Re: Epistemology 201: The Science of Science

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

Date: Mon, 28 Feb 2005 22:42:11 GMT

In article <WqednaO9CYBtnr7fRVn-rg@rcn.net>, jmfbahciv@aol.com writes:
>In article <chBUd.28$25.8789@news.uchicago.edu>,
> mmeron@cars3.uchicago.edu wrote:
>>In article <Hx7Ud.37207$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.
>
>Could one of the problems of this ignorance be due to kids
>not building Euclidean geometry in their high school plane
>geometry course? That my first encounter to the concept
>that you could start with a couple of rules (axioms) and
>build (via proofs) a geometry. Tweak one of the rules,
>and you could get a different geometry. I'm still awed by that.
>
Not teaching geometry properly, in high school, is a problem but, I
think, separate from the above.

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

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