literature seems to imply that the fifth postulate is more questionable in an absolute and obvious sense, which is what confused me. This discussion has clarified that it is not obvious.
I found an interesting relevant discussion about this issue at http://www.cuttheknot.org/triangle/pythpar/Geometries.shtml
1. There are several nonscientific (historical  Euclid didnt introduce it for a while, aesthetic  it "looks" uglier) reasons why it turned out that the fifth postulate was debated more than the others. 2. The negation of the fifth postulate led to practically useful geometries and thus came to the forefront. 3. There is active work in logic that investigates negating the other postulates as well, based on (Bolyai et al's) further abstraction of denying the common meanings of line and the plane.
Thanks very much RCA

