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Re: [hameltech] i think i better post this in case anything happens to me..

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  • George T. Pantos
    this is like a riff to a song I’m still working out.. From: George T. Pantos Sent: Tuesday, August 13, 2013 7:26 PM To: hameltech@yahoogroups.com Subject:
    Message 1 of 2 , Aug 13, 2013
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      this is like a riff to a song 'I’m still working out..
      Sent: Tuesday, August 13, 2013 7:26 PM
      Subject: [hameltech] i think i better post this in case anything happens to me..

      oh by the way if I disappear call it Gazoo theory..
      work in progress..  just preliminary haven’t really figured it out yet..
      460px-Osculating_circle.svgI have said before that E=mu^3  with u being the  curvature.  u=1/r in two dimensions. see footnote.
      in three dimensions I believe curvature is 1/r^2     in four dimension curvature is 1/r^3  thus E=mu^3 also being equal to E=mc^2
      NOW HERE IS MY POINT.       now draw the hypotenuse to the triangle formed and that is c.  I have to make a bit of an assumption here.  that this  applies in general terms, to all dimensions. just being sort of a rule. when u what is ..?? tesseract or is it transform..  from one dimension to the next..   so u have the general Pythagorean theorem a^2 + b^2=c^2   remember that when I started I said 4 dimensions. so r would be r^3.  BUT YET c is still c^2.  but maybe this a flaw .. maybe it isn’t.  afterall I’m making this stuff up. creative license.  so will assume r here, means r^3  and c stays the traditional c for the hypotenuse and c^2 in Pythagorean equation.  so we’ll speak in more general terms.  just A RULE OF NATURE WHEN GOING BETWEEN DIMENSIONS.  THE a^2 in the Pythagorean theorem is the radius of curvature of the dimension being described.  and who knows what c is.. hypoteneuse.. dimensional differential..?? plancks constant h..    hypoteneuse..   looking at it with the Pythagorean theorem, is a key that leads us into further understanding..   the
      u know what, I’ve been working on this all morning.. I keep running into more material. I’m tired I’ll get back with u..

      A circle is a one-dimensional object, although one can embed it into a two-dimensional object. More precisely, it is a one-dimensional manifold. Manifolds admit an abstract description which is independent of a choice of embedding: for example, if you believe string theorists, there is a  10- or  11- or  26-dimensional manifold that describes space-time and a few extra dimensions, and we can study this manifold without embedding it into some larger  Rn.

      Incidentally, you might guess that  n-dimensional things ought to be embeddable into  Rn+1 ( n+1-dimensional space). Actually, this is false: there are intrinsically  n-dimensional things, such as the Klein bottle (which is  2-dimensional) which can't be embedded into  Rn+1. The Klein bottle does admit an embedding into  R4. More generally, the Whitney embedding theorem tells you that smooth  n-dimensional manifolds can be embedded into  R2n for  n>0, and for topological manifolds see this MO question.

      There are also other notions of dimension more general than that for manifolds: see the Wikipedia article.

      also see..

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