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June 22nd, 2018, 04:41 PM   #51
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Just another update from the other discussion.

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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, 05:07 PM   #52
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June 23rd, 2018, 01:38 AM   #53
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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 01:51 AM.
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November 6th, 2018, 07:05 AM   #54
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Amazing interactive video tutorial about quaternions:
https://eater.net/quaternions

It's important to understand that developments in spherical trigonometry halted when vector manipulation became the prevalent technology.

The geometry that we're developing has no corollary to quaternions. Octonions probably have a closer relationship to what we are doing because of the use of three complex planes instead of just two.
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November 6th, 2018, 08:14 AM   #55
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Originally Posted by steveupson View Post
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
How are these inverse functions at all?

Do you mean the reciprocal? Using the terminology inverse is bad here.
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November 6th, 2018, 09:30 AM   #56
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Originally Posted by Micrm@ss View Post
How are these inverse functions at all?

Do you mean the reciprocal? Using the terminology inverse is bad here.
Yes, I think that I mean reciprocal. The "numerical values" section of the wiki for the Lorentz factor uses this terminology, so I'm not quite sure what's wrong with it.

https://en.wikipedia.org/wiki/Lorent...merical_values
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November 6th, 2018, 09:57 AM   #57
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Originally Posted by steveupson View Post
Yes, I think that I mean reciprocal. The "numerical values" section of the wiki for the Lorentz factor uses this terminology, so I'm not quite sure what's wrong with it.

https://en.wikipedia.org/wiki/Lorent...merical_values
The linked article says:

In the table below, the left-hand column shows speeds as different fractions of the speed of light (i.e. in units of c). The middle column shows the corresponding Lorentz factor, the final is the reciprocal. Values in bold are exact.

My bolding.
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November 6th, 2018, 10:16 AM   #58
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Originally Posted by Maschke View Post
The linked article says:

In the table below, the left-hand column shows speeds as different fractions of the speed of light (i.e. in units of c). The middle column shows the corresponding Lorentz factor, the final is the reciprocal. Values in bold are exact.

My bolding.
In the wiki link, alpha is plotted as the inverse of gamma.

It still isn't clear to me what you are saying.

"α (Lorentz factor inverse) as a function of velocity - a circular arc."
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November 6th, 2018, 11:21 AM   #59
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In the wiki link, alpha is plotted as the inverse of gamma.

It still isn't clear to me what you are saying.

"α (Lorentz factor inverse) as a function of velocity - a circular arc."
Do you know about inverse functions? It's different from reciprocal.
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November 6th, 2018, 12:26 PM   #60
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The reciprocal of a number is its multiplicative inverse. If x is any non-zero number, then x(1/x)=1.

I still don't understand the error, but that's why I'm back in school studying algebra. I pretty much suck at this kind of thing. Angels on the head of a pin and such. What's the problem with this?

You said it's bad. Why? I really don't know why. Can you explain it?
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