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Bertietaylor <bertietaylor@myyahoo.com> wrote:No, it is not a matter of taste. It is invincible deductive logic and
>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.No. From axioms you find theorems including P.
You can take it as an axiom, and prove Pythagoras,
or you can take Pythagoras, and prove the //-theorem.
>Not up to the 70s when they taught Euclid in schools.
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.
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