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Topic: the ugly contradiction at the heart of High School Geometry #35.3
Uni-text 8th ed.: TRUE CALCULUS

Replies: 24   Last Post: Nov 3, 2013 7:44 PM

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plutonium.archimedes@gmail.com

Posts: 9,761
Registered: 3/31/08
We keep and maintain Parallelism in True Geometry #35.8 Uni-text 8th
ed.: TRUE CALCULUS

Posted: Nov 2, 2013 7:08 PM
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Alright, in my prior posts on parallelism I see I was mistaken for the True Geometry keeps parallelism. We may have to go far out in the search for the point of intersection which is not a finite point. Although we do have lines intersect at finite points.

So I was mistaken about parallelism, for True Geometry maintains the concept. That also means it maintains the concept for Elliptic and Hyperbolic geometry, but whether those are curved lines or not is still unclear.


On Saturday, November 2, 2013 5:59:04 PM UTC-5, Archimedes Plutonium wrote:
> Alright, in my prior posts, I mentioned how parallelism in True Geometry was no longer valid, since a line can be parallel to a given line and never meet at a intersection even if the lines go to infinity. We can imagine this in the 10 or 100 or 1000 Grid that a line of the x-axis can never intersect with a line that has a gentle slope of x= 0, y = 10 and x=10, y = 9.5 in 10 Grid.
>
>
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> Now we lose parallelism in True Geometry, unless, however, you want to include the idea that at some infinity point that the line y = 0 and the line of (0,10),(10,9.5) do meet and intersect at some distant infinity point in 10 Grid.
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> So, at this writing, I am not sure if parallelism falls to the wayside in True Geometry or whether we best preserve it as a far distant intersection at some infinity point.
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> So Parallelism is a major issue to contend with in True Geometry.
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> Another major issue is that in True Geometry there are no curved lines but that curved lines are all compilations of tiny straight line segments. Now that is true for Euclidean Geometry because we cannot have a Calculus with curved lines.
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> However, are "lines in elliptic and hyperbolic geometry" also compilations of straight line segments? Here I am not so sure. My first guess is that there are no curves in either Euclidean, Elliptic or Hyperbolic. I say that because I am going with the famous relationship that Euclidean geometry is the union of Elliptic with Hyperbolic. That relationship is a smooth one if no curves exist at all. But this needs further study. Perhaps we need curved lines in Elliptic and Hyperbolic by using the infinity numbers of empty space, just as I am not sure if Parallelism is abandoned in Euclidean Geometry.
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> So the above is a short summary of major changes for True Geometry in that we have points then empty space and then successor point, and we have no curves, and we lose the principle of parallelism (unless needed by something unforseen).
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> AP


AP


Date Subject Author
11/1/13
Read the ugly contradiction at the heart of High School Geometry #35.3
Uni-text 8th ed.: TRUE CALCULUS
plutonium.archimedes@gmail.com
11/1/13
Read Re: the ugly contradiction at the heart of High School Geometry #35.3
Uni-text 8th ed.: TRUE CALCULUS
Brian Q. Hutchings
11/2/13
Read 1 Grid System and the Naturals and Empty Space is *Infinity numbers*
#35.4 Uni-text 8th ed.: TRUE CALCULUS
plutonium.archimedes@gmail.com
11/2/13
Read yeajh, but I don't hate you, THAT much
Brian Q. Hutchings
11/2/13
Read some changes in True Geometry, once "empty space" is factored in
#35.5 Uni-text 8th ed.: TRUE CALCULUS
plutonium.archimedes@gmail.com
11/2/13
Read Re: the ugly contradiction at the heart of High School Geometry #35.3 Uni-text 8th ed.: TRUE CALCULUS
Wally W.
11/2/13
Read remarkable how few people recognize a contradiction when shown one
#35.6 Uni-text 8th ed.: TRUE CALCULUS
plutonium.archimedes@gmail.com
11/2/13
Read Re: remarkable how few people recognize a contradiction when shown one #35.6 Uni-text 8th ed.: TRUE CALCULUS
Wally W.
11/2/13
Read why the nonscientist has such a difficult time of comprehending what
a contradiction is and what it means
plutonium.archimedes@gmail.com
11/2/13
Read Re: why the nonscientist has such a difficult time of comprehending what a contradiction is and what it means
Wally W.
11/2/13
Read what a real rebuttal of AP's claim of a contradiction in the heart of
Geometry looks like #35.9 Uni-text 8th ed.: TRUE CALCULUS
plutonium.archimedes@gmail.com
11/2/13
Read Re: what a real rebuttal of AP's claim of a contradiction in the heart of Geometry looks like #35.9 Uni-text 8th ed.: TRUE CALCULUS
Wally W.
11/2/13
Read Re: what a real rebuttal of AP's claim of a contradiction in the
heart of Geometry looks like #35.9 Uni-text 8th ed.: TRUE CALCULUS
plutonium.archimedes@gmail.com
11/2/13
Read rebuttal in defence of establishment Geometry is weak with its
distance rather than length #35.11 Uni-text 8th ed.: TRUE CALCULUS
plutonium.archimedes@gmail.com
11/3/13
Read Re: what a real rebuttal of AP's claim of a contradiction in the heart of Geometry looks like #35.9 Uni-text 8th ed.: TRUE CALCULUS
Wally W.
11/3/13
Read establishment Geometry still has the contradiction and needs a
mechanism to survive #35.12 Uni-text 8th ed.: TRUE CALCULUS
plutonium.archimedes@gmail.com
11/3/13
Read getting the old fake geometry out of the High School and College
classrooms #35.13 Uni-text 8th ed.: TRUE CALCULUS
plutonium.archimedes@gmail.com
11/2/13
Read Re: why the nonscientist has such a difficult time of comprehending what a contradiction is and what it means
Jennifer Murphy
11/2/13
Read Re: why the nonscientist has such a difficult time of comprehending what a contradiction is and what it means
Wally W.
11/3/13
Read Re: why the nonscientist has such a difficult time of comprehending what a contradiction is and what it means
Jennifer Murphy
11/2/13
Read Jennifer Murphy ostrich, hiding away from intellectual debate and
wants to suppress new ideas
plutonium.archimedes@gmail.com
11/2/13
Read some huge changes to geometry of True Geometry #35.7 Uni-text 8th
ed.: TRUE CALCULUS
plutonium.archimedes@gmail.com
11/2/13
Read We keep and maintain Parallelism in True Geometry #35.8 Uni-text 8th
ed.: TRUE CALCULUS
plutonium.archimedes@gmail.com
11/2/13
Read Re: We keep and maintain Parallelism in True Geometry #35.8 Uni-text 8th ed.: TRUE CALCULUS
Wally W.
11/3/13
Read however, it is really not that funny, when you don't pretend that
it's no a.p. (you are when
Brian Q. Hutchings

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