## Visualizing the Golden Ratio in 1-Dimension

Phi is only a number – and we don’t really see numbers when we look at things.

However, there is a visual manifestation of Phi and the Golden Ratio – something that we can actually look at and see. It is this manifestation of that Golden Ratio which has been reported to be present in many things that are seen as beautiful.

This is a line which has been divided into two segments, the larger of which has a (magnitude) ratio to the smaller of 1.618:1

## Where a=1.618 and b=1

A line which has been segmented into two parts having this 1.618:1 ratio is called:

A golden cut line

A golden sectioned line

A golden divided line

A Phi cut line

A Phi sectioned line

A Fibonacci sectioned line

This division of a line in such a manner is referred to variously as:

The golden cut

The golden section

The golden division

The Phi cut

The Phi section

The Fibonacci section

## Creating the Golden Sectioned Line:

### Create a line from a point

We create a line of any length.

### Section that line

There are an infinite number or places that we can divide that line into two segments, and we can section (or cut) that line at any point we desire.

### “The Golden Section”

However there is one place (and only one place – a unique place) where that line can be divided or “sectioned” so that the ratio of the smaller segment of the sectioned line to the larger segment of the sectioned line is 1:1.618

This ratio of 1:1.618 is called **“The Golden Ratio”**.

The interesting and remarkable thing about this sectioning of the line into the golden ratio is that not only is the ratio of the smaller segment or the line to the larger segment of the line equal to 1:1.618

*BUT*

the ratio of the larger segment of the line to the whole line is also equal to 1:1.618.

And this particular division, or sectioning, of a line into segments with a ratio of 1:1.618 is called:

“The Golden Section”

**The “Golden Sectioned Line”
**And the line which is cut into the Golden Section is called:

“The Golden Sectioned Line”

**The “Golden Section Point”
**This place or point on the line where this golden sectioning occurs is called:

“The Golden Section Point”

## The Repeating Phi Ratio & Phi Ratio Duplication (Growth):

Intriguingly, if we duplicate that golden sectioned line to form a new longer line, consisting of the smaller and larger segments of the original line plus a duplicate of the original line, then the ratio of the larger segment of the original line to the duplicate of the original line is also = 1:1.618.

If we delete the smaller segment of the original line, we are left with a new line consisting of the larger segment of the original line and the duplicate of the original line.

If we duplicate this new line, then the ratio of the larger segment of this new line to the whole new duplicate is also = 1:1.618.

This self-duplication can continue on to infinity (i.e. forever) with each line segment in a ratio of 1:1.618 with its adjacent and succeeding line segment along the formed line.

This self-duplication never occurs at any other division, section or ratio of any line or line segments. This continuous self-duplication only occurs with the golden section.

Because of its unusual properties, the number “1.618” has been given its own name – that name is “Phi”.