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elementary geometry astronomy golden ratio geography

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#1 PleiadianGeography

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Posted 15 February 2020 - 01:59 PM

.. so I picked math, because it is about math. 

 

Hi all!

 

I bring here to all of you some, so far unknown, results of the 20 yrs research on geography, astronomy, history (...) embeded in geometry.

 

Few tips:

 

- there is a mathematical relation between geography, geomorphology, astronomy, distribution of urban and sacral infrastructure, myths, historical events, anatomy... 

 

- there is a simple geometrical procedure (within 15 steps) of constructing geometrical matrix that resembles relative positions of 9 brightest stars (Alcyone, Electra, Caleano, Taygeta, Sterope, Maya, Merope, Pleione and Atlas) in M45 cluster (Pleiades, Seven sisters, Subaru..), as it is seen from the Earth.

 ATINER 07 03g Slika 17 Vlasici i geometrija,  DuAstro.jpg

 

 

-when applied and developed on Earth this matrix with its elements re-create completely meaningful image of geomorphological cardinality:  "randomly" distributed coast lines, capes, mountain peaks, bays and straits, river deltas (mouth), in other words - present geomorphological situation.

 

- distribution of urban (ports, cities, ..), and sacral infrastructure (chruches, temples, sanctuaries, cults, tombs, pyramids...), toponimy, myths and legends, historical events and other appearances generated by human activity since first known civilizations, obeys this mathematical model.

 

the research and application of the model includes the Mediterranean and its gravitating mainland, West , South and Central Europe, North Africa, the Asia Minor and the Arabian Peninsula, as well as the maritime cultures of two important seas - the Black Sea and the Sea of Azov. 

 

- the model is functionally tuned to the distances between coasts, on the principle of toolbox technologically closest to the “portolan” era (13th -15th century). All analyses were conducted on maps in Mercator's flat cylindrical projection.

 

-...

 

 

Few examples:

 

- between the parallel of Monfalcone, the northernmost point of the Adriatic (as well as the Mediterranean basin), and the parallel of the southernmost point of the Mediterranean Sea in the Gulf of Sidra at Al Uqaylah in Libya, the golden ratio is the parallel of the easternmost point of the Mediterranean Sea, the city of Iskenderun in Turkey 

National geografic Monfalcone Iskenderun Agheila.jpg

 

3 720 km east of the Strait of Gibraltar, there is Mount Aqra (36° N, 36° E), a holy mountain on the Middle Eastern coast, on the border of Turkey and Syria. The parallel of the very top of Aqra (35°57' N) bisects the Strait of Gibraltar. If we place the line on the position of Aqra, at an angle of α with respect to parallel, directed northwest, this line will reveal Troy in Asia Minor, the peninsula Ljuba (Croatia) and French cities of Troyes and Paris. The prehistoric site of Ljuba is situated on the meridian of 15°18' E, which is also the meridian of the Italian city of Troia. Ljuba is half the distance from Troy to Troyes, and at the same time, the golden ratio from the mountain Aqra to Paris. Same distance is measured from strait of Gibraltar to Ljuba, and from Ljuba to Aqra. On the meridian of  Ljuba, from its position to the Libyan coast, the golden ratio is on the parallel of the Troy in Asia Minor. Between the Meridian of Troy to Atlantic Moroccan Coast at Agadir, the golden ratio is the Meridian of  Troyes

National geografic Troyan Eponimy Matrix.jpg

 

Ljuba (croat. Love) is located at the parallel 44°17' N, which is also parallel of the very top of the mountain Vlašić in BiH (Bosnia and Hercegovina), while the west side of Ljuba peninsula is faced with the easternmost cove of the island of Pag, called Vlašići (croat. Pleiades, jap. Subaru, M45 cluster). 

 

-...and this is the moment where Pleiades enters the game :)

 

 

Few thoughts and welcome word:

 

- this topic could be equally posted in forums such as astronomy, history, archeology, biology, computational science, etc..., because it entangles in all of these disciplines, directly or otherwise.

 

- brief insight to the model, basic definitions, mathematical development of M45 geometrical matrix with its applications, available at:

https://www.atiner.g...EO2019-0139.pdf

 

- this is work in progress, model is still under re-construction, anyone can test it, develop it further, contribute from any scientific aspect or disciplineInterdisciplinary, natural science, philosophical and theosophical approach is proposed, in order to provide a critical review of this work.

 

I wish happy journey to those eager something different, new, but same old - from Euclidus onwards. 

 

... and, of course, Q&A very welcome here..

 

Cheers!

 

:)


Edited by PleiadianGeography, 16 February 2020 - 10:16 AM.


#2 PleiadianGeography

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Posted 02 May 2020 - 08:50 AM

new video related the topic

 

https://www.youtube....ZZnEC1VgxdRlkJf



#3 GAHD

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Posted 02 May 2020 - 01:29 PM

.. so I picked math, because it is about math. 

 

...

 

- brief insight to the model, basic definitions, mathematical development of M45 geometrical matrix with its applications, available at:


 

:)

You should put the actual math here if you want to claim you're here for the math. Lots of people are too lazy to click your link after reading through a long ramble that has no math in it.

 


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#4 PleiadianGeography

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Posted 02 May 2020 - 03:11 PM

You should put the actual math here if you want to claim you're here for the math. Lots of people are too lazy to click your link after reading through a long ramble that has no math in it.

 

You are right...long ramble...

 

Is it possible to construct 45°/φ angle by classical constructionruler-and-compass construction, whereas φ = (√5 + 1)/2 is golden ratio coefficient?

 

Meanwhile, have a look what's going on links provided earlier :)
 



#5 GAHD

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Posted 02 May 2020 - 05:29 PM

You are right...long ramble...

 

Is it possible to construct 45°/φ angle by classical constructionruler-and-compass construction, whereas φ = (√5 + 1)/2 is golden ratio coefficient?

 

Meanwhile, have a look what's going on links provided earlier :)
 

I don't follow the question in relation to the context... By classical I assume you mean Euclidean, correct? I suppose "if you had a big enough ruler" you could take an irrational number "close enough" to reality.

That in itself makes me raise an eyebrow regarding your map images, since euclidean geometry breaks down on global scales(and flat maps are NOT accurate for straight lines). It's a big reason I pointed out you should copy and paste the actual math you want to discuss away from whatever postscript document and into this thread proper. Particularly:

  1. The exact equation you're using to calculate "relation between geography, geomorphology, astronomy, distribution of urban and sacral infrastructure, myths, historical events, anatomy..."
  2. The exact "simple geometrical procedure (within 15 steps) of constructing geometrical matrix that resembles relative positions of 9 brightest stars"

 

I mean, I can do a simple Det vs Shark attacks, date, and ice creme sales. On it's own that calc would seem to indicate that Ice creme in summer makes sharks bite humans...



#6 PleiadianGeography

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Posted 03 May 2020 - 01:15 AM

I don't follow the question in relation to the context... By classical I assume you mean Euclidean, correct? 

 

Euclidean, right, with "big enough ruler".. If we can construct √5, hence φ = (√5 + 1)/2,..., I wonder is it possible to construct 45°/φ, or any angle divided by φ?

 

 



#7 PleiadianGeography

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Posted 03 May 2020 - 02:44 AM

  1. The exact equation you're using to calculate "relation between geography, geomorphology, astronomy, distribution of urban and sacral infrastructure, myths, historical events, anatomy..."
  2. The exact "simple geometrical procedure (within 15 steps) of constructing geometrical matrix that resembles relative positions of 9 brightest stars

1. equation :)... this is the equation φ = (√5 + 1)/2 

 

2. From the origin of the Cartesian coordinate plane, we draw a circle K of arbitrary radius r. The centre of the circle at the origin is denoted by B.

On negative part of Y-axis, we denote the point Z that divides radius of the circle K according to the golden ratio. We denote these segments by x and y, such that the length x of BZ is the smaller segment, i.e.:

r = x + y, 

 

x/y = y/(x+y) = Φ = 1/φ ≈ 0.6180339887...

 

x = y/φ

y = x·φ

 

φ = 1/Φ  ≈ 1.6180339887...

 

Through the point Z we draw a line parallel to X-axis and we denote the intersections of this line and circle K in the third quadrant by A and in the fourth quadrant by E. Through the point B we draw a line p at angle α with respect to positive side of  X- axis and we denote its intersection point on the circle K in the first quadrant by V. 

α = (360°/8) * (1/φ) = 45°/φ ≈ 27,8115295°

From the point E we draw a normal on the line p and we denote its intersection with the circle K in the first quadrant by S. We got a chord ES of the circle whose perpendicular bisector is line p. Since ES is perpendicular to line p, ES and Y-axis form an angle α, hence ES and X-axis form an angle 90° + α.

Through the point S we draw a line that forms an angle –α with respect to a line through S that is parallel to the X-axis, and in the first quadrant we denote the intersection of this line with circle K by T. Reflecting point T with respect to line p we get the point C, which is also on the circle K. Hence the line p is the bisector of  TC  which is parallel to ES, while segments ST and CE have the same length.

 

In the second quadrant, on the chord AS we denote a point O, whose coordinates on the X and Y axis ratio is b/a = 2/1. These sections form a right triangle in which the length of the hypotenuse to the lengths of the other side’s ratio is √5/2 and √5/1.  This hypotenuse and negative side of X-axis form an angle

γ = arctg(1/2)≈ 26,5650512°

 

From the point B we draw a circle with the radius BO and denote it circle Q. 

On the circle Q in the first quadrant we mark a point whose X to Y coordinate ratio is c/d = 1/φ. We denote it by M. We draw a line from point B through point M. That line and positive side of X-axis form an angle δ

δ = arctg(φ)≈ 58,2825256°

 

Other matrix angles..

 

β = arcsin(1/(1+φ))≈ 22,4555152°
ζ = 90 - (α+β)≈ 39,7329553°
σ = 2*α+β = 2*(45°/φ) + arcsin(1/(1+φ))≈ 78,07857412°
η = 90°-2*α ≈ 34,376941°
ω = σ-(180°-2*η-2*ζ)≈ 46,2983668°
ψ = σ - ω - β = 9,3246922°
ε = (90°-σ)/φ ≈ 7,36784639°
 
Image of this geometric construction, and M45 cluster alignement provided earlier

Attached Thumbnails

  • Proracun P kutovi r.jpg
  • Proracun P r.jpg


#8 PleiadianGeography

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Posted 03 May 2020 - 03:13 AM

 since euclidean geometry breaks down on global scales(and flat maps are NOT accurate for straight lines

 

True...map used for analyses is Mercator's flat cylindrical projection.

 

I am not able to answer any question, and I have more questions that claims.  Cartographers, geographers, astronomers could help here with their knowledge for sure, but I came to math forum, bcs it is about math :).

 

Makes no sense copying all of materials here...so, anyone interested in this theory should check it on his own, and is very welcome to ask, debate, collaborate, develop system...



#9 PleiadianGeography

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Posted 03 May 2020 - 06:06 AM

That in itself makes me raise an eyebrow regarding your map images, since euclidean geometry breaks down on global scales(and flat maps are NOT accurate for straight lines). 

 

That's a good point! Earth is supposed to be a sphere (spheroid), while Mercator's conform cylindric projection is flat. In Mercator's projection angles are preserved, while distances between specific places (cardinal geomorphological, eponymical - Troy, Troyes, Paris, etc.., sacral.etc..) fits into the rules of planar euclidean geometry. Moreover, "random" lines of coastline, appear to be dependent on those rules, at least when it comes to the cardinal points. But, that's just beginning. To bring more confusion here - there is a star cluster M45 which corresponds to projected Earth's surface, which is happening only in Mercator's projection. So, the context of my question of dividing angles according to the golden ratio, using elementary (clasical, euclidean, ruler-and-compass) method, comes out of possibility to construct cardinal Earth's surface, (coastlines, gulfs, straits, capes...) using the same method. Considering this, I put just few examples in map images....





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