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Further Cube geometry in Nature

The Golden Ratio, and the Golden Rectangle

We obtain an approximate golden rectangle by adding squares together in a rotating pattern. It's a 4-corner rotation with 4-corner squares.

Cubic 4-corner-quadrant division. Squares, larger and larger, are added to each other to form a Golden Rectangle and a golden mean.

The more times this process is repeated, the closer the rectangle approaches to a perfect golden ratio.

What is the golden ratio?—It exists as the ratio of the long side to the shorter side of a golden rectangle.

Also, note the side-lengths of the squares. If we start with 1, the series is as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34... etc. This is the Fibonacci series.

Now, in the converse of the previous diagram...

A golden rectangle is divided repeatedly with the division whereby it is divided into a square and a smaller golden rectangle, adjacent to each other.

...we begin with a perfect golden rectangle, subsequently dividing it. On each division, we divide the golden rectangle into a square and a smaller golden rectangle. We then take the smaller one and divide it the same way. We do this in a rotating pattern, such that the divisions correspond to a golden spiral.

And now, a diagram illuminating the Fibonacci series:

Illustration of the Fibonacci-series, illustrating it using branching paths with nodes

Cube matrix

It's easy to represent horizontal and vertical lines in a grid.

In a grid here, we see a horizontal line and a vertical line.

But what about diagonals?—Here's how we represent them:

A diagonal movement occurs through alternating movements horizontally and vertically

A similar representation is achievable within a 3D matrix:

A diagonal movement across a 3D matrix occurs by alternating forwards, upwards and depthwards motions

Maybe the universe, at its lowest level of quantisation, forms a cubic lattice like this one. Could be a different structure, though. All we know is that the universe's full geometry is inherently Cubic.

Diagonal through the matrix

It's the universe's inherent cubicity that no doubt causes the prevalence of structures that are in the form of platonic solids. We take a cube—perhaps a cell from the 3D cube-matrix proposed above—and flatten it along one of its diagonals:

A diagonal of the Cube, passing through the centre of the cube, and through two of the Cube's vertices

This leads us to the Metatron's Cube figure, shown below.

The geometrical figure of Metatron's Cube

For further details on this, see the emotion tetrahedron subpage covering the subject of Metatron's Cube.

Opposites create Opposites. Mom & Dad opposites create son & daughter opposites. Opposite Creators required, Depicted by Earth's opposite hemispheres. Singularity God impossible. Opposites de-god  Religion. Opposites create the universe. Opposites compose the Earth. Opposites compose humanity. Opposites create your body. Opposites de-god academia. Opposites de-god singularity taught by religious/academia.
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