The golden ratio is a unique number approximately equal to 1.6180339887498948482. The Greek letter Phi (Φ) is used to refer to this ratio. The exact value for the golden ratio is the following:
A popular example of the application of the golden ratio is the Golden Rectangle. Interestingly enough, many artists and architects have proportioned their works to apply the golden ratio in the form of the golden rectangle. A golden rectangle is a rectangle where the ratio of the longer side (length) to the shorter side (width) is the golden ratio If one side of a golden rectangle is N ft. long, the other side will be approximately equal to N(1.62) or N(Φ). One interesting attribute about the golden rectangle is that if you cut a square off it so that what remains is a rectangle, the remaining rectangle will also have the length to width properties of the golden ratio, therefore making it another golden rectangle. What happens is that if you keep cutting squares off, each time you get a smaller and smaller golden rectangle. Leonardo Da Vinci, the famous mathematician and artist from the Renaissance, featured the golden ratio in many of his paintings. For example, lets take a look at the world famous "Mona Lisa". If a rectangle were drawn around her face, the measurements would be that of a Golden Rectangle.