The Phi Ratio In 2-Dimensions: Intro
Although we can visualize the golden ratio as a golden sectioned line, a line is only one dimensional (a one-dimensional image).
When we visualize (or “see”) things we see essentially in 2 dimensions.
Interestingly, the Golden Sectioned Line can duplicate itself not only in 1-Dimiension – but in 2-Dimensions as well.
And there, even more remarkable things occur:
The Phi Ratio In 2-Dimensions:
SEE GRAPHIC ANIMATION ABOVE
The Golden Sectioned Line
If we start with the original line sectioned into the “Golden Sectioned Line”
The Golden Acute Triangle
We can duplicate the larger part of the line and fold it up and over to form:
The Golden Acute Triangle
The Golden Obtuse Triangle
We can then duplicate the smaller part of the line and rotate it up on the right of the inside of the Golden Acute Triangle to form:
The first Golden Obtuse Triangle
We can then duplicate the smaller part of the line and rotate it up on the left of the inside of the Golden Acute Triangle to form:
The Second Golden Obtuse Triangle
The Golden Pentagon
We can then fold both of the Golden Obtuse Triangles from the inside to the outside of the Golden Acute Triangle and this forms (with the Golden Acute Triangle inside it):
The Golden Pentagon
The Golden Star Pentagon
We can then rotate the left side of the Golden Acute triangle from one vertex (or point) of the Golden Pentagon to another to include all of the vertices to form:
The Golden Star Pentagon
The Golden Double Star Pentagon Complex
The Golden Star Pentagon can then duplicate itself, turn 180 degrees (i.e. turn around or mirror image itself) and then re-merge with itself – forming:
The Golden Double Star Pentagon Complex
The Golden Double Star Decagon
Connecting the vertices (or points) of the Golden Double Star Pentagon Complex forms:
The Golden Double Star Decagon
The “Golden Decagon Matrix”
Finally connecting all the vertices (or points) of the Golden Double Star Decagon with all it’s other vertices forms:
The Golden Decagon Matrix
THE GOLDEN DECAGON AND THE “GOLDEN ELEMENTS”
The Golden Decagon Matrix is the most complete 2-dimensional structure formed from the Golden Section.
It contains and includes all of the 1-dimensional and 2-dimensional geometric “Golden Elements” formed from the Golden Sectioned Line, and used in the construction of the complete Golden Decagon Matrix.
These Golden Elements Include:
The Golden Sectioned Line
The Golden Acute Triangle
The Golden Obtuse Triangle
The Golden Pentagon
The Golden Decagon
Each of these “Golden Elements” were used in the progressive creation of the Golden Decagon Matrix and each of these individual elements can still be seen in the final constructed geometric figure of the Golden Decagon Matrix.