Sacred Geometry Flowers petal count matches the Fibonacci sequence: 3, 5, 8, 13,
21, 34 or 55. In the Fibonacci sequence (fn are given by the formula f1 = 1, f2
= 2, f3 = 3, f4 = 5 and generally f n+2 = fn+1 + fn) each number is obtained
from the sum of the two preceding: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc.
When one observes the heads of sunflowers, one notices two series of
curves, one winding in one direction and one in another; the number of spirals
not being the same in each sense.
Why is the number of spirals in
general either 21 and 34, either 34 and 55, either 55 and 89, or 89 and 144?
Why do they have either 8 spirals from one side and 13 from the other,
or either 5 spirals from one side and 8 from the other?
Why is the
number of diagonals of a pineapple also 8 in one direction and 13 in the other?
The answer to these questions is efficiency during the growth cycle of
The ratio between successive Fibonacci numbers approximates an
important constant called "the Golden Mean" or sometimes phi, which is
approximately 1.61803. The higher you go in the Fibonacci sequence, the more
closely the ratio between two successive numbers in the sequence approximates
phi. (By the way phi2=phi + 1!). The Fibonacci sequence also shows up in
Pascal's triangle, first used by the Chinese mathematician Chu Shih Chieh in
providing coefficients for the binomial expansion in his 1303 treatise "The
Precious Mirror of the Four Elements", if you add the diagonals!
Sacred Geometry involves using
sacred universal patterns in everything we design.
Sacred Geometry as
seen in sacred architecture, sacred art and Nature can be heard in sacred
found that an oscillating string stopped halfway along its length produces an
octave relative to the string's fundamental, while a ratio of 2:3 produces a
perfect fifth and 3:4 produces a perfect fourth.
Pythagoreans believed that
these harmonic ratios gave music powers of healing which could "harmonize" an
The Sacred Geometry of mathematical ratios,
harmonics and proportion were first noted in nature, music, light and cosmology
by the Ancients in poetry, stories, music and art work.
Those who see
the Sacred Geometry of the Pattern of Reality attempt to express their
worldview of pattern recognition with
a complex system of metaphorical allegories by building conceptual structures
initially involving light(good) and darkness(bad) to address all
levels of human
The golden ratio, also known as the god ratio, golden proportion,
golden mean, golden section, golden number, divine proportion or sectio divina,
is an irrational number, approximately 1.618 033 988 749 894 848, that
possesses many interesting properties.
Shapes proportioned according to
the golden ratio have long been considered aesthetically pleasing in Western
cultures, and the golden ratio is still used frequently in art and design,
suggesting a natural balance between symmetry and asymmetry.
Pythagoreans, who defined
numbers as expressions of ratios (and not as units as is common today),
believed that reality is numerical and that the golden ratio expressed an
underlying truth about existence. Plato
said in the Republic (VII, 527 d, e) that it is through geometry that one
purifies the eye of the soul, "since it is by it alone that we contemplate the
truth." Although Plato, for instance,
discusses their importance to both music and esoteric philosophy, he
concentrates on the latter. Thus his discourses do not provide physical
demonstrations of the ratios, for they were not meant as textbooks, but as
"We must endeavour to persuade those who are
prescribe to be the principal men of our State to go and learn arithmetic, not
as amateurs, but they must carry on the study until they see the nature of
numbers with the mind only; nor again, like merchants or retail-traders, with a
view to buying or selling, but for the sake of the soul herself; and because
this will be the easiest way for her to pass from becoming into truth and
being." - Socrates (according to
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American social mores and values have
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bulk of the population has been directed toward solutions proposed by the
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