The Golden Proportion
What is 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:
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
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or
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1.000 : 0.618 = 1.618
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1.618 x 1.618 = 2.618
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or
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1.618 : 0.618 = 2.618
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2.618 x 1.618 = 4.236
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or
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2.618 : 0.618 = 4.236
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In the arithmetic progression each term is the
sum of the preceding two terms:
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0.618 + 1.000 = 1.618
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1.000 + 1.618 = 2.618
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1.618 + 2.618 = 4.236
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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.
Golden Proportions have also been found in facial
and dental elements:
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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.
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