FrankM

YT2095 "LESS detailed and more conscise/simple would work for me" The web pages on the following site can help you understand the principles involved in the geometric-mathematical relationship. http://www.physicsclassroom.com/Class/waves/wavestoc.html The only thing that should be added is to examine the parameters presented in Lesson 1-1 The Sinusoidal Waveform at the following site: http://www.sweethaven.com/acee/forms/coursemain.asp and proceed to the Definition for "The Sinusoidal Waveform". All the information you need to understand what is presented in the emtriangle1.pdf article is provided in the above web pages, and I can't explain it simpler.

For those that want a detailed explanation of the concept presented in this post, the universal.pdf attachment expands upon the process. universal.pdf

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

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

I have modified the attachment to reflect the 10^2 multiplier, such that the results are absolutely symmetrical. mathperfect.pdf

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.

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

The following URL presents a paper that uses a facet of the concept as the basis for establishing a natural time base. http://www.journaloftheoretics.com/Articles/4-6/makinson.pdf I have yet to find any articles on the unique triangle symmetry by any other academic or scientific institution. The shortest comment I have received was from a Professor of Electrical Engineering who responded with "interesting". Electrical Engrs. are rigorously introduced to transverse wave notation, thus the radian/wavelength relationship presented by the particular triangle isn't as strange as it appears to other scientific/mathematical disciplines.

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.

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.

Attachment added. emtriangle1.pdf

The right triangle presented in the small pdf attachment (9k) has a mathematically perfect solution for one particular angle. The use of the wavelength of the precession emission of neutral hydrogen as the wavelength multiplier is the significant feature of the geometric-mathematical relationship. I have not been able to find any literature that involved the use of the stated wavelength multiplier and wonder if any forum members have knowledge of its use elsewhere.

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