Re: Epistemology 201: The Science of Science

mmeron_at_cars3.uchicago.edu
Date: 02/28/05 

Date: Mon, 28 Feb 2005 09:13:44 GMT

In article <Hx7Ud.37207$uO.1008161@news20.bellglobal.com>, Wolf Kirchmeir <wwolfkir@sympatico.ca> writes:
>Allan C Cybulskie wrote:
>[...]
>> My question is whether or not Euclid's geometry assumes straight -- not
>> curved -- lines connecting all points of the geometric shapes. If it does,
>> then his geometry is incomplete, since it doesn't cover curved lines.
>
>Euclid dealt withn circle, so there's your answer. He also cliamed that
>the inerior angle sum of a traingle is pi. That's true if the tyraingle
>is drawn on a zero-curvature surface, but not it it's drawn on a curves
>surafce. Euclid did not consider whether lines drwn on the surface of a
>sphere were straight or not. As any surveyor knows, you can draw
>straight lines on the surface of a sphere. Just point your transit and
>go. So ---
>
And the equation of a circle *in Euclidean geometry*is x^2 + y^2 =
R^2. And the equation of a sphere *in Euclidean geometry* is
x^2 + y^2 + z^2 = R^2. And the *moronic* notion that Euclidean
geometry cannot deal with curved lines and surfaces should be banished
to the coffee table books it came from and ***burned*** with them.
This is pure nonsense.

Euclidean geometry deals perfectly well with curved lines and
surfaces. Newton, Euler and Gauss managed this with no problem. It
doesn't deal with spaces posesssing an intrinsic curvature but thats
another story altogether.

Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"

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