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MT Chapter2: The use of Phi, Golden Numbers and Fibonacci Numbers in Architecture from Antiquity
This chapter will look at the history and application of use, throughout Ancient Times, of the Golden Numbers, such as Phi, the Fibonacci Sequence. It will examine the different places that they were used, by the ancients and their reasons for using these mathematical systems.
Doczi, 1981, examines the meaning of Golden Numbers to different peoples throughout history. He pays specific attention to Proportional Harmonies, within architecture. reference1a In Wiltshire, England, around an estimated YEARSAGO, SH reference an astoundingly incredible monument was built. Believed to be a calendar, of sorts; a place of spiritual and religious significance; or possibly a compass, this structure possesses geometry involving Golden Numbers too. reference1a
One of the other first recorded uses, of these particular number systems, can be traced back to the early days 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 world. On a corner stone of the Masonic Hall in Halifax, Canada, it can be seen that two different dates are inscribed upon one of the corner-stones. These two dates, 1875, and 5875, seem to suggest that the Masons believe that their society dates back as far as 4000bce. reference1 In Manly P. Hall, 1973, he discusses the apparent likely-hood that the Ancient Egyptians had the most knowledge about the sciences of nature. Hall goes on to tell us that Steinmetz, 1976, states:
"Regardless of the origin of the modern lodge, or of the name "Freemason," we can, after freeing the symbolism of modern adaptations, discern in Freemasonry the outline of the teachings of the ancient mysteries of Egypt." reference 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 instance, with an Egyptian ceremonial system, some 5,000 years old, which taught precisely the same things as Masonry does,..." reference The Meaning of Masonry, by Past Provincial Grand Registrar, W.L. Wilmshurst
This shows us that Freemasonry was a part of Ancient Egyptian culture and also displays that these skills and "Secret Knowledge" have been passed down from ancestors, thousands of years ago.
Investigating Steinmetz, shows us that the Freemasons are taught that their secret-knowledge has been passed down by generation-after-generation of their brotherhood's members since the time of the, legendary as yet unfound sunken, city of Atlantis. reference Freemasonry Its Hidden Meaning, by George H. Steinmetz
Arpat, 2004, discusses the use of these Golden Numbers and sequences in architecture throughout both the Islamic, Ottoman and Christian Empires. Also he draws iteration to the fact that the very same principles and techniques are still used in architecture today. reference1
In 1861 a certain Mr. William Preston, past master of the Lodge of Antiquity, wrote "Instructions of Masonry". In this book he draws attention to the meaning and significance of geometry, to the Masons:
"Geometry or Masonry originally synonymous terms, is of a divine and moral nature and enriched with the most useful knowledge: whilst is proves the wonderful properties of nature, it demonstrates the more important truth of morality." reference2
This evidence shows that geometry and the Golden Numbers are intrinsically linked with spirituality, religion and morality, for many different cultures. 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 public. It is no accident that their most significant and recognisable insignia has a letter "G" as its central feature. It can be seen that a capital "G" has a similar shape as the Fibonacci Spiral. reference1
A very old book, Leader Scott's 1899 issue of "The Cathedral Builders", clarifies part of the reason that the Freemasons had such an influential effect upon the building of churches, throughout history. He describes how a particular group of people known as "Liberi Muratori", who lived near Como, Italy around 643ce were formed. Once this faction began to grow in numbers, they were sent out, across the world, to teach, build and recruit new members. They soon became a large and organized society of architects, sculptors, and professionals of arts and crafts. This proliferation of their joint knowledge bled into every group of society that they came upon. Scott goes on to describe that there were edicts from the Catholic Church, in Rome, to protect any members of the Freemasons' Brotherhood, in any Catholic country that they might be in. These papal bulls also allowed the masons to work, without competition from local competitors, in their respective field of expertise. This left control of architecture design, of churches, solely to the Freemasons who always followed the set patterns, principles, and sequences which were laid down before them, by their ancestral Mason brothers. reference "The Cathedral Builders"
Further evidence of significant geometric patterns can be found in Islamic Mosques, all over the world. One of the most noteworthy examples of this is the Hagia Sophia in Istanbul. This monumental structure was built, between 532ce - 537ce, in what was then known as Constantinople. Byzantine Emperor, Justinian the Great commissioned Anthemius of Tralles and the Elder Isidore of Miletus, who hailed from Western Anatolia, to build this structure as a Church. reference1 These two figures were not known as architects, rather, 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 position, as builders of this monument, was "mechanikoi". http://www.hagiasophia.com/listingview.php?listingID=6 Anthemius was left to design and produce the architectural drawings of this church, whilst Isidorus was in charge of the actual construction of the building. It is interesting to note that although the Hagia Sophia was built as a church, in the 6th century ce, today it is used as a museum, but for approximately five hundred years, after the Ottoman Empire conquered Constantinople, it served as a mosque, for the then Islamic incumbents. The Faculty of Architecture of the Technical University of Istanbul holds a document drawn up by a Åžinasi BaÅŸeÄŸmez, in which he includes exact plans of the Hagia Sophia. With the help of his assistant, Ahmet Alptekin, he was able to discover that Phi had been explicitly used through-out the whole design of the Hagia Sophia. reference1 The figure below, shows an example of these geometrical patterns, which have been used, in the interior space of the Hagia Sophia. Diagram1
This example of ancient architecture demonstrates the use of Golden Numbers, within building construction, perfectly. Another excellent example of this is the Mosque of Rum Mehmet PaÅŸa. This religiously significant structure is also found in Istanbul. Constructed around 1471ce the Greek builder also appears to have used the same unit of length, as was used in the design and construction of the Haga Sophia. This "Byzantine Foot" would now, in today's world, be seen as being 31.23centimetres long. It was divided into sixteen "Fingers" and a metallic rod of this length, believed to have been used by Åžinasi BaÅŸeÄŸmez, and also before him the Ottomans, has been preserved in the TopkapÄ± Museum of Istanbul. Arpat, 2004, describes how with his assistant, he measured the precise dimensions of the Mosque of Rum Mehmet PaÅŸas' exterior width of the Mosque (without porch), the thickness of the walls, the doors and the area around the main-entrance. With these measurements he was able to show that, once again, the Golden Ratio and the Fibonacci Spiral had been major factors involved with producing the architecture of the entire building. reference1 Diagrams2
In Greece itself, the most well known building in Athens is the Parthenon. This testament to the ingenuity of the Ancient Greeks is yet another example of where the Golden Ratio is used repeatedly, in almost all aspects of its design. Built around 440ce, Pythagorean Geometry, as well as the Fibonacci Sequence can be seen to have been utilised in the core 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 plans in his book, The Secret of Ancient Geometry and its Use (Vol. 2, 1967) analyses these plans and describes the prolific use of these sequences, in the design of the Parthenon's ground-plan. reference5 The front-facade of the Parthenon also displays many charactistics, which use the Golden Ratio. The diagram below displays this: reference6 Diagram3
In England, Golden Numbers can be found in the architecture of many churches. One example of this is Vere Street Anglican Church, London. Built in 1721, architects AyÅŸe and Nigel Walding from Derby, painstakingly measured every dimension of the church. Arpat, in his 2004 book, sets down the procedure that AyÅŸe and Nigel would have used to do this:
- Draw line AB = 636" (1615.122cm)
- Draw a line AC = 4/3 x AB
- Draw a half circle around BC and a vertical from A until D.
AD = = 734.39" (=1865 cm; Diff. 1cm)
- Draw a half circle A with r = AD until intersection E. AE = 734.39"
- Extend AE by 1/5, mark point F.
- Draw a half circle around AF, mark intersection G;
EG = = 328.429"
This is the width of the central nave (= 834.05cm)
- Divide the interior length in five equal sections; these are the width of the bays:
734.392 / 5 = 146.878", mark point H.
- Halve the central nave, mark point K; HK = 164.215"
- Extend HK by 5/7 x HK, mark point L.
- Draw a half circle around LK and a vertical from H until intersection M.
- Draw an arc around H with r = HM until intersection N.
HN = HM = EG = = 138.787" (= 352.75cm)
This is the width of the side naves. The interior width of the church is:
2 x 138.787" + 328.429" = 606", as measured (1538.94cm) reference1
The diagram below should be used as a reference for the instructions, quoted above.Diagram4
This theme of Christians using Golden Numbers, in architecture, can also be seen in St. Johannes Basilica, in Catholic Berlin, Germany. This example was built in 1897 by architect August Menken, who was also involved with the construction of some of the other important churches, in Berlin. Once again it is largely in the ground floor plan, that the Fibonacci Sequence can be found. Diagram5
It can also be shown that the radius of the circular wall behind the altar, and the relationship between the altar, 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 generations, and dispersed through other cultures, by trade routes as they appeared in the Middle Ages. As well as this, the spread of Freemasonry and other religious factions has contributed greatly to the increase in similar methods of architecture, in different parts of the World. Originally, it seems that, the patterns and designs used were created using nature as inspiration. In the modern world of science we are able to more closely, and more accurately, examine nature's artefacts, and it has been seen that these specific number sequences (like the Fibonacci Spiral) can be found almost everywhere. reference7
Bangs, H. and Arch, M. (2007) discuss the findings of the Ancient Greek Thinker, Plato. Plato describes different sets of proportions, stating:
"the three-term proportion as essential knowledge, the knowledge through which the mind is able to comprehend the world." reference8
Plato claimed that using the methods to find the mean of a three-term proportion, such as a/b = b/c, (which is most commonly used by architects), an understanding of the laws that govern the creation of all things can be formed. A two-term proportion can be expressed as:
As shown previously, in this document, this is the Golden Proportion. reference9
These Golden Numbers, sequences and patterns are probably most noticeable in religiously significant buildings because large architectural projects have, more often than not, been commissioned by religious groups. Religions have, historically, possessed the largest amount of funds for such undertakings. It is common knowledge that religions have many secrets, in order to protect their knowledge of the world, they would only allow certain people to become privy to aspects, such as their architectural techniques and methods.
Religion has always been the mainstay for the guidelines and rules, of different societies. Taxes upon the general population, connected with a particular religious building, were common in days gone-by. Both in the form of offerings to deities, and payments for (as Christians might say) "shepherding their flock", goods, money and food items were, and still are, commonly given to these religious 'benefactors'. This is how the Church and other religious cultural leaders harnessed the largest amounts of power and money, in whole kingdoms and across continents.
Ancient Grecian times seem to be an exception. It has been documented that here, most of the "Thinkers", in Ancient Greece, focused their attentions upon mathematics and lay-down our first laws, instructions and rules, which govern the worlds of science, engineering and the universe. These early Mathematicians and Structural Engineers were mostly taught at UNIVERSITY NAME, in Egypt, where they were able to study many buildings which were already thousands of years old. reference10
Notable Grecian Thinker, and Mathematician, Pythagoras, was taught in many Egyptian Temples, like NameOfTemple. He was also a Mason and so when he returned home, it was prohibited for him to relay the secret instruction that he had been taught in Egypt, to anyone else. Pythagoras taught along different avenues of geometry and instructed "non-initiated Greek students" in this new methodology. reference11
Schwaller de Lubicz, in his 1981 publication, was able to recreate the approach that Pythagoras used in applying his geometric methods to architecture. These two tomes, The Temple of Man, discuss Pythagorean Theorems in great detail, however they do not delve deeply into the "Lost Knowledge of the Ancient Egyptians" it is necessary to study other resources to gain this information. reference "The Temple of Man".
It is widely recognised that the Christian Bible has been translated many times, from and into many different languages. Translations can rarely be exact and the meaning of certain phrases is often lost during conversion, from one language into another. One example 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." reference King James Bible, Gospel of Saint John
As Bangs and Arch, 2007, explain:
"The translator, working in the time of King James, chose to use word for the Greek 'logos'. Logos implies an active principle and would be more accurately translated as 'verb'. What, then, is the word, or verb, of which St John has written? According to the anthropocosmic understanding, it can only be the marvellous transforming power of Phi (Ð¤), the Golden Proportion." reference9