Hush : More information about the Kepler right triangle revealed part 3:
Panagiotis Stefanides fourth order equation:
http://www.stefanides.gr/Html/piquad.html
• Panagiotis Stefanides: Quadrature of circle, theoretical definition:
http://www.stefanides.gr/Html/QuadCirc.html
The square root of Phi = √φ = 1.272019649514069:
Minimal polynomial: (-1 - x2 + x4)
http://www.wolframalpha.com/input/?i=%E2%88%9A%CF%86
The square root of the square root of Phi = √√φ = 1.127838485561682.
Minimal polynomial: (-1 - x4 + x8)
http://www.wolframalpha.com/input/?i=√√φ
PLEASE CLICK ON THE RED DOTS IN THE FOLLOWING LINK TO CONFIRM THAT THE REAL VALUE OF PI = 4/√φ = 3.1446 IS NOT TRANSCENDENTAL.
THE REAL VALUE OF 𝝿 = Pi = 4/√φ = 3.144605511029693144.
https://www.wolframalpha.com/input/?i=4+divided+by+the+square+root+of+the+golden+ratio
Minimal polynomial: x4 + 16x2 – 256 = 0
https://www.wolframalpha.com/input/?i=x4+%2B+16x2+%E2%80%93+256+%3D+0
The knowledge of the square root of the Golden ratio being applicable to the diameter of a circle divided by 1 quarter of the circle's circumference can easily be verified if 2 right angles are created and the vertical right angle is used for the diameter of the circle while the horizontal right angle has 1 quarter of the circle's circumference placed on to it resulting in a Kepler right triangle with the diameter of the circle being the second longest edge length of the Kepler right triangle while the shortest edge length for the Kepler right triangle is equal in measure to 1 quarter of the circle's circumference.
The fact that the result of creating 2 perfect right angles with the vertical right angle being used as the diameter of the circle while the horizontal right angle is used as 1 quarter of the circle's circumference results in a Kepler right triangle is 100% proof that the real value of 𝝿 = Pi = 4/√φ = 3.144605511029693144.
Apply the Pythagorean theorem to al the edges of the Kepler right triangle to get the exact measure for the diameter of the circle then divide the circumference of the circle by the diameter of the circle to get 𝝿 = Pi = 4/√φ = 3.144605511029693144.
The Kepler right triangle is also featured in the Great Pyramid of Giza and also the Earth and moon ratio according to Pi as 22 divided by 7 = 3.142857142857143.
Pythagorean theorem:
https://en.wikipedia.org/wiki/Pythagorean_theorem
There's something about phi - Chapter 12 - Pythagoras theorem and the golden ratio:
https://www.youtube.com/watch?v=2IemLpxJ5SI
Kepler right triangle:
https://www.goldennumber.net/triangles/
Method for constructing a Kepler right triangle:
https://en.wikipedia.org/wiki/File:Kepler_Triangle_Construction.svg
Drawing a Kepler Triangle (Great Pyramid):
https://www.youtube.com/watch?v=vutUKmWFJ0w
constructing the kepler right triangle:
https://www.youtube.com/watch?v=LFBW9CY9PkQ
GOLDEN GEOMETRY: Draw Phi, the Golden & Kepler's Triangles, and Fibonacci's Spiral (Sacred Geometry):
https://www.youtube.com/watch?v=TCaA5nToTlg
Kepler right triangle in the Great Pyramid of Giza:
https://houseoftruth.education/en/teaching/mona-lisa/theorem-5-kepler-triangle-in-the-great-pyramid
How to Draw: Great Pyramid Triangle Using Phi and Sacred Geometry:
https://www.youtube.com/watch?v=YyxNqnIWomE
Pyramid and Squaring the circle:
http://www.dailymotion.com/video/xijbpv_pyramid-and-squaring-the-circle_tech?GK_FACEBOOK_OG_HTML5=1
The square root for the square of the Golden ratio = sqrt[sqrt(phi)] √√φ = 1.127838485561682 is the key to creating a circle and a square with the same surface area:
http://www.wolframalpha.com/input/?i=√√φ
51.82729237298776 degrees converted to arc minutes and seconds
51.82729237298776 degrees converted to arc minutes and seconds =
51° 49' 38.25254"
51 degrees, 49 minutes, 38.25254 seconds
Converting to only minutes or seconds
= 3109.63754 minutes
= 186578.25254 seconds
https://www.calculatorsoup.com/calculators/conversions/convert-decimal-degrees-to-degrees-minutes-seconds.php
48.43814254219005 degrees converted to arc minutes and seconds
48.43814254219005 degrees converted to arc minutes and seconds =
48° 26' 17.31315"
48 degrees, 26 minutes, 17.31315 seconds
Converting to only minutes or seconds
= 2906.28855 minutes
= 174377.31315 seconds.
https://www.calculatorsoup.com/calculators/conversions/convert-decimal-degrees-to-degrees-minutes-seconds.php
More information about the Kepler right triangle revealed part 4:
“Constructing a golden ratio spiral from whirling Kepler right triangles”:
If a line is divided into the Golden ratio-Phi of Cosine (36 degrees) multiplied by 2 = (φ) = (√(5) plus 1)/2 = 1.618033988749895 and that line that is divided into the Golden ratio-Phi of Cosine (36 degrees) multiplied by 2 = (φ) = (√(5) plus 1)/2 = 1.618033988749895 is used as the diameter of a semi-circle then Kepler right triangles can be formed that can help to create a spiral that is similar to a Nautilus shell and can be expanded to infinity if the point that divides the starting line into the Golden ratio-Phi of Cosine (36 degrees) multiplied by 2 = (φ) = (√(5) plus 1)/2 = 1.618033988749895 is used as the center of the Golden spiral.
The longer measure of any of the 2 right angles that make up the Golden spiral are in the ratio to each other in the square root of the Golden ratio-Phi of Cosine (36 degrees) multiplied by 2 = (φ) = (√(5) plus 1)/2 = 1.618033988749895 = √φ = 1.272019649514069.
Please remember that if the second longest edge length of a Kepler right triangle is divided by the shortest edge length of a Kepler right triangle the result is the square root of the Golden ratio-Phi of cosine (36 degrees) multiplied by 2 = 1.618033988749895 = √φ = 1.272019649514069.
Please remember also that if the hypotenuse of a Kepler right triangle is divided by the second longest edge length of a Kepler right triangle the result is also the square root of the Golden ratio-Phi Cosine (36 degrees) multiplied by 2 = (φ) = (√(5) plus 1)/2 = 1.618033988749895 = √φ = 1.272019649514069. Please remember that if the hypotenuse of a Kepler right triangle is divided by the shortest edge length of a Kepler right triangle the result is the Golden ratio-Phi of Cosine (36 degrees) multiplied by 2 = (φ) = (√(5) plus 1)/2 = 1.618033988749895.
Constructing a whirling of multiple square root of the Golden ratio = √φ = 1.272019649514069 rectangles:
A square root of Phi = √φ = 1.272019649514069 rectangle can be constructed from a Phi = Cosine (36 degrees) multiplied by 2 = (φ) = (√(5) plus 1)/2 = 1.618033988749895 rectangle if the longer edge of the Phi = cosine (36 degrees) multiplied by 2 = 1.618033988749895 rectangle is swung like an arc towards the other longer edge of the Phi rectangle thus the longer edge of the Phi rectangle becomes the diagonal of a Square root of Phi rectangle and the hypotenuse of a Kepler right triangle.
A rectangle with ratio 1: square root of Phi = √φ = 1.272019649514069 and with diagonal Phi = Cosine (36 degrees) multiplied by 2 = (φ) = (√(5) plus 1)/2 = 1.618033988749895 is a Square root of Phi rectangle.
The edges of a Square root of Phi rectangle can be divided by Phi such that the major part is another Square root of Phi rectangle and the minor part are two Square root of Phi rectangles.
This division of the square root of Phi = √φ = 1.272019649514069 rectangle divided into smaller Square root of Phi rectangles can be repeated ad infinitum (fractal) if the edges of the square root of Phi = √φ = 1.272019649514069 rectangle are enlarged in the square root of Phi = √φ = 1.272019649514069 ratio. Every division of the square root of Phi rectangle is a smaller square root of Phi rectangle and is rotated 90 degrees.
A Square root of Phi rectangle is also related to Ammann chair pattern tilings.
Diagonal division of a Square root of Phi = √φ = 1.272019649514069 rectangle makes a Kepler right triangle with the edges in geometrical progression, 1: square root of Phi = √φ = 1.272019649514069: Phi = Cosine (36 degrees) multiplied by 2 = (φ) = (√(5) plus 1)/2 = 1.618033988749895.
MOV01270.MPG P.C.STEFANIDES NAUTILUS:
https://www.youtube.com/watch?v=j0EYyWHS1Mw
Golden spiral derived from the square root of the golden ratio rectangle:
http://www.janmaris.nl/sqrphi/
Kepler right triangle information axial:
http://www.watermanpolyhedron.com/PHI.html
Logarithmic spirals and continue triangles (The Kepler right triangle and spirals):
https://www.sciencedirect.com/science/article/pii/S0377042715004562?ref=pdf_download&fr=RR-9&rr=7f40d6200af3dc6b
Google search images for Logarithmic spirals derived from both the Golden ratio and the square root of the Golden ratio for Spira Solaris:
https://www.google.com/search?client=firefox-b-d&sxsrf=AB5stBjFw1tLufPtvb6vSLcLxFZoos0WTA:1691593067819&q=spirasolaris&tbm=isch&source=lnms&sa=X&ved=2ahUKEwjio6Wf68-AAxULJ8AKHXyTCAQQ0pQJegQICxAB&biw=1438&bih=873&dpr=2
Spira solaris:
https://spirasolaris.ca/
The Ordered Distribution of Natural Numbers on the Square Root Spiral:
https://arxiv.org/pdf/0712.2184.pdf
Fermat's spiral:
https://en.wikipedia.org/wiki/Fermat%27s_spiral