Using what I call cosmic mathematics, we can (for instance) detail the geometry of a triangle without using trigonometry or the Pythagoras theorem. And that is good.

Based on a simple equation, it adds a level of sophistication to the normal method, giving us a deeper level of understanding. Taking into account the usually ignored negative principle is a bit of a mind-bender, so, patience is a virtue.

We can link this equation with Pythagoras’s theorem.

Adding some more information. Below the 345 triangle and more cosmic geometry.

and more geometry.

More phi.

achieve: The golden ratio is one of the most interesting cosmic number.

Below we can see how we can use cosmic geometry to generate the Metallic means.

Interestingly we can generate the Pythagorean triples, without using the Pythagoras theorem. Below we can see that using cosmic geometry provides us with a lot more useful information when compared with other methods.

As we can see the 345 Triangle is very special case of Pythagorean triple.

The 345 triangle is interesting for many reasons, below we can see its amazing symmetry (platonic solids) and its relationship with the golden ratio.

Some examples using the cosmic equation of cosmic mathematics

And some more advanced cosmic geometry examples.

The Golden ratio is maybe the greatest number, lets explore why?

The golden ratio can be found in both the Hexagon and the Pentagon.

Phi (golden section) triangle and the 345 triangle have a unique relationship.

And in order to understand phi we must look in detail at this relationship. Below showing the most important angles related to the 345 triangle.

This relationship becomes very sophisticated very quickly.

Below we can see the complicated world of phi, showing relationships to many interesting numbers and angles.

Yes it is complicated.

Both the first (GOLD) and fourth (NICKEL) metallic mean is related to Phi.

The metallic means using cosmic geometry. Again phi triangle is mean 1 and 4.

Here we can see that there is also a relationship between the golden ratio and the number sequences (Fibonacci and Lucas).

We can also relate phi to Binet’s formulas, as shown below.

It is because of its unique fractal nature. (incommensurability, phase conjugation, harmonic convergence) Only Phi has this fractal nature.

Below we can see the golden Spiral, along with the golden rectangle. Light and Magnets both share this fractal nature.

Here we can see the symmetry of the magnetic flux lines. (ferro-cell image)

Light and Magnetism both use the magical ratio.

The colours of the visible light spectrum and Phi. This electro-magnetic universe has a favourite number and it appears to be a golden.

A geometrical figure, where each part has the same character as the whole.

They are seen in things like snowflakes in which patterns recur at different scales.

If you know of any interesting phi relationships, please comment.

Art by Ken Wheeler, Dan Winter, Clay Taylor and me.

The Golden Ratio

345 triangle and Metatron’s cube.

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How to fold a Great Pyramid of Giza from a circle.

Simply print out, cut out the circle and fold the dotted lines only.

It is assumed that (x) is always ≥ 1 and the (1/x) is always ≤ 1.

The ‘cosmic’ equation

Linking the ‘cosmic’ equation with Pythagoras.

Linking the ‘cosmic’ equation with trigonometry and the trigonometric functions.

Simplifying the tan relationship.

more stuff

more stuff

The Triangles

The relationship between the red and blue triangles.

More stuff.

Example A

Visualising the triangles using the ‘cosmic’ equation.

Substituting x₁ (from above) into the green triangle.

Scale by x₁ and substitute cos. Using circles to perform square-roots (more information).

Example B

More stuff.

And then..

The amazing mathematics at the root of all geometry.

“Numbers and equations are signs that mark the music of the spheres.” Nikola Tesla

Lets explore some of the most interesting angles.

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Video

Squaring the Circle

A ‘squared circle’ is when a circle and square have equal area, or equal perimeter.

Does the Golden Ratio (phi) define the squaring of a circle. According to some, in ancient Egypt, this mystery was encoded in the mathematics of Giza.

It is well known that the value of pi (3.14) is encoded in the great Khufu pyramid, but when we run the numbers, we find a value for pi that is different to the value on your calculator. Most people think ‘obviously’ that the Egyptians where wrong, with many modern mathematicians claiming it is impossible to square the circle.

What is most interesting about the value encoded at Giza, is that it based on the Golden Ratio, which is the most beautiful number in all the mathematical universe.

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Lets explore. If we use what we learnt from the mathematics of the Giza plateau, we get this ‘self referencing’ equation for pi.

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“The squaring of the circle is one of the many archetypal motifs which form the basic patterns of our dreams and fantasies. But it is distinguished by the fact that it is one of the most important of them from the functional point of view. Indeed, it could even be called the archetype of wholeness.” Carl Jung

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Seems to be a squared circle encoded at Stonehenge.

Mandalas

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Back to The Giza Plateau.

The Menkaure Pyramid

The Menkaure/Mykerinos or small pyramid …

Menkaure (final scaled ratios)

Back to The Giza Plateau.

Back to The Giza Plateau.

The Khafre Pyramid

The Khafre/Chephren or middle pyramid is the key to understanding the geometry and mathematics of the Giza plateau, pointing to the cosmic identity/equation.

The Khafre Pyramid was built according to a 3,4,5 triangle, considered very important by the Egyptians.

The ratios

Scaling the ratios by a half, we can see the the hidden mathematics.

The Cosmic Identity

Khafre points to this cosmic identity, and the relationship to Pythagoras formula.

For each number (x) we have a corresponding right angled triangle.

The link to Pythagoras formula. For Khafre x=2.

We can use this as a key to further understand the geometry of the other pyramids.

Khafre (final scaled ratios)

Back to The Giza Plateau.