The Brachistochrone & Snell's Law & & Catenary & Cycloid
https://docs.google.com/document/d/1Cq0t0Hfm6eOlzfCbmeLHwixlRa2Gyj3pW1xsseVw4hI/

https://www.mathcurve.com/surfaces/catenoid/catenoid.shtml

https://www.mathcurve.com/courbes2d/chainette/chainette.shtml

Volume * Pressure = Joules

(Area of Catenary)^2 * (Radians per Second) = Volume

Volume * Pressure = Joules

Joules / c = Momentum = Catenary = 6.5248935

(Planck Energy / c) = Momentum = Catenary = 6.5248935

https://www.mathcurve.com/courbes2d/chainette/voilechainette.gif

https://www.mathcurve.com/surfaces/catenoid/chainettecatenoide.GIF

https://www.mathcurve.com/surfaces/catenoid/catenoidloxo.JPG

https://www.mathcurve.com/surfaces/catenoid/catenoid2helicoid.gif

Cycloid Catenary Curve = 1.03846153846 Faster

https://photos.app.goo.gl/LB6w6urXpnq91BPd9

http://www.etudes.ru/data/etudes/cycloid/25.jpg

https://upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Isochronous_cycloidal_pendula.gif/220px-Isochronous_cycloidal_pendula.gif

(27 * pi) / 13 = 6.52484628053

((6.524846280532647495268567026811275/4)/(2pi/4)-1)*26 = 1

1 / (((6.524846280532647495268567026811275 / 4) / ((2pi) / 4)) - 1) = 26

(((6.524846280532647495268567026811275 / 4) / ((2pi) / 4)) - 1) * 27 = 1.03846153846

(((6.524846280532647495268567026811275 / 4) / ((2pi) / 4)) - 1) * 27 * (2 * pi) = 6.52484628053

hbar/planck length/2pi = 1.03846153846

(27 / 13) / 2 = 1.03846153846

(27 / 13) * pi = 6.52484628053

3^3/(3^3-1)*2pi/(hbar/planck length) = 0.999992764

((4pi * (1.5^3)) / ((4pi * (1.5^3)) - ((4pi) * (0.5^3)))) / ((hbar / planck length) / (2pi)) = 0.999992764

https://photos.app.goo.gl/sfrZJ14iZN4t9LdE8

The Brachistochrone & Snell's Law & & Catenary & Cycloid

https://youtu.be/Cld0p3a43fU?t=476

https://www.youtube.com/watch?v=Cld0p3a43fU&list=PLcZ1XhcAT8NQiruqoITCj21h0k_3v-VKg

Mass of String = hbar / planck length / c

(54870469331 * 2pi/1150 ) = 299792457.999

54870469331 is a prime 23 is Prime 23*50 = 1150

(54870469331 * pi) / (23 * (5^2)) = 299792457.999

https://www.mathcurve.com/surfaces/helicoidminimal/catenoid2helicoid.gif

9:00 …. 99 & 51 = Catenary
https://www.youtube.com/watch?v=qhbuKbxJsk8&t=540s

200 /(51-1) = 4 or 90 degrees

https://www.mathcurve.com/surfaces/catenoid/catenoidloxo.JPG

https://photos.app.goo.gl/gt1nc27otRRXu4iF9

https://www.mathcurve.com/surfaces/catenoid/catenoid.shtml

Varied Wavelengths all travel at the speed of light
Wavelength is “Pascals”

Photon = ...... https://www.wolframalpha.com/input/?i=(e%2F4+*+cos(x)+*+phi)

(hbar/Planck length) = 6.52484628053

3pi/6.52484628053 = 1.444444444444444

(27pi) / 13 = 6.52484628053

Narrowing in on how the cycloid is combined with the Fine Structure constant

(13.8880509 billion light years * 0.5pi)*(160.790955 Ghz CMBR)/c^5 = 1.37035999e-5 s^4 / m^4

((((13.8880509 billion light years) * (0.5pi)) * (160.790955 Ghz CMBR)) / (c^4)) / 137.035999 = 29.9792458

((acoustic ohms)/( ohms))^0.5 = Coulombs/meter^3

((((planck length / hbar)^2) / hbar) / (0.5pi)) / ((((13 / (27pi))^2) / hbar) / (0.5pi)) = 0.999985527 m^-2 kg^-2 s^2

(((planck length / hbar)^2) / hbar) / (0.5pi) = 1.41793759e+32 m^-4 kg^-3 s^3

(((13 / (27pi))^2) / hbar) / (0.5pi) = 1.41795811e+32 m^-2 kg^-1 s

Planck temperature nist Value 1.416808e+32 K

1.41795811e+32 / 1.416808e+32 = 1.00081176137

(c / ((1.41796837e32 kelvin) / (13.8880509 billion light years))) / (((27pi) / 13)^3) = 1

https://physics.nist.gov/cgi-bin/cuu/Value?plktmp

((hbar / planck length) * c) / Boltzmann constant = 1.41680799e+32

((((26^2) / (27^2)) / (pi^3)) / 2) / hbar = 1.41795811e+32 = https://youtu.be/Vroq9ZH_YBY

(((27pi) / 13) * 299792458) / (((((26^2) / (27^2)) / (pi^3)) / 2) / hbar) = 1.37951869e-23 Boltzmann’s

(0.5pi*299792458)/((13/pi/3^3)^3/hbar) = (1.37951869e-23) Boltzmann’s Constant

(Nist Boltzmann constant) / ((0.5pi * 299792458) / ((((13 / pi) / (3^3))^3) / hbar)) = 1.00081901

(0.5pi*299792458)/((13/pi/3^3)^4/planck length/m) = (1.379508703e-23)

1.379508703e-23 / Boltzmann constant = 0.999174434

https://youtu.be/Vroq9ZH_YBY

(((((2^(3 / 2)) * ((27pi) / 13))^0.25) / Boltzmann constant) * planck length) / 2.4263102367e-12 = 1.0000048

On Sunday, October 31, 2021 at 8:21:13 AM UTC-7, David (Kronos Prime) Fuller wrote:
> The Brachistochrone & Snell's Law & & Catenary & Cycloid
> https://docs.google.com/document/d/1Cq0t0Hfm6eOlzfCbmeLHwixlRa2Gyj3pW1xsseVw4hI/
>
> https://www.mathcurve.com/surfaces/catenoid/catenoid.shtml
>
> https://www.mathcurve.com/courbes2d/chainette/chainette.shtml
>
>
> Volume * Pressure = Joules
>
>
> (Area of Catenary)^2 * (Radians per Second) = Volume
>
>
> Volume * Pressure = Joules
>
> Joules / c = Momentum = Catenary = 6.5248935
>
> (Planck Energy / c) = Momentum = Catenary = 6.5248935
>
>
>
> https://www.mathcurve.com/courbes2d/chainette/voilechainette.gif
>
> https://www.mathcurve.com/surfaces/catenoid/chainettecatenoide.GIF
>
> https://www.mathcurve.com/surfaces/catenoid/catenoidloxo.JPG
>
> https://www.mathcurve.com/surfaces/catenoid/catenoid2helicoid.gif
>
>
> Cycloid Catenary Curve = 1.03846153846 Faster
>
> https://photos.app.goo.gl/LB6w6urXpnq91BPd9
>
> http://www.etudes.ru/data/etudes/cycloid/25.jpg
>
> https://upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Isochronous_cycloidal_pendula.gif/220px-Isochronous_cycloidal_pendula.gif
>
>
> (27 * pi) / 13 = 6.52484628053
>
> ((6.524846280532647495268567026811275/4)/(2pi/4)-1)*26 = 1
>
> 1 / (((6.524846280532647495268567026811275 / 4) / ((2pi) / 4)) - 1) = 26
>
> (((6.524846280532647495268567026811275 / 4) / ((2pi) / 4)) - 1) * 27 = 1.03846153846
>
> (((6.524846280532647495268567026811275 / 4) / ((2pi) / 4)) - 1) * 27 * (2 * pi) = 6.52484628053
>
>
> hbar/planck length/2pi = 1.03846153846
>
> (27 / 13) / 2 = 1.03846153846
>
> (27 / 13) * pi = 6.52484628053
>
> 3^3/(3^3-1)*2pi/(hbar/planck length) = 0.999992764
>
> ((4pi * (1.5^3)) / ((4pi * (1.5^3)) - ((4pi) * (0.5^3)))) / ((hbar / planck length) / (2pi)) = 0.999992764
>
>
> https://photos.app.goo.gl/sfrZJ14iZN4t9LdE8
>
>
> The Brachistochrone & Snell's Law & & Catenary & Cycloid
>
> https://youtu.be/Cld0p3a43fU?t=476
>
>
> https://www.youtube.com/watch?v=Cld0p3a43fU&list=PLcZ1XhcAT8NQiruqoITCj21h0k_3v-VKg
>
> Mass of String = hbar / planck length / c
>
> (54870469331 * 2pi/1150 ) = 299792457.999
>
> 54870469331 is a prime 23 is Prime 23*50 = 1150
>
> (54870469331 * pi) / (23 * (5^2)) = 299792457.999
>
>
> https://www.mathcurve.com/surfaces/helicoidminimal/catenoid2helicoid.gif
>
>
>
> 9:00 …. 99 & 51 = Catenary
> https://www.youtube.com/watch?v=qhbuKbxJsk8&t=540s
>
> 200 /(51-1) = 4 or 90 degrees
>
> https://www.mathcurve.com/surfaces/catenoid/catenoidloxo.JPG
>
> https://photos.app.goo.gl/gt1nc27otRRXu4iF9
>
> https://www.mathcurve.com/surfaces/catenoid/catenoid.shtml
>
>
> Varied Wavelengths all travel at the speed of light
> Wavelength is “Pascals”
>
>
>
> Photon = ...... https://www.wolframalpha.com/input/?i=(e%2F4+*+cos(x)+*+phi)
>
> (hbar/Planck length) = 6.52484628053
>
> 3pi/6.52484628053 = 1.444444444444444
>
> (27pi) / 13 = 6.52484628053
>
>
>
>
>
> Narrowing in on how the cycloid is combined with the Fine Structure constant
>
> (13.8880509 billion light years * 0.5pi)*(160.790955 Ghz CMBR)/c^5 = 1.37035999e-5 s^4 / m^4
>
> ((((13.8880509 billion light years) * (0.5pi)) * (160.790955 Ghz CMBR)) / (c^4)) / 137.035999 = 29.9792458
>
> ((acoustic ohms)/( ohms))^0.5 = Coulombs/meter^3
>
> ((((planck length / hbar)^2) / hbar) / (0.5pi)) / ((((13 / (27pi))^2) / hbar) / (0.5pi)) = 0.999985527 m^-2 kg^-2 s^2
>
> (((planck length / hbar)^2) / hbar) / (0.5pi) = 1.41793759e+32 m^-4 kg^-3 s^3
>
> (((13 / (27pi))^2) / hbar) / (0.5pi) = 1.41795811e+32 m^-2 kg^-1 s
>
> Planck temperature nist Value 1.416808e+32 K
>
> 1.41795811e+32 / 1.416808e+32 = 1.00081176137
>
> (c / ((1.41796837e32 kelvin) / (13.8880509 billion light years))) / (((27pi) / 13)^3) = 1
>
> https://physics.nist.gov/cgi-bin/cuu/Value?plktmp
>
> ((hbar / planck length) * c) / Boltzmann constant = 1.41680799e+32
>
> ((((26^2) / (27^2)) / (pi^3)) / 2) / hbar = 1.41795811e+32 = https://youtu.be/Vroq9ZH_YBY
>
> (((27pi) / 13) * 299792458) / (((((26^2) / (27^2)) / (pi^3)) / 2) / hbar) = 1.37951869e-23 Boltzmann’s
>
> (0.5pi*299792458)/((13/pi/3^3)^3/hbar) = (1.37951869e-23) Boltzmann’s Constant
>
> (Nist Boltzmann constant) / ((0.5pi * 299792458) / ((((13 / pi) / (3^3))^3) / hbar)) = 1.00081901
>
> (0.5pi*299792458)/((13/pi/3^3)^4/planck length/m) = (1.379508703e-23)
>
> 1.379508703e-23 / Boltzmann constant = 0.999174434
>
> https://youtu.be/Vroq9ZH_YBY
>
>
> (((((2^(3 / 2)) * ((27pi) / 13))^0.25) / Boltzmann constant) * planck length) / 2.4263102367e-12 = 1.0000048

The catenary's a great curve because it's the shape of the
hanging line, i.e. that shape that if a given line was flexible
then between two points it hangs catenary.

Then, having that under inverse squared, is here basically
"_if_ there was a central moment that this inverse square
was pulled out to a corner", ..., "it would fall catenary".

Or, that's a physical interpretations.

Many the physical interpretations are of couse the most usual
sorts of physical laws, then that the higher or "more theoretic"
interpretations have those laws, but some symmetry of them reversed,
"in the interpretation": for example some result that was least
or not flexible, that fell catenary.