Re: Euclids postulates and non-Euclidean geometry
- From: "Eric Gisse" <jowr.pi@xxxxxxxxx>
- Date: 7 Mar 2006 16:08:55 -0800
RCA wrote:
Hi,
I am trying to understand the motivation behind non-Euclidean geometry.
You would be better off asking this in sci.math.
Simply put, the motivation was to prove that Euclid's 5th postulate is
provable from the others. What came out of that are things such as
Hyperbolic, Elliptic, and Spherical geometry. It was nearly 2,000 years
before there was a self-consistant non-Euclidian geometry.
1. I do not understand why Euclid's fifth postulate is any different
from the other postulates. For instance, it seems as intuitive to me to
accept the fifth postulate as to accept the first one in one viewpoint.
The fifth postulate is independant from the first four. In other words,
you cannot prove the fifth postulate from the first four.
2. If I assume that a Euclidean geometry refers to an infinite plane
surface which closely matches our intuition at small scales, I find
both the first and the fifth postulate to be equally believable (purely
by intuition in both cases).
Euclidian geometry is in fact a model that satisfies Euclid's 5 axioms.
It isn't the only one, though.
[snip]
.
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