I would like to create a new version in python as JavaScript is not good enough. If there is anybody out there in the cosmos that knows python and has a keen interest in geometry and the golden ratio and would like to collaborate on the next version, leave a comment or send a smoke signal, carrier pidgeon, bat man sign, smoke me a kipper.
The geometry machine uses a method I call cosmic (±) geometry and allows us to get to the roots of geometry and the triangle, trigonometry and the Pythagoras theorem.
I can then use the code to create moving geometry animations.
The Middle pyramid at Giza. Follow my current progress at folding circles.
The 345 code is fascinating and shows how whole numbers are connected by an elaborate set of geometry.
Then we can see how the 345 triangle is connected to the golden ratio and the double Spiral of Theodorus.
Next we can see how the 345 triangle is connected to the square, equilateral triangle and the infinite spiral. Below we can see the whole numbers 1-10.
Next we see the importance of √5 and how it connects to the square and octagon.
Below the Metallic Means 1-10 and the amazing connection to the golden ratio.
This is just the tip of an infinite geometric iceberg.
The345 triangle was revered by the Egyptians, each side given a divine name.
Also we see the geometry of the 345 triangle in many Egyptian Hieroglyphs.
The middle pyramid (Khafre) at the Giza plateau encodes a 345 triangle.
Basic Numbers using cosmic geometry.
Below the Metallic Means 1-14 showing cosmic (±) geometry and 345 triangle.
This hidden pattern in the Metallic Ratios links the 345 with the Spiral of Theodorus.
Update : Start here to understand the cosmic (±) geometry method.
This gives us the following geometry and the cosmic triangle.
And then completing the geometry and unifying diameter and radius.
And using this method we get the amazing geometry of the folding fish.
There are two different kinds of fish. (square and non-square base)
Folding circles (Beware : everything below this point is old and confusing)
Archive
Using this method we can detail the geometry of a triangle without using trigonometry or the Pythagoras theorem. And that is good.
The Cosmic Equation
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.
Cosmic Geometry
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.
The golden ratio is one of the most interesting cosmic number.
Phi and the 345 Triangle
Phi ratios (circles and squares)
Below we can see how we can use cosmic geometry to generate the Metallic means.
Metallic Means using Cosmic Geometry
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.
Pythagorean Triples using Cosmic Geometry
As we can see the 345 Triangle is very special case of Pythagorean triple.
The 345 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.
345, phi and the platonic solids
Some examples using the cosmic equation of cosmic mathematics
Mathematics Dude 