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Understanding the Rbtx Quadronometric method of Quadrangles ...

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Question by Rbtx
Submitted on 12/27/2005
Related FAQ: sci.physics.relativity Welcome - read this first!
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Understanding the Rbtx Quadronometric method of Quadrangles
by Robt. W. Brown

A Quadrangle is a 4-sided linear structure. One side is parallel to the X axis. One side is parallel
to the Y axis. One side is parallel to the Z axis. The structure is then completed by the Hypoteny.

Hypoteny= [sqrt](X^2 + Y^2 + Z^2)

Golden Quadrangle Rule:  If X,Y or Z equals zero an 'implied quadrangle' can still be present.
This implication will only disappear when all three distances equal zero.

Where T= time ....and......V= velocity of signal/object,  we fully understand these trigonometric related physics equations:

TV = Hypotenuse
TV*cosine-angle = X ................
TV * sine-angle = Y
***********
We also have this covert definition of a Hypotenuse:
TV * [sqrt] (cos^2 + sin^2)= Hypotenuse

In Quadronometrics, we must understand some, new but similiar statements.
Now recalling these 3 Quadronometric definitions:

hypoteny= [sqrt] (X^2 + Y^2 + Z^2)..........definition 1
coziny = X / hypoteny..................................defintion 2
ziny = [sqrt](Y^2 + Z^2) / Hypoteny...........definition 3

X= TV * coziny-of-angle ......................definition A
Y = [sqrt]{(TV * ziny)^2 - Z^2}..............definition B
Z= [sqrt]{(TV* ziny)^2 - Y^2}................definition C

It is also easy to see that:
TV = hypoteny
So we can sub into the following equation:
ziny = [sqrt](Y^2 + Z^2) / hypoteny
ziny = [sqrt](Y^2 + Z^2) / TV
Therefore:
TV* ziny-angle = [sqrt](Y^2 + Z^2)
**********
Now in regard to Quadrangles that are 'light created' we can always
assume (in any frame of reference) that Velocity of light per sec. = 1c

Then we can sub in for Velocity where V = c ....

X= TV * coziny-of-angle
X= Tc * coziny-of-angle ...................special definition 4
then:
Y = [sqrt]{(Tc * ziny)^2 - Z^2}..........special definiton. 5
Z= [sqrt]{(Tc* ziny)^2 - Y^2}............special definition 6
Finally we also have the implied complex definition of the Hypoteny:
Hypoteny = Tc* [sqrt] (coz^2 + zin^2).......s. defintion 7

Anyone that knows 'special relativity' will readily agree that definition 4,5
and 6 will most likely be generally true in 'special relativity'.

Now I am going to make a 'radical statement' that will astound even the most
open minded. All of the above definitions of Quadrangles and Quadronometrics
are also TRUE, in the physics created by the Rbtx-galilean transform which I have recently proposed!

Part #2 : +++++++++++++++++++++++++++++++++++++++++

Now recalling these 3 Quadronometric definitions:

hypoteny= [sqrt] (X^2 + Y^2 + Z^2)
coziny = X / Hypoteny
ziny = [sqrt](Y^2 + Z^2) / Hypoteny

****************************
If we apply Quadronometrics to Light related Quadrangles, let's assume we are
measuring 'light velocity' in a standard format of relativity. Let's next suppose that
we have determined an Einsteinian Quadrangle in the 'motion frame' to have these dimensions:

X= 1.3938464c...................................Table 1
Y= .5c
Z= .5c

Hypoteny=  [sqrt](1.3938464c^2 + .5c^2 + .5c^2)
Hypoteny = [sqrt] 2.4428077c^2
H= 1.5629484c

Since we are measuring light speed as it travels along the 'Hypoteny' we can assume then:
T= 1.562948 sec.

Because:

H/T = velocity of light
1.5629484c/1.5629484 sec = 1c per sec.

Meaning:  distance/time = velocity!

Now let's determine the related Ziny and Coziny according to the Quadronometric definitions:

Coziny = X distance / Hypoteny

Coz = 1.3938464c/ 1.5629484c = .8918057
Coziny= .8918057  

Ziny = {[sqrt](Y^2 + Z^2)} / Hypoteny
Ziny = {[sqrt](.5c^2 + .5c^2)}/ Hypoteny
Ziny=  .7071067c / Hypoteny
Ziny = .7071067c / 1.5629484c
Ziny= .4524184

Now returning to these Basic Quadronometric relationships:

X=TV * coziny-angle  .......................definition A
or:
X= 1.5629484 sec. * 1c * coz
X= 1.5629484 sec. * 1c * .8918057
X= 1.3938464c....................CORRECT

Then we test this second relationship of ziny and Light Quadrangles:

TV* ziny=.......................... = [sqrt](Y^2 + Z^2)
1.5629484 * 1c* .3199081 = [sqrt](.5c^2 + .5c^2)
.5c =................................... = .5c ..............proven!

Then the third basic Quadronometric relationships is:
Hypoteny = TV* [sqrt] (coz^2 + zin^2).............(definition 7)
Hypoteny = 1.5629484* 1c * [sqrt](.8918057^2 + .4524184^2)
Hypoteny = 1.5629484* 1c * [sqrt] 1
Hypoteny = 1.5629484c   .......................correct

These calculations may seem rather basic, but now let's consider this table of
Galilean Distances, which relate to the above Einsteinian distances:

x= 1.2071067c ................................table 2
y= .5c
z= .5c
t= 1.3989662 sec'...............consider this a 'projected anwer only'.
We see that the only difference in Table 2 as compared to Table 1 is in distance X & x:

X= 1.3938464c  
x= 1.2071067c .........
x = / = X

This "gamma difference" is reflective of the difference in the Lorentz & the Galilean definitions of the coordinate X:

where [gamma]= 1.1547004:

X = [gamma](X'- VT')
x= X' - VT'

therefore:  
X/x = [gamma] = 1.1547004

While the definitions of the Y and Z coordinates are the SAME in both transforms so:

Y=y  and Z=z

Next we look at the Quadronometric factors of the Galilean related Quadrangle:

hypoteny = [sqrt](X^2 + Y^2 + Z^2)
h = [sqrt](1.2071067c^2 + .5c^2 + .5c^2)
h = [sqrt] 1.9571065c^2
h= 1.3989662c.................................galilean hypoteny

Now to arrive at the galilean coziny:

coziny = x / hypoteny
coz = 1.2071067c / 1.3989662c
coz= .8628562.............................galilean coziny

Now to arrive at the galilean ziny:

Ziny = {[sqrt](y^2 + z^2)} / hypoteny
ziny= {[sqrt](.5c^2 + .5c^2)} / hypoteny
Ziny = {[sqrt](.5c^2)} / hypoteny
Ziny = .7071067c / 1.3989662c
Ziny = .5054494..........................galilean ziny
**************

Now knowing that the Galilean hypoteny is:

h=1.3989662c

If we know that light velocity also measures an invariant 1c per sec'  along the Galilean hypoteny we must have this related interval of time:
t= 1.3989662 sec'
since:
hypoteny / t = 1c per sec. ...........the velocity of light
1.3989662c / 1.3989662 sec' = 1c per sec'.................

Then the following previously-stated equation can also be true in Rbtx-galilean physic!

x= tV * coziny .......................definition #A

Then if we rearrange the equation:

x= coziny * V * t
t= x/coz*V ................................time interval equation !

We then have arrived at a general 'time interval equation' that can be applied to both einsteinian physics AND  Rbtx math soon to be called 'Galitivity physics'.

Testing the time-interval equation:
t= 1.2071067c / .8628562c ................Rbtx-galilean
t= 1.3989662 .....................................correcto!

Testing the time-interval equation:
t= 1.3938464c / .8918057c ................Rbtx-galilean
t= 1.5629484.....................................correcto

Contrary to Mr. Michaeld's attempt to cast doubt on the Rbtx-galilean transform which I recently posted/published on MMB, under the title "The New Quadronometric System" (under the theoretical link)I promise that the time interval given in Table 2 can be actually derived through the Rbtx Coordinate Transform! (t'= 1.3989662 sec')
Which means that all the relationships given above are not based on conjecture but instead on mathematical evidence.

It can be argued that the 'time interval' has been manipulated to 'fill a need'...but on the other side of the issue, it can also be argued that the 'time interval above' is a result of the related 'quadronometric factors' and their constant relationships!
R.Brown/ emusicka@yahoo.com...*****************


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