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## Exploring Geographic and Geometric Relationships Along a Line of Ancient Sites Around the World (cont)

### LINES THROUGH THE CIRCLE

The line of ancient sites may be viewed as a circle because all of the sites are on a straight line around the center of the Earth. The intervals between the sites are based on their great circle distances from each other.

The circle is oriented so that the two points where the circle crosses the equator are on the horizontal axis, and the two points where the circle reaches its greatest latitudes are on the vertical axis.

 G = The Great Pyramid C = Cape Verde Islands M = Machupicchu N = Nazca E = Easter Island V = Anatom Island A = Angkor Wat I = Indus Valley D = Mohenjo Daro P = Perseopolis U = Ur R = Petra

Straight lines may be drawn through the Earth, connecting Easter Island to Machupicchu, the Great Pyramid, Angkor Wat, and the Indus Valley (antipodal to Easter Island).

The straight line distance, through the Earth, from Angkor Wat to Easter Island (7,574 miles), plus the straight line distance from Easter Island to Macchupicchu (2,522 miles), equals the great circle distance from Angkor Wat to Easter Island (10,096 miles).

The straight line distance from the Great Pyramid to Easter Island (7,566 miles) is three times the straight line distance from Easter Island to Machupicchu (2,522 miles).

The straight line distance from Easter Island to its antipodal point in the Indus Valley (7,924 miles), which is also the diameter of the Earth, is 3.1416 times the straight line distance from Easter Island to Machupicchu (2,522 miles), a precise expression of π.

Since the circumference of the Earth is also 3.1416 times the diameter of the Earth, the straight line distance from Easter Island to Machupicchu times π² equals the circumference of the Earth.

The angle formed by the lines from Easter Island to Machupicchu, and to the Indus Valley, is 72°. The angle formed by the lines from Easter Island to Machupicchu, and to the Great Pyramid, is 54°.

 The ratio of the base to the slant height of the Great Pyramid is exactly two times the ratio of the base to the height of the triangle formed by through the earth straight lines connecting the Great Pyramid, Angkor and Easter Island.

Lines connecting Easter Island, the Great Pyramid, and the Angkor temples near Rolous, form an isosceles triangle with base angles of 72.9°. The base of this triangle (AG) is 4462 miles long. The height of this triangle (HE) is 7220 miles long. The length of the base of the triangle times φ equals the height of the triangle:

4462 miles x 1.618 = 7220 miles

The length of the base of each face of the Great Pyramid is 755.6 feet. The slant height of each face is 611 feet. One half of the length of the base times φ equals the slant height of the Great Pyramid:

755.6 feet ÷ 2 = 377.8 feet

377.8 feet x 1.618 = 611 feet

Because the distance between the Great Pyramid and Angkor is very nearly 20% of the circumference, they are very nearly 72° apart, along the circle. Because the distance from the Great Pyramid to Easter Island is very nearly 40% of the circumference, and the distance from Angkor to Easter Island is very nearly 40% of the circumference, the Great Pyramid and Angkor are both very nearly 144° away from Easter Island, along the circle.

The number 72, and to a lesser extent the numbers 54, 108, and 144, have been associated with the designs of these sites, particularly at the Great Pyramid and Angkor. The ratio of the height and the perimeter of the Great Pyramid, to the size of the Earth, is a multiple of 72. The number of temples built around Angkor is 72, and the number 54 is reflected in the numbers of statuary in the temples at Angkor. The use of these numbers is also prevalent in ancient writings and folklore surrounding these sites. The number 54 is itself a factor of 72, in that 72 plus ½ of 72, or 36, equals 108, which divided by two equals 54.

The number 72 is also associated with the astronomical phenomenon known as precession, because 72 years is the length of time it takes for the constellations to move one degree due to precession. This has been offered as an explanation for the use of these numbers, suggesting that the builders of these sites were aware of the precession of the equinoxes. In the 2nd century B.C., the Greek mathematician, Archimedes, wrote an article entitled The Sand Reckoner, in which he cited earlier Greek mathematicians (like Archimedes, they had studied in Alexandria and Heliopolis) who had calculated that the Sun occupied 1/720 of the circle of the constellations. This may be an additional, or alternative, explanation for the prevalence of the number 72, and its multiples and factors, found in these sites. In any event, the existence of these numbers in the geometric relationships between these sites is complementary to the use of these numbers in their internal designs.