Order Pocket Fold Envelopes

PHI = 1.618 ..... Φ φ


SACRED GEOMETRY

The harmonic proportions of certain geometric shapes seem to be able to show us certain laws that govern the creative processes of nature.


The Golden Ratio The golden ratio, phi = 1.618 ... (Indicated by the Greek letter PHI) is an irrational number with many curious and mysterious properties:

1 - In the line.
There is one point that divides a line into two segments so that the entire
is the largest segment as the segment is more to the child.
Full = Major = 1.618 ... PHI =
Major minor
2 - In the rectangle
Take a rectangle with sides in golden ratio PHI PHI = 1.618 = AB

AD
If we draw a square inside the rectangle will have less remaining sides in golden ratio
AD = 1.618 PHI = AE

This operation, defined as "recursion", can be repeated a infinite number of times and always get the rectangles with sides in the golden ratio. With a similar process, but the opposite, we can create larger rectangles and the golden ratio PHI would use on a scale of expansive. We can thus see how PHI is a natural harmonic proportion that recreates itself with each successive step.



3 - The Pentagon and Pentangolo
Given a pentagon Regular ABCDE (fig 1) with equal sides and equal angles, draw a diagonal AC combining any two vertices of the pentagon.



dividing the length of the diagonal AC to the length of a side AB, and we value PHI = 1.618 ... Now, draw a second diagonal BC inside the Pentagon. Each diagonal is divided into two parts, and each is related to PHI with each other and with the whole diagonal. By drawing all diagonals of a pentagon, they will form a five-pointed star, or pentangolo, in which appears the Pentagon will be reversed in the golden ratio PHI with the first pentagon!
now Draw the diagonals in the pentagon small inverted to create a new star within which there will be a small pentagon, this time with the point upward.
You can continue to draw diagonal indefinitely. Not only is the golden ratio, PHI, but also forms occur in each step.

Imagine:
infinitely harmonic forms: what kind of vibration waves generated? What
waves / sound generated harmonic forms as the Pentagon and the pentangolo?



The Golden Spiral

Mysteriously, PHI reappears exactly after some numbers of the Fibonacci series (the thirteenth-century Pisan mathematician): 1 1 2 3 5 8 13 21 34 55 89 144 ... in which each number after the second is the sum of these two and the ratio of each number with the previous one gradually converges to a limit of around 1.618 (which is the golden ratio PHI!).

If we transform the sequence of numbers in a series of diagonals that the result is a Fibonacci spiral, which often reappears in the building schemes of nature.
Recently, a French mathematician Jean Claude Perez, confirmed the nature of perfection of the DNA in it architecture of thousands of sequences obeys exactly the Fibonacci series.