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.
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 plants.
The ratio between successive Fibonacci numbers
≈ an important constant, Π.
The Golden Ratio or sometimes
Π, which is ≈ 1.61803.
The higher you go in the Fibonacci
sequence, the more closely the ratio between two successive numbers in the
sequence approximates Π.
Π2 = Π1 +
The Fibonacci sequence shows up in Pascal's triangle,
first used by Chinese mathematician Chu Shih Chieh in providing coefficients
for the binomial expansion in his 1303 treatise "Precious Mirror of the Four
Sacred Geometry involves using sacred
universal patterns of design.
Sacred Geometry is seen in
sacred architecture and
Geometry of Nature can be heard in
Pythagoras 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 in poetry, stories, music and art work.
Those who see the Sacred
Geometry with the Pattern of Reality attempt to express their
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
Shapes proportioned according to the Golden Ratio
aesthetically please Western cultures, and so the golden ratio is still used
frequently in art and design, suggesting a natural balance between symmetry and
The ancient Pythagoreans, who defined numbers as expressions
of ratios (not as units as is common now), believed reality could be expressed
numerical and that the golden ratio expressed an underlying truth about
"This at least,"
said Plato, "will not be
disputed by those acquainted with geometry;
science is in direct
contradiction with the language employed."
"How so?" Socrates said.
"They speak as if they were doing something, as if the words were
directed towards action. For all the talk of squaring and applying and adding
and the like, whereas in fact the real object of the entire study is gnostic
"That is absolutely true," he said. "Must we not agree on a
"That gnostic knowledge always is, always has been and
always will be, not of a something which at some time comes into being and
"That is readily admitted," Socrates said. "
2 + 2 = 4."
"Then nothing is surer," said Plato,
"we must also require the people shall
never neglect geometry, for even the derivatives of such study are not slight."
"What are they?" said he.
"In all studies there is an
immeasurable difference between the student who has been imbued with
understanding geometry and the one who has not."
"Shall we, then, lay
this down as a second branch of study?"
"Shall we set down astronomy as
a third, or do you dissent?"
"I certainly agree," Socrates said; "for
quickness of perception about the seasons and the courses of the months and the
years is serviceable, not only to agriculture and navigation, but still more to
the military art."
"I am amused," said
Plato, "at your apparent lack
of fear lest the multitude may suppose you to be recommending useless time
Platonic dialogues defined the literary genre of
Plato's dialogues are not meant as
endeavour to persuade those who prescribe culture to
study until they see the nature
of numbers with the mind only for the sake of the soul herself; the easiest
way for her to pass from intention into being." -
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