<<What about considering two half-planes, tiled, and then connect them, have them perpendicular to each other? Would this be a manifold with zero ...
<<No, if we only fold the plane upon a line.<br>But if make a hole in the plane, for example taking out a triangle, or more traingles around a vertex, ...
I was trying to understand Smarandache's counter axioms for counter-projective geometry. It looks like he has a finite/incidence geometry in mind.<br><br>In ...
Howard is right. I think we should read the third Smarandache Counter-Projective axiom as follows:<br> "Not every line contains at least two distinct ...
(I) There exist: either at least two lines, or no line, <br> that contains two given distinct points.<br><br> (II) Let p1, p2, p3 be three non-collinear ...
If we consider the normal Projective geometry:<br><br> (I) There exist one and only one line that contains two given distinct points.<br><br> (II) Let p1, p2,...
Howard,<br>maybe you're gone now traveling, I post this in the club just in case you migh access it from your trip.<br><br>If AB = A'B' and AB = A"B" then ...
<<If AB = A'B' and AB = A"B" then A'B'=A"b" (Hilbert).<br><br>However it is possible to S-deny it: imagine a close curve and two points A, B, on it,...
<<Smarandache does something like this in his model. It seems, however, to<br> be better if we can S-deny referring to the same segment. I don't see ...
<<Then, there might be axioms that can not be S-denied? If so it's okay anyway, because we study those that are S-deniable.>><br><br>I think there...
i want to reconcilate everybody, i agree with howard that it might be difficult to s-deny all axioms, however there miht be possible to exist a such a space ...
<<however there might be possible to exist a<br> such a space where any axiom could be s-deniable>><br><br>First, for a given axiom there should be...
<<Therefore, as Howard said, the S.E.R. should be defined as follows:<br> 1) S-Reflexivity: Not always "a" is equivalent to "a".<br> 2) S-Transitivity: ...
We might construct a dual of a Smarandache geometry replacing lines by points and points by lines - for example in Howard's two-dimensional models does it...
<<< 1) S-Reflexivity: Not always "a" is equivalent to "a".<br>2) S-Transitivity: Let "a" be equivalent with "b" and "b" equivalent with "c". Then ...
<<< 1) S-Reflexivity: Not always "a" is equivalent to "a".<br> 2) S-Transitivity: Let "a" be equivalent with "b" and "b" equivalent with "c".<br> Then...
<Perhaps some sort of quantum mechanical thing would apply here.><br><br>That would be great, Howard, if you can write a paper or book on s-quantum ...
<<what's the difference between quantum physics and quantum mechanics?<br><br>also what quantum theory means?>><br><br><br>I don't know what the ...
I got a definition from a Dictionary of Physics about "Quantum Mechanics" that I copy below:<br>"A methematical physical theory that grew out of Planck's...
I come back because I found a definition for Quantum Theory as well from the same dictionary:<br>"A departure from the classical mechanics of Newton involving ...
I think I have a reasonable definition for "quantum" congruence of segments.<br><br>On the sphere, antipodal points have infinitely many segments joining them,...
Looks interesting, Howard, can we connect quantum theory with geometry? It seems that a probabilistic s-geometry would be better used in quantum physics than...
<<Definition: The q-segment AB is the set of all possible segments AB. Each<br> mention of the q-segment AB refers to one particular segment AB with<br> ...
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