EM Triangle

[FrankM]

The geometric-mathematical relationships in the pdf attachment were identified empirically when studying an unusual cavity configuration. What forum would be best for this subject?

emtriangle1.pdf

[blike]

if I had any idea what that was about I might have some input

[FrankM]

For those that haven't already noticed, if the wavelength multiplier is increased by 10^2, and then everything recalculated, the results are absolutely symmetrical. The triangle then is mathematically perfect, at least to the precision of the known physical constants.

[uscphysics]

I would have to say that is a good question, but I would say it best fits in a math forum(probably the Algebra section). My reason would be that it seems to be more of an exercise in math rather than E&M. However, it does appear to be a neat problem to solve in almost any field.

[FrankM]

I used the term ElectroMagnetic to present the concept because the 21cm wavelength and related frequency are well known values.

 

I suggest that the process that produced the symmetry is another variant of the geometric/trigonometric forms, which are plane, spherical and hyperbolic geometry, and their associated plane, spherical and hyperbolic trigonometry. I do not have a name for it.

 

The use of the linear and angular notation associated with transverse waveforms is "unconventional" but it results in geometric/mathematical relationships that have unusual scope. You can translate (rotate) the angle to 45 degrees and still get symmetry, but you have recognize what is and is not a variable. The relationships and numeric values that result for the 45 degree angle are actually the general case and the angle presented in the EMTriangle article is a special case.

 

What I was hoping to do when posting the "EM Triangle" was to elicit aid in defining the underlying mathematical relationships of the geometric structure that produced the symmetry. The process to produce the symmetry requires one element of the right triangle be "constrained" and I choose the vertical leg for the constrained element in my example, and it will always be equal to one.

 

The "triangle" is described in more detail in the Universal.pdf article, the only change is that I used the 21.106 cm value without its 100 multiplier. The results are still "numerically" symmetrical.

universal.pdf

[Kedas]

I dont' understand, I don't see the link between time and a triangle.

 

Maybe a mathematician could help.

[FrankM]

The results of the equation set must be symmetrical to be valid. In mathperfect.pdf it was demonstrated that symmetry exists at 26.25400 deg, however, the numeric value for the speed of light is based upon the length of a second. If I make the angle fixed, say 45 degrees, the only variable is the numeric value for the speed of light. The speed of light is constant, but its numeric value can be different if the time segment is longer or shorter than the Earth second.

 

The calculated time segment that gives symmetry at 45 degrees is about 0.6256944 of an earth second, or the earth second is longer by 1.598224 than the time segment "defined" at 45 degrees. The 45 degree "constrained" triangle has other features that may be of interest to quantum/particle physicists.

 

It is my contention that the"constrained" triangle at 45 degrees represents the general case and the angle that corresponds to the earth second is a special case.

[FrankM]

I have made a few changes to the attachments in an attempt to present the concept of the post and its potential value.

universal.pdf

[FrankM]

As noted earlier, a change in one multiplier will result in the mathematical values being absolutely symmetrical. This process is described in the MathPerfect.pdf article that is attached.

mathperfect.pdf

[FrankM]

I have added a figure to illustrate how a triangle can be used to represent "time", MathPerfect04.pdf. I noticed my first attachment (EMTriangle1.pdf) on the forums server has become corrupted and I cannot even view it. MathPerfect04.pdf will be available also at,

http://www.vip.ocsnet.net/~ancient/MathPerfect04.pdf

 

The radius of the inner and outer circles essentially represent "time vectors". The outer "hydrogen circle" vector is a value that represents the equivalent to the SI second.The inner vector represents a geometric-mathematically defined "unit of time" (which gives a Larmor frequency in that unit that can be calculated to our current computational limits).

 

The following URL gives a history of how the "second" has been defined.

 

http://www.cl.cam.ac.uk/~mgk25/time/metrologia-leapsecond.pdf

 

The atomic referenced SI second is an attempt to emulate the 1/86,400th division of one revolution of an earth sized planet that has a perfect rotation. Physical scientists could define a unit of time that is independent upon any planets characteristics, and the concepts presented in Universal.pdf could be the basis for defining the time unit.

mathperfect04.pdf