وابر ِ زرین vâbar-e zarrin
*Fr.: nombre d'or*
If a line segment is divided into a larger subsegment (*a*) and a smaller
subsegment (*b*), when the larger subsegment is related to the smaller
exactly as the whole segment is related to the larger segment, i.e.
*a/b = (a + b)/a*. The golden ratio, *a/b* is usually represented by
the Greek letter φ. It is also known as the *divine ratio*,
the *golden mean*, the → *golden number*, and the
*golden section*.
It was believed by Greek mathematicians that a rectangle whose sides were in this
proportion was the most pleasing to the eye. Similarly, the ratio of the radius
to the side of a regular → *decagon*
has this proportion.
The numerical value of the golden ratio, given by the positive solution of the
equation φ^{2} - φ - 1 = 0, is φ = (1/2)(1 + √5),
approximately 1.618033989. The golden ratio is an
→ *irrational number*. It is closely related to the
→ *Fibonacci sequence*. → *golden*; → *ratio*. |