The Golden Proportion

The Golden Proportion results from the division of a straight line in such a way that the shorter part is to the longer part as the longer part is to the whole. Each ratio equals 0.618:

S/L = L/(S+L)= 0.0618

Linear progressions and surface division by the same number are common in nature both geometrically and arithmetically. The geometrical progressions can be obtained by multiplying each term by 1.618 or dividing by 0.618:

1.000 x 1.618 = 1.618  OR  1.000 : 0.618 = 1.618

1.618 x 1.618 = 2.618  OR  1.618 : 0.618 = 2.618

2.618 x 1.618 = 4.236  OR  2.618 : 0.618 = 4.236

In the arithmetic progression each term is the sum of the preceding two terms:

0.618 + 1.000 = 1.618

1.000 + 1.618 = 2.618

1.618 + 2.618 = 4.236

As can be seen here, the progression using the Golden number is unique because three different methods produce the same results.

Obviously, the Golden Proportion is not the only parameter that defines harmony and therefore beauty. However, numerous studies and experiments have demonstrated that this surface division creates an aesthetic appeal, independently from ethnic or civilization factors.

	The nasal height (A) is related to the maxillary height (B) as 1.000 : 0.618. The sum of nasal height and maxillary height (A + B) are related to the mandibular height (C) as 1.618 : 1.000.
	The mandibular height (C) is related to the maxillary height (B) as 1.000 : 0.618.
	The orofacial height (B + C) is related to the nasal height (A) as 1.618 : 1.000.
	Note that each ratio is 1.618