The Phi proportion


A great deal of hoopla has emerged lately with one of the most fundamental constants in nature,a constant which has been known for centuries as the Divine proportion which can be expressed as 1.618033…

My area of study about 14 years ago involved Penrose tiling which have a high Phi content and I am rightly proud of my work which now remains private.

For those who wish to evaluate the Phi proportion along with the Pi proportion (3.1415…) there is much on Mr Knott’s site that is quite good however there is something more I can add.

Begin with a line and add another two lines to create a triangle,another to form a square then a pentagon,hexagon and adding more and more lines moves towards a circle.

The point is that all geometric forms exist between line and circle.

The natural patterns of nature follow a particular geometry associated with the Phi proportion where spirals grow a particular way,branches divide at 137.5 deg and so on.

As a consequence of my work on Penrose tiling and in a similar vein ,I have found that the ideal compromise for representing Pi and Phi simultaneously is 51.84 deg or 51 deg 50 min 36 sec.Those who are good enough will recognise where 51.84 deg shows up as the angle of inclination of the Great Pyramid.

Geometrical progressions such as Penrose tiling 36,72,108 and 144 deg provide the basis for considering 51.84 deg as an umbrella figure for the geometric compromise between the Pi and Phi proportions .

Begin with an approximation of the Phi value - 1.62 and keep doubling it.

A better progression is 25 -30 -36- 43.2 and 51.84 deg (each term multiplied by 1.2)

The great natural mysteries come from recognising the patterns that resonate with us as beautiful music generates the same underlying experience.Our ancestors took to these things without much fuss and often left testaments to their understanding of the patterns that thread their way through natural forms.Today the phi proportion is hijacked by creationists or cryptos while the opposition want everything to be chaos and arbitrary.

Where are the Catholics who recognise that nature works on balances just as our Faith operates on that balance between God and man ?.


Hi Oreal36.

Thank you so much for posting this! I am providing a similar link that is not as good but may be less mathematically daunting to some.

I am an engineer who deals in new product development in a field that requires artistic like aesthetics. I have come to appreciate the aesthetic side of product development and consequently art in general.

Having no prior training in art or aesthetic design I have found it difficult (and mysterious) to understand why something is more pleasant to look at. My industrial designers have helped me out with this to some degree. Warm/Cool colors, consistency of shape and feature, the golden proportion etc.

However, it is always so much more fascinating to see these in Gods creation (Nature) and in mathematics.

I did not recognize that this was the Fibonacci series.

I will take some time to study what you have provided and will hopefully have some comments and questions. Until then:

Thanks again for the post!



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