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Newsgroups: sci.physics.relativity,sci.physics
Subject: Re: How do Universities Sell Prestigious Baubles?
From: nospam@de-ster.demon.nl (J. J. Lodder)
Reply-To: jjlxa31@xs4all.nl (J. J. Lodder)
Date: Sun, 2 Feb 2025 21:30:16 +0100
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Bertietaylor <bertietaylor@myyahoo.com> wrote:

> On Sun, 2 Feb 2025 10:39:19 +0000, J. J. Lodder wrote:
> 
> > Maciej Wozniak <mlwozniak@wp.pl> wrote:
> >
> >> W dniu 01.02.2025 o 23:28, J. J. Lodder pisze:
> >>
> >>>>>> Nobody is "rejecting Euclid"
> >>>>>
> >>>>> A lie. Of course.
> >>>>
> >>>> Because you say so? I checked: nobody is "rejecting Euclid".
> >>>
> >>> Indeed, and au contraire:
> >>
> >>> Nowadays Euclidean geometry is -defined- as that kind of geometry
> >>> in which the Pythagorean theorem holds.
> >>
> >> And - according to the teachings of your moronic church -
> >> does  Pythagorean theorem hold? For real?
> >> Poor stinker Python has never answerred, he's always
> >> dodging and changing the subject. How about you?
> >
> > You might have noticed that I make it a habit
> > of never replying to your silly rants.
> > I'll make an exception for once,
> > because you are trying to mislead the innocent kiddies
> > who might stray in here.
> >
> > Of course the Pythagorean theorem holds -in Euclidean geometry-.
> > A forteriori, it -defines- Euclidean geometry, nowadays.
> 
> The Pythagoras theorem is just that. Euclidean geometry is defined by
> axioms or self-evident and unquestionable truths upon which all theorems
> are derived. Not the other way around.

What is axiom, and what is theorem,
is in some cases merely a matter of taste.
The // axiom-theorem is a case in point.
You can take it as an axiom, and prove Pythagoras,
or you can take Pythagoras, and prove the //-theorem.

And FYI, the // axiom was never accepted as 'self-evident',
by the most mathematicians.
There have been lots of attempts to prove it from the other axioms,
until Gauss and others proved that this is a futile excercise,
by showing that it is an independent axiom that you can leave or take.

> > It does of course not hold in any other kind of geometry,
> > by definition,
> 
> All other geometries are mappings based on Euclidean geometry, if we are
> talking engineering sense.

The // axiom/theorem has nothing to do with engineering. [1]
OTOH, Pythagoras does,

Jan

[1] Engineers don't build infinitely large structures.