iPhone version:

## Golden ratio - φ(phi)

In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one.
The golden ratio is an irrational mathematical constant, approximately 1.6180339887.
Mark Barr (20th century) suggests the Greek letter phi (φ), the initial letter of Greek sculptor Phidias's name, as a symbol for the golden ratio.

Ancient Greek mathematicians first studied what we now call the golden ratio because of its frequent appearance in geometry. The division of a line into "extreme and mean ratio" (the golden section) is important in the geometry of regular pentagrams and pentagons. The Greeks usually attributed discovery of this concept to Pythagoras or his followers. The regular pentagram, which has a regular pentagon inscribed within it, was the Pythagoreans' symbol.

Euclid's Elements (Greek: Στοιχεία) provides the first known written definition of what is now called the golden ratio: "A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less." Euclid explains a construction for cutting (sectioning) a line "in extreme and mean ratio", i.e. the golden ratio. Throughout the Elements, several propositions (theorems in modern terminology) and their proofs employ the golden ratio. Some of these propositions show that the golden ratio is an irrational number.

Other terms encountered include extreme and mean ratio, medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut, golden number, and mean of Phidias.  Source: Wikipedia

This application allows you to see and discover harmonious dimensions and forms using the golden ratio proportion visually over your preffered photo, directly from your device camera or photo gallery, any time, anywhere you are...!

### Help

#### How to use

Several sample projects are included (you can modify the sample projects and you can save them as projects).

Here is how you can make your own project:
• Step 1: Tap on New Project icon or "New Project" from the main menu.  Insert an image from your photo gallery or camera(if your device supports it). Modify its scale or angle.
• Step 2:  Apply a grid, a line or a Fibonacci spiral over the inserted image. Modify its scale or angle.
• Step 3:  Modify the properties of the shape(for grid & line only)
• Step 4:  Save your project for later use or export it as an image to your photo gallery

#### Buttons

 Shows main menu (New project/Projects[Open/Delete] /Samples/Help/About) Creates a new blank project. Then you have to insert an image ( from the camera or from photo gallery) and a Golden Ratio Grid , Line or a Fibonacci Spiral. Save current project. Exports current project as an image to your photo gallery Inserts a Golden Ration Grid into the current project. Inserts a Golden Ration Line into the current project. Inserts a Fibonacci Spiral into the current project. (double tap the inserted spiral to flip it) Locks/Unlocks current size, angle and position of the Golden Ratio Grid or Line or the Fibonacci Spiral Locks/Unlocks current size, angle and position of the inserted image Inserts an image from the photo album Inserts a new photo from the camera(for iPhone version) Shows/Hides toolbars The following buttons can only be used with Grid and Line shapes, not the Fibonacci spiral. Adds a new vertical line according to Golden Ratio Takes away the last vertical line of the Golden Ratio Grid or Line Adds a new horizontal line according to Golden Ratio Takes away the last horizontal line of the Golden Ratio Grid or Line 3 states button: - Disabled - Converts current shape(Grid or Line) to a symmetrical shape (x axis-decreased) - Converts current shape(Grid or Line) to a symmetrical shape(x axis-increased) 3 states button: - Disabled - Converts current shape(Grid or Line) to a symmetrical shape(y axis-decreased) - Converts current shape(Grid or Line) to a symmetrical shape(y axis-increased)