Geometry can be referred to in the "sacred" sense as the realm of irrational numbers which derive from nature. More than just shapes such as rectangles, squares, circles, etc., "sacred geometry" makes explicit those fundamental mathematical laws and principles which govern nature. Wittkower asserts that Plato, following in the tradition of Pythagorus, "in his Timaeus explained that cosmic order and harmony are contained in certain numbers." (Wittkower, p.105, 1988) He also states:
Probably continuing Egyptian usage, Pythagoras applied theoretical findings to natural phenomena and discovered wonderful and unexpected regularities and relationships. His observations led him to believe that certain ratios and proportions embodied the absolute truth about the harmonic structure of the world. (Wittkower, p. 147, 1988)
Seyyed Hossein Nasr makes reference to the relative importance of "sacred geometry" in the preface to Keith Critchlow's Islamic Patterns: An Analytical and Cosmological Approach. Although his relationship of "sacred geometry" is through Islam, one can still extract useful notions as to its importance, especially in the religious world. He asserts:
There is within the spiritual universe of Islam a dimension which may be called "Abrahamic Pythagoreanism", or a way of seeing numbers and figures as keys to the structure of the cosmos and as symbols of the archetypal worlds and also a world which is viewed as the creation of God in the sense of Abrahamic monotheisms.
Here, we have the general description of "sacred geometry" and its relative importance to certain scholars. Judging from their interpretations, there exist an unseen connection between the universe, as well as those things that fall under its domain, and "sacred geometry". The possibility of this "invisible relationship" makes available the coexistence of a cosmic, universal order and harmony within nature. Again, the common denominator being those numbers consistently found within nature being the "gateway" towards the understanding of this relationship.
Relationship to the Universe and Nature
It has been mentioned that "sacred geometry" is found within numerous aspects of nature. One example of this link is in the growth of plants. Ardalan and Bakhtiar explain how the grow of a plant relates to the harmonious, rhythmic progression of the so-called Fibonacci series. The stem of a plant rotates as it grows. As it climbs during its growth, the spiraling relates to the fraction of a complete rotation, from one leaf to the next, around the stem. The fraction of growth is proportionate to the so-called Fibonacci series. (Ardalan and Bakhtiar, p. 25, 1973) Many other examples could be referred to here such as the spiral ratio of pine cones. Also, the horns of some animals and certain shells relate to the golden proportion or logarithmic curve. Thus, it can be assumed that the argument of "sacred geometry" and nature's relationship is, indeed, possible.
From these examples, the following becomes increasingly apparent. There is an interconnection between the universe and nature with harmony and proportion. If so, it becomes possible that harmony and proportion are the fundamental "laws" which govern the grand "cosmic order" within the universe. They allow for the general comprehension of the assumed "universal order". This suggested theory is extended to the architectural expression via the use of "sacred geometry" which are spefically inherent in nature. De Lubicz asserts that proportion belongs to geometry and harmony. "Proportion is the comparison of sizes; harmony is the relationship of measures; geometry is the function of numbers." (de Lubicz, p. 61, 1977)
Thus, one can postulate as to whether the basic, underlying principles of the universe are all the same. If they are, then an analogy can be drawn from one relationship to the next. We see in living organism, in some form or fashion, a cyclical nature. "...the cycle of fertilisation, birth, growth, maturity, senescence, death, and renewal is common to all hierarchies." (West, p.92, 1993) In a similar tone, Wittkower provides an insightful perspective. Here he concludes that "...the Renaissance attitude to proportion was determined by a new organic mathematical approach to nature in which everything was related to everything by number." (Wittkower, p. 152, 1988) Within this everything is related to everything approach is the ordering principle of hierarchies. If true, these hierarchies provide a further inter-relationship to the natural order of things. Again, West asserts:
Individual man is a hierarchical organism, or unity. He is part of a higher organism or unity: mankind. Mankind is part of organic life, which is part of earth, which is part of the solar system, which is part of our glaxay. Each represents a higher hierarchy or realm, with inferrable higher degrees of sensitivity and sentience, etc. (West, p. 92, 1993)
Relationship to Man
We can infer, from the above, that man is related to nature as is nature to the universe. Therefore, man is related to, or an analogy of, the universe. As with the universe, man, too, is bound by the underlying principles of geometry which manifest themselves everywhere. Adds de Lubicz, "but if a man constitutes an ensemble, a Unit that has its harmony, he is himself part of a whole. He cannot be born without being in relationship with his environment, and this environment extends as far as the solar system." (de Lubicz, p. 61, 1977) This relationship finally provides a comprehensive glimpse of the cyclicle nature of the natural order and universal continuum.
Relationship to Architecture
In the grand scheme of things, geometry makes itself visible, time and time again, once the outer layers of implicity are uncovered. If geometry is found within so many aspects of the universe, then it is logical to conclude that its use in architecture is just as feasible. If used in architectural design, geometric principles will provide an extension from the harmonious, rhymic, natural order of the universe to the architectural artifact. In a similar fashion, Wittkower states that:
We have already seen that the architect is by no means free to apply to a building a system of ratios of his own choosing, the ratios have to comply with conceptions of a higher order and that a building should mirror the proportions of the human body; a demand which became universally accepted on Virtruvius' authority. As man is the image of God and the proportions of his body are produced by divine will, so the proportions in architecture have to embrace and express cosmic order. (Wittkower, p. 104, 1988)
Just as geometry enables the universal continuum to exist, architecture serves as the edifice from which geometry can extend itself to the man-made world. It has been suggested previously that geometry has continued to display itself in the architectural design. Many cultures have embraced its use to manifest beautiful architectural expressions. Wittkower suggests that "all higher civilizations (classical) believed in an order based on numbers." (Wittkower, p. 146, 1988) He goes on further to assert that geometry was instrumental in Greek and Renaissance aesthetics. He notes how the Renaissance artists and architects believed in an all embracing numerical harmony in terms of the Pythagorean-Platonic tradition. As well, Kemetic architectural design readily utilized geometric principles to articulate the natural order.
We have seen where numerous civilizations of antiquity incorportated geometric principles within their architectural design scheme. This insight allows a full circle return to the universal continuum. The suggested theory that there exist a cosmic or natural order is extended to the architectural expression via the use of these fundamental principles. Thus, incorporated within its confines are the notion of a universal law of harmony, proportion and man. All intertwined within the weaving web of the ever, encompassing universe. Our task now is how to manipulate geometric principles in order to extend this universal continuum to architecture.