1-My 236th book Proof that Light Waves are cycloid waves, not sinusoid and not semicircle. by Archimedes Plutonium 12m views

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Archimedes Plutonium
Mar 30, 2023, 1:09:16 AM (23 hours ago)
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236th book Proof that Light Waves are cycloid waves, not sinusoid and not semicircle.

by Archimedes Plutonium



But now I uncovered significant math-physics science in able to make closed loop functions-- circle, coil, spiral all represented as functions. Let that be my 235th book of Science.

While making closed loops be functions of math, valid functions that do not upset the restriction of Perpendicular that results in two or more y-values for a give x-value, while running into that construction of closed loops be functions, I come upon an
old problem of mine-- is the Cycloid wave the true wave of Light and not the sinusoid nor semicircle.

So let my 236th book of Science be a proof that Light Waves are Cycloid waves, not sinusoid nor semicircle. Where sinusoid and semicircle are up and down waves, and have to cover too much distance while a cycloid wave gets to a location the fastest. The
speed of light is the fastest possible speed in the world, and hence, it would not travel a path that takes more distance than a path that is a wave and covers the least distance to get to a end point. The Least Action principle along with tenets of
speed of light, force the Light Wave to be cycloid. Here-in I offer a proof that Light Waves are cycloid waves.

AP
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Archimedes Plutonium
Mar 30, 2023, 1:23:43 AM (23 hours ago)
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Here are some graphs of periodic functions and we want to show students these graphs so that they do not mistake sine and cosine as sinusoid waves but are cycloid waves. Take a look at animations of a cycloid on Wikipedia.

This below first picture is the sine cycloid wave

semicircle cycloid
1. . . . . . . . . . x . . . . . . . . . . . . . . .
.9 . . . . . x . . . . . . . x . . . . . . . . . . .
.8 . . . x . . . . . . . . . . . x . . . . . . . x .
.7 . . . . . . . . . . . . . . . . . . . . . . . . .
.6 . x . . . . . . . . . . . . . . . x . . . x . . .
.5 . . . . . . . . . . . . . . . . . . . . . . . . .
.4 x . . . . . . . . . . . . . . . . . x . x . . . .
.3 . . . . . . . . . . . . . . . . . . . . . . . . .
.2 . . . . . . . . . . . . . . . . . . . . . . . . .
.1 . . . . . . . . . . . . . . . . . . . . . . . . .
0 x . . . . . . . . . . . . . . . . . . . x . . . . .
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 x-axis -->

This is the cosine cycloid wave


semicircle cycloid
1. x . . . . . . . . . . . . . . . . . . . x . . . . .
.9 . . . . x . . . . . . . . . . . x . . . . . . . x .
.8 . . . . . . x . . . . . . . x . . . . . . . . . . .
.7 . . . . . . . . . . . . . . . . . . . . . . . . . .
.6 . . . . . . . . x . . . x . . . . . . . . . . . . .
.5 . . . . . . . . . . . . . . . . . . . . . . . . . .
.4 . . . . . . . . . x . x . . . . . . . . . . . . . .
.3 . . . . . . . . . . . . . . . . . . . . . . . . . .
.2 . . . . . . . . . . . . . . . . . . . . . . . . . .
.1 . . . . . . . . . . . . . . . . . . . . . . . . . .
0 . . . . . . . . . . x . . . . . . . . . . . . . . .
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 x-axis -->


quartercircle centered on (1,0), draw with compass
x y angle in degrees
0 0 0
.1 .42 6
.2 .58 11
.3 .70 17
.4 .79 22
.5 .86 27
.6 .92 31
.7 .95 35
.8 .97 39
.9 .99 42
1 1 45

1.1 .99 48
1.2 .97 51
1.3 .95 55
1.4 .92 59
1.5 .86 63
1.6 .79 68
1.7 .70 73
1.8 .58 79
1.9 .42 84
2.0 0 90
2.1 .42 6
2.2 .58 11

Remember, in the above those starting numbers like .4, means 10 unit squares long and 4 unit squares high for tangent with protractor angle of 22degrees. All angles come from how many unit squares long by unit squares high and a protractor that measures
the angle degree.

Well, in New Math, we throw out altogether, all trig functions. Because in New Math, all functions are polynomials. We have no trigonometry functions in New Math. We do have periodic functions in math. Periodic functions repeat an "image of themselves"
over and over again.

The graph of the semicircle cosine cycloid repeats itself over and over again. The graph of cosine was a semicircle cycloid displaced by a length of 1 from the semicircle sine cycloid. Both are the same thing, only displaced by a distance of 1 unit. This
is where the complament angles of the Right Triangle switches as it goes from 0 degrees to 45degrees and switches at 45 degrees.

We have the same right triangle and instead of focusing on 6degrees we focus on the dual angle 84 degrees, instead of 11 degrees the dual angle of 79 degrees is focused upon. Notice the two dual angles add up to 90 degrees.

The angle 6 degrees is 1/10

The angle 11 degrees is 2/10

The angle 17 degrees is 3/10

The angle 22 degrees is 4/10

Their duals are

The angle 84 degrees is 1/10

The angle 79 degrees is 2/10

The angle 73 degrees is 3/10

The angle 68 degrees is 4/10

The graphing of tangent would also be a Semicircle-Cycloid.


semicircle cycloid
sine portion cosine portion sine portion
1. . . . . . . . . . x . . . . . . . . . . . . . . .
.9 . . . . . x . . . . . . . x . . . . . . . . . . .
.8 . . . x . . . . . . . . . . . x . . . . . . . x .
.7 . . . . . . . . . . . . . . . . . . . . . . . . .
.6 . x . . . . . . . . . . . . . . . x . . . x . . .
.5 . . . . . . . . . . . . . . . . . . . . . . . . .
.4 x . . . . . . . . . . . . . . . . . x . x . . . .
.3 . . . . . . . . . . . . . . . . . . . . . . . . .
.2 . . . . . . . . . . . . . . . . . . . . . . . . .
.1 . . . . . . . . . . . . . . . . . . . . . . . . .
0 x . . . . . . . . . . . . . . . . . . . x . . . . .
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 x-axis -->

The semicircle-cycloid is a sine alternating with cosine. The above semicircle cycloid cannot be a sine alone nor a cosine alone graph, but has to be both together, as duals to make a graph possible, for it is that switching off in the right triangle
that spins inside the unit circle, the 45 degree angle where they must switch off the angle.
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Archimedes Plutonium
Mar 30, 2023, 1:35:09 AM (22 hours ago)
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Now the proof I am going to offer that the Light Wave is a cycloid wave, is the idea that the cycloid wave gets to a destination point covering the least amount of distance.

Here we see the semicircle wave and the sinusoid wave (a fictional wave created when one axis is not equal to the other axis) Wavelength is longer than the wavelength of a cycloid wave.

So say we start at 0 on the x-axis and send a semicircle wave to the point 3 on x-axis. So we need a full wavelength of an up and down ^v to get from 0 to 3.

For the sinusoid, the same picture of a up and down full wavelength ^v to get from 0 to 3.

For the cycloid wave, it is all ups and no downs so it is just one ^ to get from 0 to 3.

In this sense, the cycloid wave is the wave nearest to being like a direct straightline segment from 0 to 3. While semicircle and sinusoid have that extra down portion to takes too much more distance length to get from 0 to 3.

AP
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Archimedes Plutonium
Mar 30, 2023, 1:40:32 AM (22 hours ago)
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In this sense, the cycloid wave is the wave nearest to being like a direct straightline segment from 0 to 3. While semicircle and sinusoid have that extra down portion which takes much more distance length to get from 0 to 3. This extra distance is
called arclength traveling distance. Apparently the cycloid wave is the least arclength wave to get from point A to point B. And it is this shortest distance arclength that the cycloid wave possesses that is evidence in proof the Light Wave is cycloid.

AP
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Archimedes Plutonium
Mar 30, 2023, 1:51:32 AM (22 hours ago)
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Now there is another parameter of waves that is seldom mentioned. It is called the Wave Height. It is double the amplitude. The most used parameter is the wavelength-- from one crest to the next crest.

But one line of evidence in proof that the Light Wave is cycloid and not the up and down semicircle or sinusoid. One line of evidence is that light experiments point to a Wave Height as being 1/2 of what is measured from that of theory.

In other words, in experiments, the Wave Height favors light being a cycloid wave.

AP
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Archimedes Plutonium
Mar 30, 2023, 2:39:08 AM (21 hours ago)
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Alright speaking of anomalies in Light Wave Height -- pointing to the idea that Light Waves are cycloid waves not the up and down waves Old Physics believes in.


--- quoting Anomalies in Light Scattering, Alex Krasnok, Denis Baranov, et al ---

1.5 Q-factor
In scattering problems, QNMs of a system manifest themselves as resonant enhancement of scattering/extinction cross-section, reflection/transmission coefficients, etc. at real frequencies. Since the energy leaks out from the scatterer and gets dissipated,
each specific quasinormal mode
l is characterized by a complex frequency l  Re[l ]  i Im[l ] , with the position at the real axis
Re[l] andafinitelifetimel 1/l 1/Im[l],where l isthedecayrateanddeterminesthe
resonance linewidth at its half-maximum[54]. A resonance is usually described by quality (Q) factor, which is defined as
Re[ ]
Q l . (18)
2 Im[l ]
Factor 2 occurs in the denominator because the energy decays with the decay rate 2 . In general,
the cavity decay rate includes both radiative and absorptive parts    rad   loss , such that the
quality factor can be expresse