Following on from Marko Rodin’s cues,we now place the 24 reduced Fibonacci numbers around a circle in 15 degree increments.
We now note that all numbers taken with their 180 degree opposite add or reduce to 9.
Marko Rodin identifies 3 key constructs within the device;
What he defines as two doubling circuits running in opposing directions following the numeric patterning of 1-2-4-8-7-5.
The numeric sequence of the 1-2-4-8-7-5 doubling circuit is highly significant and we will later explore its visible presence in other mathematical constructs such as Pascal’s triangle.
”The Star Tetrahedron, which is the 3-Dimensional form of the Star of David, is the geometric equivalent to the Phi Code expressing precisely the 24ness exhibited in the Reduction or Compression of the Fibonacci Numbers.”
Here we are beginning to see evidence of nacent geometrical structures manifesting from the reduced numbers contained within the sequence.
Following the blue lines on the illustration below we also note that this patterning also gives rise to the first signs of a more evolved 3-dimensional geometric structure,an octahedron.
This octahedron appears to to be set within the outline of a rudimentary cube.
This is interesting viewed from the perspective of the Platonic solids.
According to the Wiki entry on the Platonic solids, ”In Euclidean geometry, a Platonic solid is a regular, convex polyhedron. The faces are congruent, regular polygons, with the same number of faces meeting at each vertex. There are exactly five solids which meet those criteria; each is named according to its number of faces.
The aesthetic beauty and symmetry of the Platonic solids have made them a favorite subject of geometers for thousands of years. They are named for the ancient Greek philosopher Plato, who theorized that the classical elements were constructed from the regular solids.”
Is this construction of the classical elements from the regular solids something akin to what we are witnessing here?
In this arrangement of the five Platonic solids,the cube and the octahedron form a pairing,just like we see in the above illustration.
A cube has 8 vertices,12 edges and 6 faces.
A octahedron has 6 vertices,12 edges and 8 faces.
The two 1-2-4-8-7-5 doubling circuits each form a perfect hexagonal structure as does the doubled 3-6-9 vector.
Thinking about these two 1-2-4-8-7-5 doubling circuits running in opposing directions and the vector,I am reminded of comparisons with the Hermetic Caduceus with its two serpents wound around the staff.
1 4 7=3
2 8 5=6
3 6 9=9
”If you only knew the magnificence of the 3, 6 and 9, then you would have the key to the universe.”
Our 1-2-4-8-7-5 also crops up in a few other places,mathematically speaking.
One notable example I mentioned earlier is the Pascal Triangle,or more accurately the Meru Prastera configuration.
As explained in the above diagram,not only does the Meru Prastera contain the 1-2-4-8-7-5 doubling sequence accessed by counting the value of each horizontal line working top-down,and reducing the numbers by base 9,but it also,by adding up the diagonals and subjecting them to the same reduction schema,provides us with the Fibonacci numbers running in perfect sequence.
More to follow.