## Phi

### Divine Proportion and the Golden Spiral

Pleasing shapes, interesting coincidences, existential ramifications, and some mathematics reality... using this unique set of mathematical concepts can create an innate linear balance when used formally for composing your artwork. This is one of those weird places where science interacts with visual aesthetics, philosophy, and the meaning of life. Maybe.

: Phi = 1.618033988749895... The Golden Number, prounounced "fi" as in "fly." In the Golden Rectangle with A as the height and B as the width, the ratio reveals itself: A is to B as B is to the sum of A and B. This number reflects the ratio of unfolding growth found in the structure of living things. If you look you can find it everywhere. Explore the links at the bottom of the page if you dare to try and add things up.
Phi was apparently discerned as fact by ancient observation and calculations. I've read that Phi can be found in the geometry of the Great Pyramids, ancient Greek architecture, the works of Leonardo Da Vinci, Georges Seurat, and other artists, and in the basic three dimensional geometry of reality. Nature offers up clues to its structure and order that only need be observed to be understood.
Like

(Pi) and e, Phi is an irrational number with interesting relationships with the fabric of reality. But unlike Pi, Phi is embeded in the geometry of life and the universe.
Phi was found to be so pleasing that it was deemed an eternal, natural law which is reflected in the use of the term "golden" to describe the number with universal reverence. The Golden Mean, the Golden Ratio, the Golden Section (Rectangle), and the Golden Spiral embody Phi in the visual and natural world.

### The Golden Spiral step-by-step

I'll explain some functional aspects of Phi using the following standard graphic example. You'll have to research the Divine and Golden attributes on math, religion, or philosophy in the library or internet. You can read all about Phi starting with the links at the bottom of this page.

The ratio of Phi is 1:1.618. A rectangle with an aspect ratio of 1:1.618 is of Divine Proportions and is called a Golden Rectangle.

Add another Golden Rectangle within the first at a 90 degree rotation and you start an interesting process.

Continue nesting Golden Rectangles within each other in diminishing sizes at 90 degree rotations until things get small.

Important points of intersection are indicated in each Golden Rectangle and the first arc is plotted.

By connecting the nesting points with the arcs of 1/4 of a circle, sized to fit; you end up with a Golden Spiral.

From the depths of Galaxy M51 to the Nautilus shells on the shore, matter naturally unfolds according to Phi.

### Now Go Explore!