View Part: 1 2 3 4 5 6 7 8 9 10 11 12

**
PART 2 - THE GOLDEN SECTION**

*
The Greek letter phi (φ)
signifies the golden section, also known as the divine proportion of 1.618
to one. The mathematical formula for
φ is the square root of five plus one, divided by two. If a
line is divided with the ratio of
φ between the longer segment and the shorter segment, the ratio
between the whole line and the longer segment is also
φ.
Given a length of one for the shorter segment, the length of the longer
segment is φ and the
length of the entire segment is
φ plus one.
φ
plus one is also equal to φ²:
*

*
1.618 + 1 = 2.618 and
1.618 x 1.618 = 2.618*

*
Given a length of one for the longer segment, the shorter
segment is 1/φ (.618)
and the length of the entire segment is
φ.
1/φ is also equal to
φ minus one:*

*
1 ÷ 1.618 = .618 and1.618 minus 1 = .618*

*
There is also an extremely close mathematical relationship
between φ and
π
expressed as φ² x 6
= π x 5 (2.618 times
6, divided by 5, equals 3.1416). There is an ongoing dispute about whether
or not there was an ancient awareness of
φ
and π. In the ancient
world, φ existed naturally
in the proportions and growth rates of plant and animal species, as well as
spirals ranging from microscopic to flowering plants and seashells to the
spiral arms of the galaxy. The π
ratio between the diameter and the circumference of a circle also existed
naturally in the ancient world. It has also been shown that
φ and
π existed
in many man-made ancient buildings, including the great pyramid of Giza.
*

*
The ancient Egyptian royal cubit, equal to 20.625 English
inches, was used to build the great pyramid. The height of the pyramid is
280 cubits and the baselength of the sides at ground level is 440 cubits.
The ratio between the height and two baselengths of the pyramid is an accurate
expression of π (880/280
= 3.1428). The slant height of the pyramid is 356 cubits. The ratio between
the baselength of the pyramid and the two slant heights that form the pyramid
triangle is an accurate expression of
φ
(712/440 = 1.618).*

Angkor Wat is 4,745 miles from the Great Pyramid and the Great Pyramid is 7,677 miles from Nazca. This is a precise expression of φ:

4,745 x 1.618 = 7,677 |

Ninety miles northeast of Angkor Wat are the Angkor temples at Prassat Preah Vihear. Preah Vihear is 4754 miles from the Great Pyramid. The line of ancient sites crosses over the Great Pyramid and Angkor Vihear.

**
Angkor Prassat Preah Vihear**

Twenty five miles northwest of the city of Nazca is a figure known as the Hummingbird. The Hummingbird is 7,692 miles from the Great Pyramid. The line of ancient sites also crosses over the Hummingbird.

**
The
Hummingbird**

The relationship between the distances from Angkor Vihear to the Great Pyramid and from the Great Pyramid to the Nazcan Hummingbird is also a precise expression of φ:

4,754 x 1.618 = 7,692

Because the Hummingbird and Angkor Vihear are antipodal sites, with a distance between them of one-half of the circumference of the earth, two Golden Section relationships between these three sites are shown by the circumference of the earth along the line of ancient sites:

4,754 x 1.618 = 7,692

4,754 + 7,692 = 12,446, and

7,692 x 1.618 = 12,446

These Golden Section relationships may also be diagramed on a straight line:

The line of ancient sites is a line, from the perspective of the first illustration in Part One, and it is a circle, from the perspective of the azimuthal projection above. The line and the circle are found in the greek letter φ and the number 10. Zero and one are also the first two numbers and the only two numbers in the binary code.

The φ relationships between these sites are reflected repeatedly in the first 500 Fibonacci numbers. The first three prime numbers, 2, 3 and 5, approximate the intervals along the circumference of 20%, 30% and 50%, between these three sites. This same percentage of the circumference relationship, accurate to three digits, is found in Fibonacci numbers 137-139:

Percentage of circumference: |
First three digits of Fibonacci numbers: |

Angkor to Giza: 19.1% | #137: 191... (Prime) |

Giza to Nazca: 30.9% | #138: 309... |

Nazca to Angkor: 50.0% | #139: 500... |

The next prime Fibonacci number after #137 is #359. The distances between these sites, in miles, is reflected by Fibocacci numbers 359-361, accurately to five digits:

Distance between sites: |
First five digits of Fibonacci numbers: |

Angkor to Giza: 4,754 miles | #359: 47542... (Prime) |

Giza to Nazca: 7,692 miles | #360: 76924... |

Nazca to Angkor: 12,446 miles | #361: 12446... |

See Also: Golden Section Alignment of Ankgor, Nazca and San Francisco