Amazing Number 108 |
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Introduction
The number 108 is considered auspicious in Indian culture and has its significance in many rituals followed in India.
Vedic sages of later era devised a Vyjanti mala (rosary) with 108 beads/stones to keep count of mantras (hymns) in their daily ritual of meditation.
The sacred rosaries have 108 beads/Stones. Mantras like Mahamritunyaj mantra and Gayatri mantra are chanted 108 times. Most popular of all mala i.e. Rudraksha has 108 sacred beads.
The number 108 is considered holy and auspicious in Hinduism. Not only Hinduism, number 108 has its profound significance in Sikhism, Buddhism, and Jainism. In the Jain religion, 108 are the combined virtues of five categories of holy ones, including 12, 8, 36, 25, and 27 virtues respectively. The Sikh tradition has a mala of 108 knots tied in a string of wool, rather than beads.
The Chinese Buddhists and Taoists use a 108 bead mala, which is called su-chu, and has three dividing beads, so the mala is divided into three parts of 36 each. Chinese astrology says that there are 108 sacred stars. Some Buddhists carve 108 small Buddhas on a walnut for good luck. Some ring a bell 108 times to celebrate a new year.
What is so interesting about 108
Let us see how fascinating the number 108 from mathematical point of view is.
108 = 1^{1} . 2^{2} . 3^{3}
So it is the hyperfactorial of 3 since it is of the form 1^{1} . 2^{2} . 3^{3}.
The divisors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54 and 108.
2^{108} = 324518553658426726783156020576256
It can be noted that 2^{108} contain all digit from 0 to 8 but not 9 while each number 2^{n} for n = 109, 110, 111 etc contain it.
108 = 2^{3} + 10^{2} = 3^{3} + 9^{2}
The concatenation of 108 with 107 and 109 is prime, i.e., 108107 and 108109 are primes.
108^{2} = 11664, and 1 + 16 + 64 = 9^{2},
108^{2} = 11664, and 11 + 6 + 64 = 9^{2},
108^{2} = 11664, and 11 + 66 + 4 = 9^{2},
108^{2} = 11664, 129^{2} = 16641 and 204^{2} = 41616. It can be noted that all these three squares contain same digits.
The cube digits are 0, 1 and 8.
108 = 5 + 7 + 11 + 19 + 29 + 37.
It can be noted that sum of any five out of 5, 7, 11, 19, 29 and 37 is always prime.
5 + 7 + 11 + 19 + 29 = 71
5 + 7 + 11 + 19 + 37 = 79
5 + 7 + 11 + 29 + 37 = 89
5 + 7 + 19 + 29 + 37 = 97
5 + 11 + 19 + 29 + 37 = 101
7 + 11 + 19 + 29 + 37 = 103
It can be seen that 71, 79, 89, 97, 101 and 103 are all primes.
108 = 6^{2} + 6^{2} + 6^{2}
Geometric connections of 108
A heptomino (or 7-omino) is a polyomino of order 7, that is, a polygon in the plane made of 7 equal-sized squares connected edge-to-edge. When rotations and reflections are not considered to be distinct shapes, there are 108 different free heptominoes i.e. 108 free polyominoes of order 7.
This is the smallest polyomino to contain a hole as shown below. It is in the form of a 3 by 3 square with one corner and the central square missing.
Fibonacci sequence and 108
The first 24 numbers of the Fibonacci Sequence are:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657.
The digital roots of the sequence of Fibonacci numbers yields a pattern that repeats as follows:
(0), 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1.
The first term in the sequence is a zero in the first cycle but becomes a 9 every cycle thereafter. This difference is shown as highlighted below:
First sequence
(0), 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1
Every sequence thereafter
(9), 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1
On adding the repeating 23 digits , surprisingly the number 108 is obtained.
1 + 1 + 2 + 3 + 5 + 8 + 4 + 3 + 7 + 1 + 8 + 9 + 8 + 8 + 7 + 6 + 4 + 1 + 5 + 6 + 2 + 8 + 1 = 108
Astronomical Coincidences of the Number 108
Do you know why sun and moon look equally big in the sky?
The distance between the earth and the sun equals about 108 (actually 107-odd) times the sun's diameter. Likewise, it so happens that the distance between the earth and the moon equals about 108 (actually 110-odd) times the moon's diameter. So the sun and moon look equally big in the sky because of their having almost the same ratio between distance and diameter.
It is just a coincidence that the solar and lunar distances happen to match the number 108. Many ratios in Moon-Earth-Sun astronomy coincidentally converge near the number 108. Some of these are:
So the distance between earth and sun is about 108 times sun-diameter
So the diameter of the sun is about 108 times the earth diameter
The ratio of the solar diameter (km 1,392,000) to Earth diameter (km 12,756) is 109.1, close to 108 with an error less than 1%.
Increase of solar diameter is suggested by measurements taken during over a century at Greenwich Observatory; hence in earlier times the above ratios could have been much closer to 108.
So the distance between earth and moon is about 108 times moon-diameter
It has been discovered that the moon's radius is literally shrinking over the years. Hence in earlier times the ratio could have been much closer to 108.
The 108 Emergency Ambulance Service in India
The 108 Emergency Ambulance Service is a 24x7 service, which anyone can avail by dialing the number 108 on their phone during the case of any emergency.
Why Ambulance Service Named as 108 ?
The number 108 was chosen for the toll-free service because it is considered an auspicious number in multiple religions prevalent in India.
In the Holy Bible Matthews Chapter 10 Verse 8 (108) reads::: Heal the sick, raise the dead, cleanse the lepers, cast out demons; freely ye received, freely give. some believe this as the reason for choosing the number 108.
1-0-8 is a technologically acceptable number enabling the processing of calls to occur faster.
Some Interesting Observations
On New Years Eve one of the most important ceremonies in Japan is Joya no Kane, the ringing of the temple bells 108 times at midnight. It is believed that each ring represents one of 108 earthly temptations a person must overcome to achieve nirvana and ringing the bell purifies us and sets things right for the new year.
Muktinath, a temple town in Nepal is a sacred place both for Hindus and Buddhists. The main shrine of the temple is Pagoda-shaped and is dedicated to Lord Vishnu. Near the Vishnu temple the water of a holy source is distributed by a system of 108 outlets. The outer courtyard has 108 water spouts shaped as cows heads , where the devotees take their sacred bath even in the freezing temperatures.
Wat Pho is world famous temple in Bangkok for the huge image of the reclining Buddha (made of gold leaf). The soles of the feet of the Buddha are each divided into 108 unique sections, displaying 108 auspicious symbols by which Buddha can be identified, such as flowers, dancers, white elephants, tigers etc
Next to the statue lie 108 bronze bowls in the corridor representing the 108 auspicious symbols on the Buddhas foot. Visitors may drop coins into these bowls as it is believed to bring good fortune. The money collected is used to help maintain the temple.
There are 12 zodiac signs based on the movement of sun and moon . There are 9 planets whose positions represents the events that will occur in our life. Multiplying 12*9, we get 108. There are thus 108 possible ways the planets can be placed. The 27 nakshatras or lunar constellations spread over the 4 directions - north, south, east, and west. This also constitutes the whole of existence. 27 x 4 = 108.
Consider A=1,B=2...H=8,I=9,...R=18,S=19,..Z=26 so
SHRI SHRI = 19+8+18+9+19+8+18+9 =108
1- Stands for supreme truth or god consciousness.
0- Stands for nothing or emptiness.
8- Stand for eternity or infinity. Note that the symbol of infinity is obtained by rotating 8 by 90 degrees.
Thus the sacred number 108 tells us that we are at once something, nothing and everything.
In the decimal expansion of π (3.14159265358979323846264338327950288419….), the sum of first 22 digits after decimal equals 108.
1 + 4 + 1 + 5 + 9 + 2 + 6 + 5 + 3 + 5 + 8 + 9 + 7 + 9 + 3 + 2 + 3 + 8 + 4 + 6 + 2 + 6 = 108
In the decimal expansion of e (2.7182818284590452353602874713526624977572….), the sum of first 24 digits after decimal equals 108.
7 + 1 + 8 + 2 + 8 + 1 + 8 + 2 + 8 + 4 + 5 + 9 + 0 + 4 + 5 + 2 + 3 + 5 + 3 + 6 + 0 + 2 + 8 + 7 = 108
(submitted by K D Bajpai from India vide his email dated 31 January 2018)
-1 + 2 + 3*4 + 5*6 + 7*8 + 9 = 108
1 - 2 - 3 + 4*5*6 - 7 + 8 - 9 = 108
-2! * 3! + 5! = 108
(submitted by K D Bajpai from India vide his email dated 25 December 2017)
If you find any new and interesting observation about number 108, please email me.
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This page is created on 16 December, 2017.