*Phi: Noun, fI or fee – The 21st letter of the Greek alphabet used to represent the irrational number 1.6180339887…, or 1.618 for short.*

*Matrix: Noun, ‘mA-triks – A surrounding substance within which something else originates, develops, or is contained.*

Whether you look to quantum mechanics or to movies like “The Matrix,” a deeper understanding of reality is unveiled once you understand the matrix upon which it is built. The matrix upon which the proportions of life and the universe is constructed is based on the number known as Phi.

## About PhiMatrix software

PhiMatrix is a graphic analysis and design tool that lets you see and apply phi proportions to any image. It overlays any other program you have on your computer, from digital image editing software to your “My Pictures” folder, and then lets you save your analyzed image to disk.

It’s unique features include:

- Variable proportioning of the grid in height and width that allows application of the copyrighted “Golden Ruler™” and “Golden Grid™” concepts to be applied to images and objects of any dimension. Traditional golden section analysis has used a rectangle with height and width fixed in proportion to phi, or 1.618.
- A grid mirroring feature that allows the grid lines to be independently mirrored vertically on the left and right sides of the grid, and horizontally on the top and bottom halves of the grid. The grid proportions can also be locked into a user sizable golden section in portrait or landscape orientation.
- User selection of the number of grid lines to be shown, with independent selection options for the horizontal and vertical axes.
- User selectable border width outside the grid, especially useful when creating and/or cropping images to be saved to disk.

It can be used for any design application your mind can conceive, whether laying out a canvas for painting, cropping a photo, creating marketing materials or designing everything from clothes to cars to furniture to buildings.

## The Concept behind PhiMatrix

While the Golden Section has been used for centuries, the concept for PhiMatrix is based on an original insight of its developer in 1997 that the Golden Section could be applied in repetition to a line to create a “Golden Ruler™.” Each section of the ruler is in phi proportion to the section from which it came:

The Golden Section analysis is traditionally used with a fixed phi proportion of 1.618 in the height and width. The “Golden Grid” concept applied in the PhiMatrix software allows proportions to be variable in height and width, yet still shows the “golden ruler” sections on both the horizontal and vertical axes.

## Applications of PhiMatrix and the Golden Ratio

Application of these concepts to images of a variety of life forms revealed that their physical dimensions were all based upon the same proportions of design using the number phi. Examples are shown below.

These same proportions have been used by mankind to achieve some of its greatest works of art and architecture.

It’s now being used in design for a variety of applications:

- Automotive design
- Architecture
- Logos and trademarks
- Cosmetic and corrective dentistry
- Reconstructive and corrective facial surgery
- Clothing design
- Hair styling
- Design, layout and composition of marketing and advertising materials
- Photo editing and composition
- Stock market analysis

The Golden Ruler and Golden Grid were first presented in 1997 from http://www.goldennumber.net (and its predecessor site) in the form of a template that could be printed to a transparency and used as an overlay to documents. PhiMatrix expands this concept and capability to digital images.

## About Phi and its unusual properties

Phi ( = 1.618033988749895… ), most often pronounced fi like “fly,” is simply an irrational number like pi ( p = 3.14159265358979… ), but one with many unusual mathematical properties.

The ratio, or proportion, determined by Phi (1.618…) was known to the Greeks as the “Golden Section” and to Renaissance artists as the “Divine Proportion” It is also called the Golden Ratio and the Golden Mean.

Just as pi (p) is the ratio of the circumference of a circle to its diameter, phi is simply the ratio of the line segments that result when a line is divided in one very special and unique way.

Divide a line so that: |

the ratio of the length of the entire line (A) to the length of larger line segment (B)is the same asthe ratio of the length of the larger line segment (B) to the length of the smaller line segment (C).More simply, A is to B as B is to C. |

This happens only at the point where A is 1.618… times B and B is 1.618… times C. Alternatively, C is 0.618… of B and B is 0.618… of A.

Phi with an upper case “P” is 1.6180339887…, while phi with a lower case “p” is 0.6180339887, which is the reciprocal of Phi and also Phi minus 1. Phi is the only number whose reciprocal has a difference in value of 1. Phi can be calculated by adding 1 to the square root of 5 and then dividing the sum by 2.

What makes phi unusual is that it can be derived in many ways mathematically and geometrically and shows up in relationships throughout the universe. Phi appears in the proportions of the human body and face, the proportions of many other animals, plants, DNA, the solar system, population growth the stock market and in many aspects of life and the universe. Our perceptions of beauty in the humans are based on how close facial proportions conform to phi.

Some believe phi is the most efficient outcome, the result of natural forces. Some believe it is a universal constant of design, the signature of God. Whatever you believe, the pervasive appearance of phi in all we see and experience creates a sense of balance, harmony and beauty in the design of all we find in nature. It should be no surprise then that mankind would use this same proportion found in nature to achieve balance, harmony and beauty in its own creations of art, architecture, colors, design, composition, space and even music.

The Golden Section, the phi relationship, has long been used by craftsmen and professionals of many fields to understand and achieve beauty, balance and harmony in their work. Artists, architects, designers, engineers, musicians, photographers, sculptors, surgeons and stock analysts alike use this relationship to achieve excellence in their results.

The study and application of the golden section is now much easier with PhiMatrix software. Put your ruler and calculator away and let the phi relationships just jump out at you as you work or play with the software to bring your work to a new level in any field.

Learn more about phi at the http://www.goldennumber.net, also developed by Gary B. Meisner, the developer of PhiMatrix software.