MT Chapter2: The usage of Phi, Golden Numbers and Fibonacci Numbers in Architecture from Antiquity
This chapter will look at the history and application of usage, throughout Ancient Times, of the Golden Numbers, such as Phi, the Fibonacci Sequence. It will analyze the different topographic points that they were used, by the ancients and their grounds for utilizing these mathematical systems.
Doczi, 1981, examines the significance of Golden Numbers to different peoples throughout history. He pays specific attending to Proportional Harmonies, within architecture. reference1a In Wiltshire, England, around an estimated YEARSAGO, SH mention an astoundingly unbelievable memorial was built. Believed to be a calendar, of kinds ; a topographic point of religious and spiritual significance ; or perchance a compass, this construction possesses geometry affecting Golden Numbers excessively. reference1a
One of the other first recorded utilizations, of these peculiar figure systems, can be traced back to the early yearss of Freemasonry and the architecture of their Masonic Temple, in PLACE. The Freemasons call themselves a Brotherhood ; and Masonic Halls and Lodges can be found all over the universe. On a corner rock of the Masonic Hall in Halifax, Canada, it can be seen that two different day of the months are inscribed upon one of the corner-stones. These two day of the months, 1875, and 5875, seem to propose that the Masons believe that their society dates back every bit far as 4000bce. reference1 In Manly P. Hall, 1973, he discusses the evident likely-hood that the Ancient Egyptians had the most knowledge about the scientific disciplines of nature. Hall goes on to state us that Steinmetz, 1976, provinces:
“ Regardless of the beginning of the modern Lodge, or of the name “ Freemason, ” we can, after liberating the symbolism of modern versions, discern in Freemasonry the lineation of the instructions of the ancient enigmas of Egypt. ” mention Manly P. Hall Freemasonry of the Ancient Egyptians
A statement by Past Provincial Grand Registrar, W.L. Wilmshurst in “ The Meaning of Masonry ” , 1922, reads:
“ I am acquainted, for case, with an Egyptian ceremony system, some 5,000 old ages old, which taught exactly the same things as Masonry does, … ” cite The Meaning of Masonry, by Past Provincial Grand Registrar, W.L. Wilmshurst
This shows us that Freemasonry was a portion of Ancient Egyptian civilization and besides shows that these accomplishments and “ Secret Knowledge ” have been passed down from ascendants, 1000s of old ages ago.
Investigating Steinmetz, shows us that the Masons are taught that their secret-knowledge has been passed down by generation-after-generation of their brotherhood ‘s members since the clip of the, legendary as yet unfound sunken, metropolis of Atlantis. mention Freemasonry Its Hidden Meaning, by George H. Steinmetz
Arpat, 2004, discusses the usage of these Golden Numbers and sequences in architecture throughout both the Islamic, Ottoman and Christian Empires. Besides he draws loop to the fact that the really same rules and techniques are still used in architecture today. reference1
In 1861 a certain Mr. William Preston, past maestro of the Lodge of Antiquity, wrote “ Instruction manuals of Masonry ” . In this book he draws attending to the significance and significance of geometry, to the George masons:
“ Geometry or Masonry originally synonymous footings, is of a Godhead and moral nature and enriched with the most utile cognition: whilst is proves the fantastic belongingss of nature, it demonstrates the more of import truth of morality. ” reference2
This grounds shows that geometry and the Golden Numbers are per se linked with spiritualty, faith and morality, for many different civilizations. Today, the Masons continue to up-hold their belief that the architectural techniques and methods that they teach to their Members should be kept as a reverent secret from the general populace. It is no accident that their most important and recognizable insignia has a missive “ G ” as its cardinal characteristic. It can be seen that a capital “ G ” has a similar form as the Fibonacci Spiral. reference1
A really old book, Leader Scott ‘s 1899 issue of “ The Cathedral Builders ” , clarifies portion of the ground that the Freemasons had such an influential consequence upon the edifice of churches, throughout history. He describes how a peculiar group of people known as “ Liberi Muratori ” , who lived near Como, Italy around 643ce were formed. Once this cabal began to turn in Numberss, they were sent out, across the universe, to learn, construct and enroll new members. They shortly became a big and organized society of designers, sculpturers, and professionals of humanistic disciplines and trades. This proliferation of their joint cognition bled into every group of society that they came upon. Scott goes on to depict that there were edicts from the Catholic Church, in Rome, to protect any members of the Freemasons ‘ Brotherhood, in any Catholic state that they might be in. These apostolic bulls besides allowed the Masons to work, without competition from local rivals, in their several field of expertness. This left control of architecture design, of churches, entirely to the Masons who ever followed the set forms, rules, and sequences which were laid down before them, by their hereditary Mason brothers. mention “ The Cathedral Builders ”
Further grounds of important geometric forms can be found in Islamic Mosques, all over the universe. One of the most notable illustrations of this is the Hagia Sophia in Istanbul. This monumental construction was built, between 532ce – 537ce, in what was so known as Constantinople. Byzantine Emperor, Justinian the Great commissioned Anthemius of Tralles and the Elder Isidore of Miletus, who hailed from Western Anatolia, to construct this construction as a Church. reference1 These two figures were non known as designers, instead, Isidore was referred to as a Professor of Geometry and Mechanics, whilst Anthemius was thought of as a Mathematician and a Physicist. The common term that was used for their place, as builders of this memorial, was “ mechanikoi ” . hypertext transfer protocol: //www.hagiasophia.com/listingview.php? listingID=6 Anthemius was left to plan and bring forth the architectural drawings of this church, whilst Isidorus was in charge of the existent building of the edifice. It is interesting to observe that although the Hagia Sophia was built as a church, in the sixth century Ce, today it is used as a museum, but for about five hundred old ages, after the Ottoman Empire conquered Constantinople, it served as a mosque, for the so Islamic officeholders. The Faculty of Architecture of the Technical University of Istanbul holds a papers drawn up by a Azinasi BaAYeAYmez, in which he includes exact programs of the Hagia Sophia. With the aid of his helper, Ahmet Alptekin, he was able to detect that Phi had been explicitly used through-out the whole design of the Hagia Sophia. reference1 The figure below, shows an illustration of these geometrical forms, which have been used, in the interior infinite of the Hagia Sophia. Diagram1
This illustration of ancient architecture demonstrates the usage of Golden Numbers, within edifice building, absolutely. Another first-class illustration of this is the Mosque of Rum Mehmet PaAYa. This sacredly important construction is besides found in Istanbul. Constructed around 1471ce the Grecian builder besides appears to hold used the same unit of length, as was used in the design and building of the Haga Sophia. This “ Byzantine Foot ” would now, in today ‘s universe, be seen as being 31.23centimetres long. It was divided into 16 “ Fingers ” and a metallic rod of this length, believed to hold been used by Azinasi BaAYeAYmez, and besides before him the Ottomans, has been preserved in the TopkapA± Museum of Istanbul. Arpat, 2004, describes how with his helper, he measured the precise dimensions of the Mosque of Rum Mehmet PaAYas ‘ exterior breadth of the Mosque ( without porch ) , the thickness of the walls, the doors and the country around the main-entrance. With these measurings he was able to demo that, one time once more, the Golden Ratio and the Fibonacci Spiral had been major factors involved with bring forthing the architecture of the full edifice. reference1 Diagrams2
In Greece itself, the most good known edifice in Athens is the Parthenon. This testament to the inventiveness of the Ancient Greeks is yet another illustration of where the Golden Ratio is used repeatedly, in about all facets of its design. Built around 440ce, Pythagorean Geometry, every bit good as the Fibonacci Sequence can be seen to hold been utilised in the nucleus of its architectural design. reference4 Feuilles de Delphes, Topografi et Architecture Releves et Restaurations par K. Gottlob, Paris 1925, holds the ground-plans for the Parthenon, Rodos discusses these programs in his book, The Secret of Ancient Geometry and its Use ( Vol. 2, 1967 ) analyses these programs and describes the prolific usage of these sequences, in the design of the Parthenon ‘s ground-plan. reference5 The front-facade of the Parthenon besides displays many charactistics, which use the Golden Ratio. The diagram below shows this: reference6 Diagram3
In England, Golden Numbers can be found in the architecture of many churches. One illustration of this is Vere Street Anglican Church, London. Built in 1721, architects AyAYe and Nigel Walding from Derby, fastidiously measured every dimension of the church. Arpat, in his 2004 book, sets down the process that AyAYe and Nigel would hold used to make this:
Draw line AB = 636 ” ( 1615.122cm )
Pull a line AC = 4/3 tens AB
Pull a half circle around BC and a perpendicular from A until D.
AD == 734.39 ” ( =1865 centimeter ; Diff. 1cm )
Pull a half circle A withR= AD until intersection E. AE = 734.39 ”
Extend AE by 1/5, grade point F.
Pull a half circle around AF, grade intersection G ;
EG == 328.429 ”
This is the breadth of the cardinal nave ( = 834.05cm )
Divide the interior length in five equal subdivisions ; these are the breadth of the bays:
734.392 / 5 = 146.878 ” , mark point H.
Halve the cardinal nave, grade point K ; HK = 164.215 ”
Extend HK by 5/7 tens HK, grade point L.
Pull a half circle around LK and a perpendicular from H until intersection M.
Draw an discharge around H withR= HM until intersection N.
HN = HM = EG == 138.787 ” ( = 352.75cm )
This is the breadth of the side naves. The interior breadth of the church is:
2 ten 138.787 ” + 328.429 ” = 606 ” , as measured ( 1538.94cm ) reference1
The diagram below should be used as a mention for the instructions, quoted above.Diagram4
This subject of Christians utilizing Golden Numbers, in architecture, can besides be seen in St. Johannes Basilica, in Catholic Berlin, Germany. This illustration was built in 1897 by designer August Menken, who was besides involved with the building of some of the other of import churches, in Berlin. Once once more it is mostly in the land floor program, that the Fibonacci Sequence can be found. Diagram5
It can besides be shown that the radius of the handbill wall behind the communion table, and the relationship between the communion table, the columns and doors to the street, all involve the Golden Ratio. Diagram6
It is widely understood that architectural techniques have been passed down through coevalss, and dispersed through other civilizations, by trade paths as they appeared in the Middle Ages. Equally good as this, the spread of Freemasonry and other spiritual cabals has contributed greatly to the addition in similar methods of architecture, in different parts of the World. Originally, it seems that, the forms and designs used were created utilizing nature as inspiration. In the modern universe of scientific discipline we are able to more closely, and more accurately, examine nature ‘s artifacts, and it has been seen that these specific figure sequences ( like the Fibonacci Spiral ) can be found about everyplace. reference7
Knocks, H. and Arch, M. ( 2007 ) discourse the findings of the Ancient Greek Thinker, Plato. Plato describes different sets of proportions, stating:
“ the three-term proportion as indispensable cognition, the cognition through which the head is able to grok the universe. ” reference8
Plato claimed that utilizing the methods to happen the mean of a three-term proportion, such as a/b = b/c, ( which is most normally used by designers ) , an apprehension of the Torahs that govern the creative activity of all things can be formed. A two-term proportion can be expressed as:
As shown antecedently, in this papers, this is the Aureate Proportion. reference9
These Golden Numbers, sequences and forms are likely most noticeable in sacredly important edifices because big architectural undertakings have, more frequently than non, been commissioned by spiritual groups. Religions have, historically, possessed the largest sum of financess for such projects. It is common cognition that faiths have many secrets, in order to protect their cognition of the universe, they would merely let certain people to go toilet to facets, such as their architectural techniques and methods.
Religion has ever been the pillar for the guidelines and regulations, of different societies. Taxes upon the general population, connected with a peculiar spiritual edifice, were common in yearss gone-by. Both in the signifier of offerings to divinities, and payments for ( as Christians might state ) “ shepherding their flock ” , goods, money and nutrient points were, and still are, normally given to these spiritual ‘benefactors ‘ . This is how the Church and other spiritual cultural leaders harnessed the largest sums of power and money, in whole lands and across continents.
Ancient Grecian times seem to be an exclusion. It has been documented that here, most of the “ Thinkers ” , in Ancient Greece, focused their attendings upon mathematics and lay-down our first Torahs, instructions and regulations, which govern the universes of scientific discipline, technology and the existence. These early Mathematicians and Structural Engineers were largely taught at UNIVERSITY NAME, in Egypt, where they were able to analyze many edifices which were already 1000s of old ages old. reference10
Noteworthy Greek Thinker, and Mathematician, Pythagoras, was taught in many Egyptian Temples, like NameOfTemple. He was besides a Mason and so when he returned home, it was prohibited for him to relay the secret direction that he had been taught in Egypt, to anyone else. Pythagoras taught along different avenues of geometry and instructed “ non-initiated Grecian pupils ” in this new methodological analysis. reference11
Schwaller de Lubicz, in his 1981 publication, was able to animate the attack that Pythagoras used in using his geometric methods to architecture. These two tomes, The Temple of Man, discuss Pythagorean Theorems in great item, nevertheless they do non dig profoundly into the “ Lost Knowledge of the Ancient Egyptians ” it is necessary to analyze other resources to derive this information. mention “ The Temple of Man ” .
It is widely recognised that the Christian Bible has been translated many times, from and into many different linguistic communications. Translations can seldom be exact and the significance of certain phrases is frequently lost during transition, from one linguistic communication into another. One illustration of this is at the beginning of the Gospel of St John, in the King James Version, 1611. This book, of the Bible, starts with the line: reference9
“ In the beginning was the Word, and the Word was with God, and Word was God. ” mention King James Bible, Gospel of Saint John
As Knocks and Arch, 2007, explain:
“ The transcriber, working in the clip of King James, chose to utilizewordfor the Greek ‘logos ‘ .Sonsimplies an active rule and would be more accurately translated as ‘verb ‘ . What, so, is the word, or verb, of which St John has written? Harmonizing to the anthropocosmic apprehension, it can merely be the fantastic transforming power of Phi ( ?¤ ) , the Golden Proportion. ” reference9
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