**Golden Ratio**

The **golden ratio ** is also called the **golden section** (Latin: *sectio aurea*) or **golden mean**. Other names include **extreme and mean ratio**, **medial section**, **divine proportion**, **divine section** (Latin: *sectio divina*), **golden proportion**, **golden cut**, **golden number**, and **mean of Phidias**.

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 figure on the right illustrates the geometric relationship. Expressed algebraically:

where the Greek letter phi represents the golden ratio. Its value is:

At least since the 20th century, many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing (see Applications and observations below). Mathematicians since Euclid have studied the properties of the golden ratio, including its appearance in the dimensions of a regular pentagon and in a golden rectangle, which can be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has also been used to analyze the proportions of natural objects as well as man-made systems such as financial markets, in some cases based on dubious fits to data.

Read more about Golden Ratio: Calculation, History, Pyramids, Disputed Observations

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### Famous quotes containing the words ratio and/or golden:

“People are lucky and unlucky not according to what they get absolutely, but according to the *ratio* between what they get and what they have been led to expect.”

—Samuel Butler (1835–1902)

“Come live with me, and be my love,

And we will some new pleasures prove

Of *golden* sands, and crystal brooks,

With silken lines, and silver hooks.”

—John Donne (1572–1631)