Up until this point, geometrical principles have been referred to in the general sense of the term. Although it has been necessary to do so, it may have been too conceptual to gain a greater understanding without a more intimate investigation. Therefore, it is deemed imperative to take a closer, albeit, brief look at what these harmonic principles are and how they were/are used in architecture. Their individual definition may allow for a wholistic understanding and interpretation of the "universal laws" referred to previously. And from which should come a better comprehension of the specific principles that, ultimately, comprise of "sacred geometry".

The so-called Golden Section

The so-called "golden section", or phi, is but one of the many mathematical "natural phenomena". West postulates that the golden section controls the proportions of innumerable living organisms. "...the spiral of the 'spiral galaxy' is a phi spiral, that the orbits of the planets of our solar system are in complex phi relationships to each other, and that the proportions of Gothic cathedrals and Greek temples are commanded by phi." (West, p. 62, 1993)

The are numerous other instances that can be referred to in architectural design to witness is usage. Its proportion can be obtained without tools of measurement. One simply takes half a square and, with a compass, draws from the point of the top of the square (equivalent to 1) to the base line (this number is the .618... which equals the 1.618... or the so-called golden section). The width of the compass is the length of the bottom, left corner of the rectangle (created by dividing the original square) to the right, top corner. Peter Smith has this to say about it:

When considering harmony in architecture, we first think in terms of mathematical proportions, in particular the golden section (phi) and the related (so-called) Fibonacci series. Phi has proven to be the most durable proportion across time and space, defining the limits of the front of the Parthenon, the Taj Mahal and (less obviously) the interior of the Cathedral of Charteres.

This statement suggests the relative importance of the golden section according to Smith. De Lubicz theorizes that the golden section derives from the averages established from the measurement of the human body. Here, he asserts that the navel divides the total height of the body in the proportion of phi to 1. Also, he states that "the value of phi, or the Golden number, corresponds to the proportion c/b = b/a when C = a + b." (de Lubicz, p. 39, 1977) This function is translated as 1.61803395... Futhermore, de Lubicz suggests that "the golden number is not the product of mathematical imagination but the natural principle of the laws of equilibrium." (de Lubicz, p.42, 1977) Similarly, Pennick makes reference to Plato and his relationship with phi. He states: "Plato, in his Timaeus discussed it as the key to the physics of the cosmos." (Pennick, p. 28, 1980) Pennick also refers to Le Corbusier's modular system to have been a proportion based upon this ratio.

Here, one has a glimpse of the golden section and its relative importance to certain scholars. Its alleged connection to certain "universal laws" are mentioned, as well as its all too familar use in architectural design. De Lubicz asserts that "the Golden Number does not act solely as a function of an ideal proportion, but serves as teh basis for a philosophy that makes the connection between the metaphysical state and the physical state."(de Lubicz, p. 66, 1977) It is from this that de Lubicz believes the "sacred" characteristic of its function exist. He goes further in suggesting that the human body develops in terms of this number. Again, these statements respond to the alleged connection between the golden section and "universal laws".

However, the golden section is but one of a multitude of functions which exist. Many of these devolve from the golden section itself. The so-called Fibonacci series is one of these functions. Its construction is as follows. In the proportionate series of whole integers, the "harmonic progression develops where in the next term is the sum of the two previous terms, i.e., 1, 1, 2, 3, 5, 8, 13, 21, 34 and so on. It relates to the golden section due to the division of one number by the previous one it the sequence. The number which results from this division relates to the 1.618... which is the golden section. The larger the numbers in the sequence, the closer the resultant is to the golden section.

The deemed importance of the so-called Fibonacci Series is as Pennick explains. He expresses that it "has long been recognized as a principle occurring in the structure of living organisms, and thus as a principle inherent in the structure of the world." (Pennick, p. 28, 1980) If, indeed, it is an intergral part of nature, then its usage extends the speculated "universal laws" that it follows.

Assuming the above is true, proportion and harmony would, therefore, be embedded in any design where these geometric principles are used appropriately. Reinterating the perceived importance of the golden section, de Lubciz says that "the Golden Number is not a product of mathematical imagination but the natural principle of the laws of equilibrium." (de Lubicz, p.42, 1977) Perhaps then, the architectural artifact would embrace an essence of "unity" by allowing these geometric principles to flourish within its "soul".