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108
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Why 108? here are some of the answers:
1. Astrologically, it is the combination of the 9 heavenly bodies (mainly planets  Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn, the North Node and the South Node.) with the 12 houses of the Zodiac. 12 times 9 = 108. On a more secret level, the number 9 is associated with Saturn (Za Penpa) and you may have seen the 12 sets of Saturn "magical squares" set around a Tibetan astrological chart. This is used to calculate Mewas and Parkas. There are 108 squares in the diagram below.
There are also, in astrology, the 27 Lunar Mansions (Jukar) and if one combines these with the 4 phases of the Moon, that gives 108.
In the Kalachakra, these outer 108 are corresponded to the inner 108 major, secondary and tertiary channels deriving from the heart centre.
2. In Buddhism, it becomes the main number of possible experiences. It works like this  there are the six consciousnesses (seeing, hearing, smelling , tasting, physical sensation and mental). These can be either pleasant, unpleasant or neutral so that makes 18 possibilities. There are the three times (past, present and future) in which these can occur, so that makes 3 x 18 = 54. Then they can be either virtuous or nonvirtuous = 108.
3. Numerology. The number has fascinated mathematicians all over the world because it is
(1) multiplied by (2 x 2) multiplied by (3 x 3 x 3) ....one one, two twos and three threes.
4. The Greeks' famous beautiful architecture was based on a heightwidth relationship know as the "Golden Rule". You get this by taking two points 108 apart on a circle, joining them with a straight line and comparing that to the circumference of the circle.
5. The ancients didn't know all of the following, but by an incredible "coincidence" ,
the distance between the Earth and the Sun is 108 times the Sun's diameter,
the distance between the Earth and the Moon is 108 times the Moon's diameter and also
the diameter of the Sun is 108 times that of the Earth.
Just by coincidence, the radius of the Moon is 108 miles.
6.This is more debatable. The Hindu pantheon of Gods is 108: some people say that these were 'upgraded' by tantra to make 108 main deities in Buddhism. This is certainly why the Hindus think it is a holy number. Of course, the deities are representations of cosmic realites, so we come back to the inner channels and the outer cosmos.
Mathematical &Scientific Data for above
Distance between earth and sun = 108 times sundiameter
The diameter of the Sun has not been easy for scientists to measure. These are the numbers:
1,392,000 km ("Sun" Columbia Electronic Encyclopedia. 6th ed. Columbia University Press, 2003)
 1,400,000 km (Namowitz, Samuel N. and Spaulding, Nancy E. Earth Science. Evanston, IL: McDougal Littell Company, 1999)
 1,390,000 km (The Amazing Structure of the Sun. National Aeronautics and Space Administration (NASA), 2003)
 1,380,000 km (Namowitz, Samuel N., and Nancy E. Spaulding. Heath Earth Science. Lexington, MA: Heath, 1994: 398.)
The distance between the earth and the Sun is called an Astrological Unit (AU).
1 AU = 149,597,870.691 kilometers
Even though this is the number given there are multiple places where variability gets into the numbers. One way is the elliptical orbit of the earth around the Sun.
Perihelion: 147.5 million km, about January 4th
Aphelion 152.6 million km, about July 4th (http://science.nasa.gov/headlines/y2001/ast04jan_1.htm)
Findings:
Taking the mean distance between the earth and the Sun ( 149,597,870.691 km) and dividing it by the most commonly used diameter of the Sun (1,392,000 km) the result is 107.46973469181034482758620689655.
2. Distance between earth and moon = 108 times moondiameter
Moons diameter is: 3,474.8 km (http://en.wikipedia.org/wiki/Earth)
Distance from earth to the Moon:
Again the Moons rotation is elliptical and not an exact circle. But Apollo 11 astronauts put mirrors on the Moon and lasers measure the amount of time it takes for the light to reflect, this gives measurements with accuracy up to a few inches at any given time.
Perigree 363,300 km
Apogee 405,500 km
Mean Distance 384,400 km (http://www.freemars.org/jeff/planets/Luna/Luna.htm)
Findings:
Taking the mean distance from the Moon to the Earth (384,400 km) and dividing it by the Moons diameter (3,474.8 km) results in 110.62507194658685391965005180154.
3. Diameter of the sun = 108 times the earth diameter
The diameter of the earth is: Equatorial diameter 12,756.28 km
Polar diameter 12,713.56 km
Mean diameter 12,742.02 km
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The angle of 108 has a unique property: the ratio between the straight line uniting two points at 108 from each other on a circles circumference (in effect one of the sides of a 10pointed star) and the radius of that circle equals the Golden Section. Likewise, the inside of every angle of a pentagon measures 108, and the pentagon is a veritable embodiment of the Golden Section, e.g. the ratio between a side of the 5pointed star and a side of the pentagon is the Golden Section. So, there is an intimate link between the number 108 and the Golden Section.