## Golden Ratio Software For Mac

*04.08.2020*

*by admin*

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## Discover the “very secret science” that takes design from ordinary to extraordinary.

- Oct 22, 2019 Every designer and artist should know about the Golden Ratio. We explain what it is and how you can use it. Page 2 of 4: How to construct a Golden Ratio rectangle. Video editing software: The 17 best tools for 2020. The powerful tool every game designer should own.
- May 15, 2012 Software: PhiMatrix Golden Ratio Software – Design and Analyze. PhiMatrix golden ratio software is a design and analysis software application for Windows and Mac. The PhiMatrix grid system quickly overlays any image in any software on your screen to identify or apply phi proportions in various grid styles, as well as custom user-defined ratios.

Most of these grids were created with a software app I developed called PhiMatrix. The concept is simple: Every line is in a golden ratio to the ones on either side of it. Once you understand the concept, the applications are endless. You can try it for free below. Windows Control Window: Mac Control Window: Apply the Golden Ratio in any kind. 32 or 64 bit Windows® XP, Vista, 7, 8, 8.1, 10 are supported. Mac OS users can try to use it with PlayOnMac. Program works also in a portable mode. To uninstall use standard Windows settings: Start → Settings → Apps & features. Click the Atrise Golden Section icon and then click Uninstall. May 27, 2020 The 3.1.5 version of Golden Ratio is available as a free download on our software library. The software lies within Photo & Graphics Tools, more precisely Converters. The following versions: 3.1, 3.0 and 2.0 are the most frequently downloaded ones by the program users.

There are many articles on using the golden ratio in design and composition. Most present it as just a more natural and elegant alternative to the rule of thirds, and leave it at that. Some overlay a golden spiral to illustrate an image’s golden ratio proportions. Very few even scratch the surface of how experts use nature’s “secret of design” to achieve an overall visual harmony in their creative works. This one insight can make the difference between ordinary and extraordinary.

The masters of Renaissance art knew it well. Luca Pacioli, in his collaboration with Leonardo da Vinci, described his book “The Divine Proportion” as revealing a “very secret science.” It’s long been used by artists, designers, photographers and architects to achieve aesthetics in design that are natural and innately pleasing. Even the new Google search page, logo and icons are based on a simple, yet savvy, application of the golden ratio. The designers simply followed the concept of using the “ratios within ratios” that create beauty in nature, and excellence in design.

## Experience it for yourself for free.

As you explore this site, you’ll find numerous illustrations that have various grid patterns that unveil and analyze golden ratio proportions. Most of these grids were created with a software app I developed called PhiMatrix. The concept is simple: Every line is in a golden ratio to the ones on either side of it. Once you understand the concept, the applications are endless. You can try it for free below.

Windows Control Window:

Mac Control Window:

## Apply the Golden Ratio in any kind of design

PhiMatrix is used by thousands of artists, architects, designers, photographers, medical professionals, market analysts and others in over seventy countries. I’m amazed by the rave reviews it gets from my customers, some who say they couldn’t do what they do without it. Here’s what some of them have said:

“As soon as I used the trial for 5 minutes, it got a place in my iMac’s dock.”

“I’m having a blast utilizing these magical grids in my graphic design work. What a blessing.” (Mike A.)

“Love the app. Using it to edit my photos often results in striking improvement.” (Warren L.)

“I think that it is perfect the way it is. I love how it is there when I need and not intrusive when I don’t. Very much like a tool instead of software.”

“This is an amazing tool, so powerful, thank you for providing this and at such a humble cost.”

“Products like this should be taught in schools.”

“How could you use this fundamental principle of design? Compositions for photography, interior decorating, maybe a new business card? For about $20, PhiMatrix Software is insanely fun and helpful.”

“Great tool to help with compositional decisions.”

“I love that it aids me in placement and in making my images more appealing. Top notch.”

## My invitation to you to try PhiMatrix for free

My goal is to help you to better appreciate the beauty and design in the world around you, and to apply the same principles of design found in nature in any of your own creative pursuits. I invite you to try PhiMatrix for yourself. There’s a two week free trial available for either Windows or Mac. Try it and learn from the free examples and tutorials.

It can unveil a new look at nature and the arts, and open some new doors to the way you approach any kind of design or composition. I appreciate your interest in the golden ratio, and hope you will take a look at PhiMatrix, to learn more about the application of the golden ratio and perhaps to join the other enthusiastic users who love what it allows them to do.

Gary Meisner

Author, Phi 1.618: The Golden Number at www.goldennumber.net

Developer, PhiMatrix Design and Analysis software at www.phimatrix.com

## Download your free trial copy and enhance your design now!

Click on the icon for your OS below to download and install.

Windows XP / Vista / 7 / 8 / 10 | Mac OS X 10.7+ |

.exe file .zip file | .dmg file .zip file |

- Follow the prompts to complete the installation.
- No credit card or personal name or address information is required for the free trial.
- If you have any installation problems contact technical support via the Contact page.
- PhiMatrix is then ready to use and will open displaying the Control Window and overlay grid as shown below.

## PhiMatrix Software Demo

## Award-winning photo composition using the Golden Ratio

The golden ratio *(symbol is the Greek letter 'phi' shown at left)*

is a special number approximately equal to 1.618

It appears many times in geometry, art, architecture and other areas.

## The Idea Behind It

We find the golden ratio when we divide a line into two parts so that: the long part divided by the short part the whole length divided by the long part |

Have a try yourself (use the slider):

## Beauty

This rectangle has been made using the Golden Ratio, Looks like a typical frame for a painting, doesn't it?

Some artists and architects believe the Golden Ratio makes the most pleasing and beautiful shape.

Do **you** think it is the 'most pleasing rectangle'?

Maybe you do or don't, that is up to you!

Many buildings and artworks have the Golden Ratio in them, such as the Parthenon in Greece, but it is not really known if it was designed that way.

## The Actual Value

The Golden Ratio is equal to:

Download podcast episodes on Mac. In the Podcasts app on your Mac, search to find podcasts, or click an item under Apple Podcasts in the sidebar on the left. Do one of the following: Control-click an episode, then choose Add To Library. In the Podcasts app on your Mac, click Listen Now (or any item) in the sidebar. Hold the pointer over the show or episode you want to play, then click the Play button. When the episode plays, you see the playback controls at the top of the Podcasts window. Do any of the following with the playback controls.

**1.61803398874989484820.. **(etc.)

The digits just keep on going, with no pattern. In fact the Golden Ratio is known to be an Irrational Number, and I will tell you more about it later.

## Formula

We saw above that the Golden Ratio has this property:

*a***b** = *a + b***a**

We can split the right-hand fraction like this:

*a***b** = *a***a** + *b***a**

*a***b** is the Golden Ratio φ, *a***a**=1 and *b***a**=*1***φ**, which gets us:

So the Golden Ratio can be defined in terms of itself!

Let us test it using just a few digits of accuracy:

With more digits we would be more accurate.

## Calculating It

You can use that formula to try and calculate φ yourself.

First **guess** its value, then do this calculationagain and again:

- A) divide 1 by your value (=1/value)
- B) add 1
- C) now use
*that*value and start again at A

With a calculator, just keep pressing '1/x', '+', '1', '=', around and around.

I started with 2 and got this:

value | 1/value | 1/value + 1 |
---|---|---|

2 | 1/2 = 0.5 | 0.5 + 1 = 1.5 |

1.5 | 1/1.5 = 0.666.. | 0.666.. + 1 = 1.666.. |

1.666.. | 1/1.666.. = 0.6 | 0.6 + 1 = 1.6 |

1.6 | 1/1.6 = 0.625 | 0.625 + 1 = 1.625 |

1.625 | 1/1.625 = 0.6153.. | 0.6154.. + 1 = 1.6153.. |

1.6153.. |

It gets closer and closer to φ the more we go.

But there are better ways to calculate it to thousands of decimal places quite quickly.

## Drawing It

Here is one way to draw a rectangle with the Golden Ratio:

- Draw a square of size '1'
- Place a dot half way along one side
- Draw a line from that point to an opposite corner

- Now turn that line so that it runs along the square's side
- Then you can extend the square to be a rectangle with the Golden Ratio!

(Where did ** √52** come from? See footnote*)

## A Quick Way to Calculate

That rectangle above shows us a simple formula for the Golden Ratio.

When the short side is **1**, the long side is ** 12+√52**, so:

The square root of 5 is approximately 2.236068, so the Golden Ratio is approximately 0.5 + 2.236068/2 = 1.618034. This is an easy way to calculate it when you need it.

**Interesting fact**: the Golden Ratio is also equal to **2 × sin(54°)**, get your calculator and check!

## Fibonacci Sequence

There is a special relationship between the Golden Ratio and the Fibonacci Sequence:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ..

(The next number is found by adding up the two numbers before it.)

And here is a surprise: when we take any two successive *(one after the other)* Fibonacci Numbers, **their ratio is very close to the Golden Ratio**.

In fact, the bigger the pair of Fibonacci Numbers, the closer the approximation. Let us try a few:

B | B/A |
---|---|

3 | 1.5 |

5 | 1.666666666.. |

8 | 1.6 |

13 | 1.625 |

.. | .. |

233 | 1.618055556.. |

377 | 1.618025751.. |

.. | .. |

We don't have to start with **2 and 3**, here I randomly chose **192 and 16** (and got the sequence *192, 16, 208, 224, 432, 656, 1088, 1744, 2832, 4576, 7408, 11984, 19392, 31376, ..*):

B | |
---|---|

192 | 0.08333333.. |

16 | 13 |

208 | 1.07692308.. |

224 | 1.92857143.. |

.. | .. |

7408 | 1.61771058.. |

11984 | 1.61815754.. |

.. | .. |

## The Most Irrational ..

I believe the Golden Ratio is the **most**irrational number. Here is why ..

We saw before that the Golden Ratio can be defined in terms of itself, like this: | |

(In numbers: 1.61803.. = 1 + 1/1.61803..) | |

That can be expanded into this fraction that goes on for ever (called a 'continued fraction'): |

So, it neatly slips in between simple fractions.

Note: many other irrational numbers are close to rational numbers (such as Pi = 3.141592654.. is pretty close to 22/7 = 3.1428571..)

## Pentagram

No, not witchcraft! The pentagram is more famous as a magical or holy symbol. And it has the Golden Ratio in it:

- a/b = 1.618..
- b/c = 1.618..
- c/d = 1.618..

Read more at Pentagram.

## Other Names

The Golden Ratio is also sometimes called the **golden section**, **golden mean**, **golden number**, **divine proportion**, **divine section** and **golden proportion**.

### Golden Ratio Software For Mac Download

## Footnotes for the Keen

### * Where did √5/2 come from?

With the help of Pythagoras:

c^{2} = a^{2} + b^{2}

c^{2} = (*1***2**)^{2} + 1^{2}

c^{2} = *1***4** + 1

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c^{2} = *5***4**

c = √(*5***4**)

c = *√5***2**

### Solving using the Quadratic Formula

We can find the value of φ this way:

^{2}= φ + 1

Which is a Quadratic Equation and we can use the Quadratic Formula:

φ = *−b ± √(b ^{2 }− 4ac)*

**2a**

Using **a=1**, **b=−1** and **c=−1** we get:

φ = *1 ± √(1+ 4)***2**

And the positive solution simplifies to:

φ = *1***2** + *√5***2**

Ta da!

### Kepler Triangle

^{2}= a

^{2}+ b

^{2}

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That inspired a man called Johannes Kepler to create this triangle:

It is really cool because:

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- it has Pythagoras and φ together
- the ratio of the sides is
**1 : √φ : φ**, making a Geometric Sequence.