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June 22nd, 2018, 03:41 PM   #51
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Math Focus: non-euclidean geometry
Just another update from the other discussion.

Quote:
s= r*theta as I (humbly) suggested in an earlier post. For r=1 this comes out to s=theta, but r will change relativistically from r = t/tt = 1 to r' = t'/t'=1' at the end of the interaction.

If the spot interacts relativistically with the base of the hemisphere (its constraint), the great circle will wobble (the radius will precess). Only if r = 1, (no hemisphere, no B field will be no precession. The projection on the xy plane will be an ever increasing circle from the origin until it reaches the radius of the great circle at r = 0.

In the complete analysis, the wobbling of the base of the hemisphere also interacts with the increasing circle on the xy plane, making the analysis even more non-linear and intractable.

It is only if the "spot" does NOT interact with the base of the hemisphere (The geometrical tangent that ignores the curvature of the sphere) that it can be considered an E field parallel to r. This interaction (precession) is what Einstein was trying for with differential geometry, where the E field of the electron varies with r' (the curvature of the surface), but fails to take into account the interactions of the hemisphere base with the great circle in the xy plane. -- BuleriaChk
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June 22nd, 2018, 04:07 PM   #52
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June 23rd, 2018, 12:38 AM   #53
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Math Focus: non-euclidean geometry
The graph of the function and its inverse.







It intercepts the y axis at 0.009657 and the inverse intercepts at 103.550.

0.009657153 * 103.550188399 = 1.000000001

Last edited by steveupson; June 23rd, 2018 at 12:51 AM.
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