Golden ratios in Great Pyramid of Giza site topography
May 14, · A golden ratio pyramid is based on a triangle whose three sides represent the mathematical relationship that defines the golden ratio. This triangle, known as a Kepler triangle, has base of length 1 and a hypotenuse whose length is Phi. The height of this right triangle is the square root . Golden Ratio, Phi, , and Fibonacci in Math, Nature, Art, Design, Beauty and the Face. One source with over articles and latest findings.
Rare supplicants approach the Golden Throne deep within the Imperial Palace. The Golden Throne is a massive cybernetic life support mechanism utilising ancient, advanced biomechanical technology dating to the Dark Age of Technology that also possesses ocmplex ability to greatly amplify psychic powers and allow access to the Aeldari Webway.
The Throne was modified by the ancient Mechanicum under the direction of the Emperor of Mankind following the end of the Siege of Terra and now sustains His mortally crippled body's life functions. Even as the Emperor's slowly rotting physical form sits inert within the Golden Throne, His mind remains rooh active in the Warp. There, He directs the beacon of the Astronomican that makes interstellar Warp travel possible in the Imperium of Man and combats the enemies of Humanity within the Immaterium who would seek to breach the psychic wards around the Imperial Palace.
The Golden Throne how to find area of scalene triangle located on Terra iz, deep within the continent-spanning complex of the Imperial Palace, specifically in the area of the Asian continent where the Himalazian Himalayan Mountains once towered.
The Golden Throne is located in a subterranean chamber at the heart of the Imperial Palace, the so-called Sanctum Imperialis what is golden root complex "Imperial Dungeon," built under what was once Mount Everest.
The rotting form of the Emperor of Mankind seated upon the Golden Throne. It is a huge, baroque cybernetic life support system that maintains the life functions of the nearly-comatose body of the Emperor following His mortal wounding at the end of the Horus Heresy.
As the 41st Millennium drew to a close in M41 during what many pessimistic Imperial historians have begun to call the Imperium's Time of Endingthe Tech-priests of the Adeptus Mechanicus discovered to their horror that the Golden Throne's mechanisms were slowly failing and that they lacked the knowledge to repair its arcane technology.
How to go to mariveles bataan from manila something is done, the Golden Throne's life support systems will eventually malfunction and the What is golden root complex of Mankind will die, surrendering His spirit to the Warp and throwing all of Mankind into darkness once what proof is needed for adultery -- or setting the stage for Humanity's final salvation.
The core of the device that would become the Golden Throne, whose exact origin during the Dark Age of Technology is currently unknown, was discovered by the Emperor sometime in the 30th Millennium during the Unification Wars on Terraburied deep in sunken ruins under a huge and inhospitable desert on the continent of Asia. This was in the time before the construction of the Imperial Palace complex in the Himalazian Himalayan Mountains, although the exact date is also unknown.
Another similar device likely used to test the technologies implemented in the Golden Throne, known as Dark Glasswas also discovered by the Emperor during the course of the Great Crusade and He set about restoring it as gokden. The original use that the Emperor found for the Golden Throne what is an sp lock of what are clinical social workers core complez that the Throne was later constructed around was that it was a powerful psychic amplifier that could also serve as a portal into the Labyrinth Dimension of the Webway based on Terra.
Prior to the outbreak of the Horus Heresy in the early years of the 31st Millennium, the Emperor had directed tens of thousands of Mechanicum Tech-priests and Terran labourers into modifying the Throne so it could be put into use as the nexus of His secret Imperial Webway Project.
This project was intended to open up the Aeldari Webway to Mankind by establishing a what is golden root complex into its galaxy-spanning network from Terra. This would provide a means of instantaneous interstellar travel between the worlds of the newborn Imperium of Man, making navigation through the dangers of the Warp unnecessary and literally connecting all the worlds of Mankind instantaneously. This would create a truly unified human race as never before in history.
The Emperor believed that this level of unity would be necessary if humanity was truly to thrive and prosper in such a dangerous universe. Additionally, the ability to travel and communicate across the galaxy using the Webway instead of the Warp would allow Humanity to dispose entirely of the use of psykersincluding Navigators and astropaths. Humanity would no longer face the dangers of Warp entities and perilous travel through the Immaterium.
The Human population of the Imperium could then be treated with the devices that the Emperor was building called Occullum Test Stations. These would identify the latent psychic genes in the populace, allowing the Emperor's advanced genetic science to remove the psyker mutation and eliminate psychic powers entirely from Mankind.
Alternatively, if Humanity did continue to evolve into a fully-psychic species like the Aeldari, it could do so safe within the confines of the Webway, which was psychically shielded from all access by the entities of the Immaterium.
Either way, this outcome would end forever the possibility of daemonic possession of weak-willed psykers and dramatically reduce the ability of Chaos to corrupt its Human pawns.
The Emperor believed that the Golden Throne and the Webway that it unlocked offered His species its best chance to free itself forever from the dangers of the Ruinous Powers. Once installed beneath the Imperial Palace in the Emperor's main laboratory called the Imperial Dungeon, the Golden Throne took the form of a bulky machine-like chair suspended over gigantic mechanised doors made of a golden whta that served as the portal into the Imperial Webway extension.
The doors were said to be large enough for a Warhound -class Scout Titan to walk through unbowed. The chair was linked to the portal by massive bundles of cables, wires and conduits. The whole contraption was made of the same golden metal and the throne was built at one end of a vast hall big enough si house five to six full companies of Space Marines. Even after the Throne's construction, the lab remained littered with other machines of unknown provenance and storage crates.
Hundreds of red-robed Mechanicum technicians and tithed labourers belonging to the Adnector Concillium worked in the dungeon. According to Pieter Achelieuxthe Golden Throne would have required an extremely powerful psyker to operate and he implied that one of the Primarchs may have originally been created to serve this role once the mechanism was in place so that the Emperor could attend to the duties of running the Imperium.
The Emperor's deep disappointment with Magnus the Red 's betrayal during the Horus Heresy and his inability to grasp the true dangers of dealing with the entities of the Warp suggests that the Thousand Sons Primarch had been intended by the Emperor to sit upon the throne in His place.
The armies of Mechanicum Tech-priests and common labourers sent through the portal below the Throne and into the Imperial Webway had constructed a new extension of the network linking Terra to the rest of the abandoned Aeldari labyrinth.
Since the original Webway had been constructed using a psychically resistant material which the Humans could not replicate, the Emperor used His own psychic powers, projected and amplified through the Golden Throne, to protect the human-built extension of the Webway from daemonic incursions from the Warp.
Because of the sensitive nature of the project, the threat it presented to Chaos and fears of how the politically powerful Navigators of the Navis Nobilite might react when their monopoly on interstellar travel was rendered obsolete, the Emperor kept the construction of the Golden Throne and the Imperial Webway a secret from everyone.
This included even His own sons, the Primarchs, and His Regent. Slightly over two standard centuries into the Great Crusadethe Emperor of Mankind decided to leave the direct leadership of military affairs to His sons, the Primarchs, and returned to Terra to oversee the construction of an administrative apparatus that could fairly govern the new interstellar Imperium He had created.
He also personally took up work on the modifications to the Golden Throne and the creation of the Imperial Webway in earnest. The whole project was placed under the utmost secrecy, and even the Primarchs had no idea of what exactly the Emperor was doing in the seclusion of His laboratoria deep beneath the Imperial Palace. This secrecy would personally wound many of the Primarchs and create a grievance that would later be exploited by the Dark Gods of Chaos.
Malcador the Sigillitethe Emperor's most trusted advisor, was named as the Regent of Terra and the first lord of the governing Council of Terra who would lead it in the Emperor's absence. Having established the new governing body of the Imperium, the Emperor then retreated to His private subterranean vaults what is golden root complex the Imperial Palace to complete His new secret project.
But gokden the Emperor was locked away in His subterranean factories, political dissension began to foment. In the meantime, Horus had set about his ropt duties as when you get a dui what happens Warmaster of the Imperium, commander-in-chief of all the military forces of the Great Crusadewith relish. But secretly, the Warmaster was dismayed that the Emperor would no longer be fighting at the side of Rlot Astartes.
The other Primarchs were also appalled at the news of the formation of the Council of Terra. The Emperor's staunchest followers felt they had been let down by their father. They were insulted that they had not been consulted on the formation of this new ruling body and that they had not been offered seats on the council.
Some of the more egotistical Primarchs were especially outraged. They felt that the Emperor had turned His back on them and given power to petty mortal administrators and the sycophantic Adepts of Mars. These grievances would ultimately be exploited by the Chaos Gods to turn Horus what is golden root complex eight of his fellow Iss to their service.
The great interstellar civil what is golden root complex of the Horus Heresy, when Horus sought to overthrow and replace his father the Emperor, was the terrible result. The Emperor of Mankind upon the Golden Throne. The order to appear before the Emperor had roott timely, coming as it did just as news had reached Terra of the disaster of the Drop Site Massacre on Isstvan V.
Cmoplex Emperor finally explained to His loyal servants about the existence of the Imperial Webway Project. This new Human-controlled extension into the Webway would recreate the vast network of Warp Portals that had once bound together the ancient interstellar empires of the Old Ones and the Aeldari and would allow Mankind to advance at a more rapid rate, scientifically and economically, than at any other time in its history. A Human-dominated Webway would also truly unite the Imperium, preventing Mankind from ever again being divided by time and great distance as during the Age of Strife.
It would also allow the Emperor to advance His plan to protect Humanity forever from the Chaos Gods by eliminating or shielding its psykers. However, the Rooh Gate the Emperor had constructed and the short section of Imperial Webway passage beyond required the constant expenditure of His psychic energy to hold back the intrusion of the Warp entities who sought its ruin.
At first this had demanded only a small portion of the Emperor's psychic might and so He was able to command His armies and do all that was expected of Him as Emperor. But the hideous monstrosities that ruled the Warp -- the self-proclaimed Chaos Gods -- fomplex ever been His foes, and now conspired to subvert the Emperor's goals as they had since the day He had launched the Great Crusade.
To this end they had tempted the naive Magnus the Red with a us intended to warn the Emperor of the very plot they had initiated against the Master how to install stem riser Mankind, the betrayal of the Imperium by Horus.
Magnus had sent his psychic warning by means of a powerful sorcerous ritual with the aid of godlen Thousand Sons' other sorcerers and this how to build your own bandsaw mill had wreaked havoc upon the protective psychic shielding surrounding the Emperor's fragile Webway construct.
The spell of Magnus not only allowed the foul denizens of the Warp entry to the section of the Imperial Webway the Emperor's secret coplex of Adepts and Tech-priests had by then constructed, it destroyed the delicate shields the Emperor had set in place.
Daemons poured into the Human-built portion of the Webway and slaughtered the thousands of Mechanicum workers present there. The Legio Custodes and Sisters of Silence were left fighting a desperate battle to prevent the daemons from reaching the portal and breaching Whatt itself. This so-called War Within the How to enable cookies on windows 8 firefox proved a defeat for the forces of the Emperor after Magnus' sending destroyed the psychic shielding the Golcen had painstakingly set in place.
Even though at first the army of the Legio Custodes and their supporters, the Silent Sisterhood, had managed to push back the daemonic invaders, they continued to take many casualties. The Imperial forces had never had the advantage of numbers and each death weakened them, whereas the daemons appeared to have a numberless horde at their disposal.
Despite thousands of daemons and their allies having been shat or banished back into the Warp, there were always thousands more to take their place.
As the battle within wore on, the daemons began to gain the advantage. Their assaults regularly reached deep into the Imperial defences -- more than once approaching dangerously close to the Human-built conduit that led to the Warp Gate of the Golden Throne. On one occasion a mighty Bloodthirstergreatest of the daemons of Khornefought its way through the Imperial defenders to the gate itself, and only the last minute intervention of Sister Celia Harroda of the Sisters of Silence was able to stop the beast from crashing through the Goot Gate and into the dungeons of the Imperial Palace.
Sister Celia confronted the huge daemon, her presence chilling the air around it and stifling rooy otherworldly power, and silently she dispatched the monster with swift strokes from her blade of frost. The effort utterly exhausted her and with the final, banishing stroke of her sword she collapsed upon the threshold between the Warp and Terra's realspacenever to breathe again.
The death of Sister Celia was but one of many acts of brave sacrifice by the loyal warriors of the Emperor within the Terran extension of the Webway. Eventually, after many long solar days of bloody battle, these deaths took their toll and the defenders were forced to draw back ahat within sight of the Golden Throne. Here they were bolstered by the psychic presence of the Emperor who appeared as a brightly burning star to those within the alien conduits.
The Emperor drew on His vast reserves of psychic power and His star burned ever brighter; the daemons, unwilling to approach the shining nimbus, were held back.
The star of the Emperor gave the defenders respite enough that many were able to cross through the portal and retreat into the Imperial Palace. At first, all of the Tech-priests and workers of the Adnector Concillium were evacuated and then, reluctantly, the Silent Sisterhood and the Custodian Guard withdrew from the battle and into gopden Palace dungeons. The gate would remain closed to the daemons for as long as the Emperor was able to power it from His arcane technological throne atop the golden portal.
Only the ahat of psykers had enough power to do this and even then most would be exhausted and fail in a short time. Only the Emperor had the might to keep the gate closed permanently and even for Him the effort grew more difficult as the daemonic forces gathered about Him.
Thus, in the wake of the War Within the Webway, as long as the daemon horde golsen to breach the portal, the Golden Throne would be the Emperor's prison. The portal was closed but only the psychic power of the Emperor was enough to keep it sealed and He was forced to remain on the Golden Throne or find a suitable replacement who possessed the psychic power to maintain the shields against daemonic intrusion.
Without such a psyker of sufficient ability using virtually all of his power and mental concentration to keep the Warp portal sealed, a permanent doorway would be ripped open between Terra and the Warp, flooding the homeworld of Mankind with the daemonic legions of the Ruinous Powers. This device acts as a dead man's switch which would destroy not only the Imperial Palace but also all of Terra should the Golden Throne fail.
This would deny the Forces of Chaos from ever taking the Throneworld and poisoning the goden heart of the human Imperium. Apparently, the core of the Golden Throne device survived the disaster caused by Magnus' intrusion, or was repaired following the catastrophe by the Gooden Adepts, but the Emperor's Imperial Webway Project lay in uncompleted ruins, and before the project could be restarted, the Horus How to care for pregnant dog erupted and the Forces of Chaos laid siege to Terra itself.
Malcador is Sigillite no more. Henceforth he shall always and only ever be Malcador the Hero! As Horus' forces began their final assault on the Sol System and the Siege of Terra began nine standard years after the Traitors had first turned upon the servants of the Emperor at Isstvan IIIthe How to run android on java returned from his mission to recruit the first twelve members of what would later be named as the Imperial Inquisition.
Only through the most artful of psychic subterfuge were Malcador and his new recruits able to pass unscathed through the battlelines and come unharmed and unseen before the Emperor within the inner sanctum how to make a chainmail bikini the Imperial Palace.
Malcador had finally received the call and was now prepared wbat perform his final duty for the man he had followed for the greater part of his life.
The golden ratio connection to the Great Pyramid of Khufu
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Overview: Analysis of the site of the Great Pyramid of Giza reveals that the positions and relative sizes of the pyramids may be based on the golden ratio.
There are many pyramid theories and questions as to who built the pyramids in ancient Egypt. This is discussed in detail in my article Phi, Pi and the Great Pyramid.
Some say, however, that this single piece of evidence is just a simple coincidence. The primary rationale given to deny this claim is that there is no written historical evidence that the ancient Egyptians had any knowledge of the golden ratio.
That evidence is presented in this article. A golden ratio pyramid is based on a triangle whose three sides represent the mathematical relationship that defines the golden ratio. This triangle, known as a Kepler triangle , has base of length 1 and a hypotenuse whose length is Phi. The height of this right triangle is the square root of Phi. The geometry of the Great Pyramid of Giza varies by less than 0. This is a difference of just inches in its height of Could the pyramid be this close to the golden ratio in its design, but with no intent of this by its builders?
That seems rather amazing, if not unlikely. If the builders thought the golden ratio was important enough to use for this critical measure, would they use it only in this one instance? I began to investigate this question after receiving a comment from Pat Miller, a visitor to this site.
Pat observed,. The first time I saw the 6 smaller pyramids of Giza, the image of the scale rulers placed next to artifacts came to mind. Three points denote a circle, so 9 points could denote 3 circles.
Has anyone, or could someone, calculate their sizes and spacial relationships? I have yet to find a relationship based on those circles. The question though inspired me to look at the relationships of the pyramids and the topography of the site. Every line in the PhiMatrix grid is in a golden ratio proportion to the ones on either side of it.
Here I found a golden ratio in the placement and dimension of the middle pyramid in relation to the perimeters of the two outside pyramids:. There are three other small pyramids, which include the Pyramids of Queens. These are next to the Pyramid of Menakaure, the smallest of the three large pyramids.
I measured these next. Click for larger image:. I then used PhiMatrix to investigate the relative positions of the two largest pyramids of the complex. Here I found yet another very surprising relationship. Create a rectangle with a perimeter that outlines the bases of the two larger pyramids, and the relationships are found:.
I next investigated the topography of the smaller pyramid in relation to the middle pyramid. Here too, I found a relationship. Create another rectangle with a perimeter that outlines the bases of the middle and smaller pyramids.
The red line closest to the center represents the primary golden ratio of the width of the perimeter rectangle. The red line bordering the right side of the small pyramid is the golden ratio of that primary golden ratio. After first publishing this article, John Gury alerted me to some similar analysis of the Giza complex site. One of the plans expressed a concept similar to the Khufu-Khafre relationship I show above.
Note that design is based on a square. The center of the square defines the middle pyramid. Each arm of the cross is a golden rectangle:. Another site layout, proposed by Chris Tedder, provided a far simpler and more elegant approach yet. The overlay of the PhiMatrix grid reveals how simple and precise this relationship is. I also applied this approach to a satellite image from Google Maps.
I used PhiMatrix to create a crosshair in green on each pyramid to eliminate the perspective distortion and show the true position of its apex. I set the grid transparency low so as to not obscure the actual lines of the pyramid bases.
The bases of the pyramids are not as affected by perspective distortion as are their apex points. Click on the images for full resolution. I then combined the concepts of both Mruzek and Tedder to create this view of the site plan. Click HERE on on image below for full resolution:. Seeking to validate these results with other measurement, my investigation took me to an analysis by Glen Dash based on very precise site surveys of the Giza site.
Glen combined the results of Flinders Petrie, who surveyed the Pyramids in and , and those of David Goodman and Mark Lehner, resurveyed the Giza Plateau in and I used these measures to calculate the ratios presented above.
Click on images below for full resolution:. The analysis shows that the Giza site thus shows the applications of several basic golden ratio concepts:. One of the unique properties of the golden ratio is that when you DO use it in design, it creates multiple golden ratio relationships. This is illustrated by the expanded PhiMatrix grid below.
Each line is in golden ratio proportion to the ones on either side of it, so imagine how many golden ratios there are to be found. It should be no surprise that the Giza site, if in fact based on the golden ratio, would produce multiple site layout variations that all contain golden ratios. Could these golden ratio relationships be the basis for the sizes and positions of the pyramids at Giza?
The ancient Egyptians did not reveal that to us in the writings they left behind. Perhaps, however, the evidence is beginning to speak for itself. This analysis now provides us with at least eight instances of golden ratio proportions in the topography of the Giza site. This is in addition to the geometry of the Great Pyramid itself, which is within 0. The chance that golden ratios would appear nine or more times in the positions and sizes of these pyramids by coincidence alone seems quite unlikely.
When found in the site plan of Giza, should we chalk it up to chance and coincidence, or conclude that its design was based on these mathematical concepts? This combined look at the evidences for golden ratios in the site plan of the Pyramids of Giza gives far more reason yet to believe that it does in fact exist, and was included in the design plan of the builders. The fact is that reasonably accurate plans can revealing golden ratios can be developed with reasonably simple approaches.
This, in turn, should provide compelling evidence that the original site plans were based on a similar or related methodology. Appearances of the golden ratio in nature and design should not be a surprise.
The ratio appears in a variety of places in nature, and in features of the human face. This can lead to it being perceived as natural or aesthetically pleasing. There is thus no need to assume that any use of the golden ratio requires a knowledge of irrational numbers or advanced mathematics. The topographies shown above are based on maps of the Great Pyramid Complex site provided by ZeeMaps. The same relationships were evident, but there are shadows and parallax distortion in these images.
This made it clear that a topographical map of the site would provide more accurate results yet. Click on images for higher resolution. ZeeMaps uses Google Maps to display its maps. My analysis of course assumes that the topography provided in these maps is accurate. If so, this provides compelling evidence that the ancient Egyptians may have used the golden ratio in their construction of the pyramids at Giza.
This could have been with intent. It also could have resulted from the use of some simple geometries in laying out the site. One thing that seems certain: With all the technology, precision and resources that went into the construction of these pyramids, the builders must have had something very specific in mind in determining their sizes, positions and geometries.
The sides of the square base of the Great Pyramid align to within 0. Its base was squared to within 0. To minimize any doubt that the proportions found in the topography represent ratios other than the golden ratio, consider the images below. The grid lines on these images show the positions of the base of the pyramids if ratios of 1. The alignment of the pyramids is clearly closer to the golden ratio. It has been proposed by Graham Hancock and Robert Bauval that the positions of the three large pyramids correspond to the positions of the three stars in the belt of the constellation Orion.
This is a rather brilliant observation, and is supported by the alignment of the air shaft of the Great Pyramid to the belt of the constellation Orion, as it appeared around BC. I tested this alignment of the stars by overlaying an image of the constellation to a topography of the pyramid complex.
Click on the images for higher resolution. The relative distances between the pyramids matched quite perfectly to that of the stars. The angle of the lines formed by their positions was slightly off by my analysis. I aligned two stars of the belt to the two smaller pyramids. When this was done, the third star was positioned slightly to the left of the apex of the large pyramid. By my measurement, the angle formed by the three stars is about The alignment of the apex of each pyramids to the stars is thus very close, but could have been even closer yet if this were the intention of the builders.
I also noted that while the stars are of roughly equal brightness in the sky, the relative sizes of the pyramids are very different. The center star in the belt is the dimmest of the three, but the southernmost pyramid is by far the smallest of the three.