- An approximate value of this number is 1.618 033 989.
- The golden ratio is sometimes called the
.**divine proportion** - This number is generally represented by the Greek letter φ (
*phi</em).*

### Example

The golden ratio is the algebraic number that is the real positive root of this equation:

\({x^2}\space – x\space – 1 = 0\).

This root is:

\(x_{1}\) = \(\dfrac{1 + \sqrt{5}}{2}\)

Its approximate value is:

\(1.618 033 989\).

### Historical Notes

The golden ratio was studied by artists in Antiquity, especially the sculptor Phidias, hence the choice of the Greek letter *phi* to refer to this number. This ratio can be found everywhere in the universe, from the arrangement of branches around the trunk of a tree to how some seashells grow to the specific shapes of some fruits.

For example, if we have line segment *AB* on which a point *C* is chosen so that \(\dfrac{m\left(\overline{AB}\right)}{m\left(\overline{CB}\right)}=\dfrac{m\left(\overline{CB}\right)}{m\left(\overline{AC}\right)}\), this proportion expresses the divine proportion or the golden ratio: 1.618 033 989 …

This proportion is found in the dimensions of the Parthenon’s facade high up on the Acropolis in Athens, in the Fibonacci sequence, in geometric shapes like a regular pentagonal star, etc.