Light Eye
03-19-2006, 12:08 PM
dear friends,
there are no coincidences, no accidents...
http://ourworld.compuserve.com/homepages/dp5/pattern1.htm
be well, be love.
david
patterns in nature
david pratt
january 2006
part 1 of 2
contents
(part 1)
1. phi and fibonacci
2. nature?s numbers
3. pentads and hexads
4. platonic solids
5. precession and yugas
(part 2)
6. formative power of sound
7. planets and geometry
8. planetary distances
9. solar system harmonies
10. intelligent habits
11. sources
?nature geometrizes universally in all her manifestations.? ? h.p. blavatsky
humans have always looked upon the beauty, majesty, and ingenuity of the world
around them with reverent wonder. the grandeur of the heavens, the regular
rhythms of the sun and moon, the myriads of living creatures in all their
splendid diversity, the magnificence of a rose flower, a butterfly?s wings or a
snow crystal ? the idea that all this might be the product of a mindless
accident strikes many people as far-fetched. the ancient greeks aptly called the
universe kosmos, a word denoting order and harmony. this underlying order is
reflected in many intriguing patterns in nature.
1. phi and fibonacci
consider the line abc in the following diagram:
point b divides the line in such a way that the ratio between the longer
segment (ab) and the shorter segment (bc) is the same as that between the whole
line (ac) and the longer segment (ab). this proportion is known by various
names: the golden section, the golden mean, the golden ratio, the extreme and
mean ratio, the divine proportion, or phi (φ). if the distance ab equals 1
unit, then bc = 0.6180339887... and ac = 1.6180339887... . the second of these
two numbers is the golden section, or phi (sometimes this name is also given to
the first number). many designs in nature are related to the golden section, and
it has been widely used in sacred architecture and artwork throughout the ages.
the golden section is an irrational, or transcendental, number, meaning that
it never repeats and never ends. it is unique in that its square is produced by
adding the number 1 (φãƒâƒã‚âƒãƒâ‚ã‚âƒãƒâƒã‚â‚ãƒâ‚ã‚âƒãƒâƒã‚âƒãƒâ‚ã‚â‚ ãƒâƒã‚â‚ãƒâ‚ã‚â‚ãƒâƒã‚âƒãƒâ‚ã‚âƒãƒâƒã‚â‚ãƒâ‚ã‚â‚ムâƒã‚âƒãƒâ‚ã‚â‚ãƒâƒã‚â‚ãƒâ‚ã‚â² = φ+1), and its reciprocal by subtracting the
number 1 (1/φ = φ-1). (phi equals (√5+1)/2, the positive root of
xãƒâƒã‚âƒãƒâ‚ã‚âƒãƒâƒã‚â‚ãƒâ‚ã‚âƒãƒâƒã‚âƒãƒâ‚ã‚â‚ã ƒâƒã‚â‚ãƒâ‚ã‚â‚ãƒâƒã‚âƒãƒâ‚ã‚âƒãƒâƒã‚â‚ãƒâ‚ã‚â‚ãƒâ ƒã‚âƒãƒâ‚ã‚â‚ãƒâƒã‚â‚ãƒâ‚ã‚â² = x+1.) the golden section is the only irrational number that approaches more
closely to rationality the higher the power to which it is raised. for instance,
φ3000 = 1.0000000000 x 10500.
the golden section is part of an endless series of numbers in which any number
multiplied by 1.618 gives the next higher number, and any number multiplied by
0.618 gives the next lower number:
[non-text portions of this message have been removed]
there are no coincidences, no accidents...
http://ourworld.compuserve.com/homepages/dp5/pattern1.htm
be well, be love.
david
patterns in nature
david pratt
january 2006
part 1 of 2
contents
(part 1)
1. phi and fibonacci
2. nature?s numbers
3. pentads and hexads
4. platonic solids
5. precession and yugas
(part 2)
6. formative power of sound
7. planets and geometry
8. planetary distances
9. solar system harmonies
10. intelligent habits
11. sources
?nature geometrizes universally in all her manifestations.? ? h.p. blavatsky
humans have always looked upon the beauty, majesty, and ingenuity of the world
around them with reverent wonder. the grandeur of the heavens, the regular
rhythms of the sun and moon, the myriads of living creatures in all their
splendid diversity, the magnificence of a rose flower, a butterfly?s wings or a
snow crystal ? the idea that all this might be the product of a mindless
accident strikes many people as far-fetched. the ancient greeks aptly called the
universe kosmos, a word denoting order and harmony. this underlying order is
reflected in many intriguing patterns in nature.
1. phi and fibonacci
consider the line abc in the following diagram:
point b divides the line in such a way that the ratio between the longer
segment (ab) and the shorter segment (bc) is the same as that between the whole
line (ac) and the longer segment (ab). this proportion is known by various
names: the golden section, the golden mean, the golden ratio, the extreme and
mean ratio, the divine proportion, or phi (φ). if the distance ab equals 1
unit, then bc = 0.6180339887... and ac = 1.6180339887... . the second of these
two numbers is the golden section, or phi (sometimes this name is also given to
the first number). many designs in nature are related to the golden section, and
it has been widely used in sacred architecture and artwork throughout the ages.
the golden section is an irrational, or transcendental, number, meaning that
it never repeats and never ends. it is unique in that its square is produced by
adding the number 1 (φãƒâƒã‚âƒãƒâ‚ã‚âƒãƒâƒã‚â‚ãƒâ‚ã‚âƒãƒâƒã‚âƒãƒâ‚ã‚â‚ ãƒâƒã‚â‚ãƒâ‚ã‚â‚ãƒâƒã‚âƒãƒâ‚ã‚âƒãƒâƒã‚â‚ãƒâ‚ã‚â‚ムâƒã‚âƒãƒâ‚ã‚â‚ãƒâƒã‚â‚ãƒâ‚ã‚â² = φ+1), and its reciprocal by subtracting the
number 1 (1/φ = φ-1). (phi equals (√5+1)/2, the positive root of
xãƒâƒã‚âƒãƒâ‚ã‚âƒãƒâƒã‚â‚ãƒâ‚ã‚âƒãƒâƒã‚âƒãƒâ‚ã‚â‚ã ƒâƒã‚â‚ãƒâ‚ã‚â‚ãƒâƒã‚âƒãƒâ‚ã‚âƒãƒâƒã‚â‚ãƒâ‚ã‚â‚ãƒâ ƒã‚âƒãƒâ‚ã‚â‚ãƒâƒã‚â‚ãƒâ‚ã‚â² = x+1.) the golden section is the only irrational number that approaches more
closely to rationality the higher the power to which it is raised. for instance,
φ3000 = 1.0000000000 x 10500.
the golden section is part of an endless series of numbers in which any number
multiplied by 1.618 gives the next higher number, and any number multiplied by
0.618 gives the next lower number:
[non-text portions of this message have been removed]