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From: Archimedes Plutonium on 10 Apr 2010 01:55 Of course now, I cannot draw ascii art to make it look like curves of the loxodrome and the lines of longitude. But let me sketch a intersection of a loxodrome, the golden mean logarithmic spiral and a longitude (meridian). /\ /a\ / \ L M Now the L is for the logarithmic spiral or Loxodrome and the M is for the Meridian and the "a" is the angle, the constant angle of all the intersections with Loxodrome and meridians. I suspect that angle "a" is roughly 71 degrees. Now to derive the speed of light out of purely mathematics, I am saying that "pi" is Special Relativity in Euclidean geometry, but here in Elliptic unioned Hyperbolic geometry where the loxodrome is Hyperbolic and the sphere surface is Elliptic, that Special Relativity in this broken symmetry geometry is not "pi" but is this loxodrome angle, a constant angle, no matter what frame of reference, the angle is always equiangular. Special Relativity is about the fact that the speed of light is a constant. Pi is a constant to all observers and all frames of reference in Euclidean Geometry. But this is broken symmetry of Euclidean geometry, and is Elliptic unioned with Hyperbolic. So "pi" is no longer the constant, but rather, the angle. That part of it is fine and dandy. Now comes the harder part. I have to show that all those angles involve the Planck length 10^-36 meters and the Planck time 10^-44 seconds. The fact they are small numbers makes no difference because the inverses work just as well. So I have to show that I can attach 10^-36 to one of the curves, either the loxodrome or the meridian, and then show that I can attach the 10^-44 to the other curve the results in that angle "a". So that the angle becomes a representation of the speed of light. And by dividing 10^44/10^36, I end up with 3 x 10^8. And I need to also convince that the units are taken care of, by the mechanism that any units other than meters, seconds has to be converted in order to fit through the Planck strictures of gravity, Planck constant, and speed of light. For pi, it was all easy, because all you had to do was measure the length of circumference of a given circle and divide by the length of that diameter. But here, the constant of the angle demands more of a toll. Archimedes Plutonium http://www.iw.net/~a_plutonium/ whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies |