Spiral and Sequence

A functional description of the Golden Ratio, The Fibonacci Sequence, Generalizing them and the surprising insight about the golden rule.


The spiral appears everywhere we look, from the formation of galaxies to the structure of our DNA. First we offer an abridged version of the list of places one might look to see this pattern.

The Spiral has been part of Human Knowledge and artistic practices for many millenia. This systems of logic and study extends out of a geometric principle called the Golden Rule.

The Spiral is produced using a simple, arithmetic sequence of numbers. This sequence of numbers is called the Fibonacci sequence and is the mathematical beninnig of our understanding.

The spiral is a symbol of growth and increased complexity in natural systems and uses the logic of the Fibonacci sequence. The Fibonacci sequence produces an emerging ratio of growth, a relationship of proportionality between concurrent elements. This ratio is called the Golden Ratio.

Using the Golden Logic and the Fibonacci sequence, we create a two-dimensional representation plot, which is how the spiral has been articulated expressed for many millenia

The logic of the Fibonacci sequence can be expanded upon and generalised. In doing so, we reveal the underlying use and purpose of these mathematical functions

Gibonacci Sequence provide an arithmetic means of accomplishing a geometric task. The implemetation, on a Universal scale, implies that there is a common behavior among everything in the universe and that behavioor is expressed through the Gibonacci sequences.

As the input variables grow larger and larger, a clear trend appears in the numbers that this sequences generates, and this new and emerging ratio underscores the mathematical behavior and purpose of this system of logic.

Keeping in theme with the above sections, we now reconsider the idea of the Golden Ratio, however expanding our pursuits to contemplate a Golden Ratio for each of the Gibonacci Sequences. The results confirm ideas that we have already contemplated in previous sections.

We began this pursuit by considering the geometric concept called the Golden Rule. We have expanded our system of logic so as to show that these patterns are, in actual fact, a means by which to calculate proportionality and balance. We then assert that this Geometric concept of the Golden Rule is expressing exactly the same idea as the moral maxim of the Golden Rule: Give unto others as you would give to yourself.

Finally, we offer a comprehensive summary of this section, including our findings and a little foreshadowing as to why the workings of this system of logic have, heretofore, been detailed to such an extensive degree.


Thermodynamics, Number Theory and The Goilden Ratio
Creation, Evolution and the Golden Rule
Theory of Order
Why Fibonacci and Gibonacci sequences appear everywhere in nature,
and how simple combinatoric math can describe how a Universe with simple beginnings evolved into a complex form