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¿CUÁNTO VALE LA SUMA DE LOS ÁNGULOS INTERIORES DE UN POLÍGONO REGULAR?
Si observas las figuras que tienes a continuación:
ves que en el caso del triángulo vale 180º.En el caso del cuadrado el total de grados es de 360º.En el caso del pentágono la suma de los ángulos interiores es de 540º¿Hay que aprenderse de memoria el valor de la suma de los ángulos interiores de CADA polígono regular?. NO
Te basta con hacer un cálculo muy sencillo:
1º cuenta el número de lados
2º al número obtenido de contar los lados réstale 2
3º al valor de la diferencia anterior multiplícale por 180El producto obtenido es la suma de los grados de un polígono regular.15.61 ¿Cuántos grados suman los ángulos interiores de un polígono de 5 lados o pentágono?Respuesta: 540º
Solución:
Hallo la diferencia: 
Este valor lo multiplico por 180º:  
Daría lo mismo que multiplicar 108º que vale cada ángulo del pentágono regular por los 5 que tiene:
15.62 ¿Cuántos grados suman los ángulos interiores de un tetradecágono o polígono de 14 lados?Respuesta: 2160º
 Daría lo mismo que multiplicar el valor de un ángulo de un tetradecágono regular que es de 154º17’9’’ por los 14 ángulos interiores iguales que tiene:
¿POR QUÉ LA SUMA DE LOS ÁNGULOS INTERIORES DE UN POLÍGONO REGULAR VALE: número de lados menos 2 por 180º?
Vamos a fijarnos en la suma de los ángulos interiores de cualquier triángulo:
Cualquiera que sea la forma de un triángulo, la suma de sus ángulos interiores vale 180º. Si sumas los valores de los ángulos interiores de cualquiera de los triángulos anteriores comprobarás que siempre suman 180º.
A continuación tienes dos polígonos, uno de 9 lados (ENEÁGONO) y el otro de 14 (TETRADECÁGONO).
En el primer polígono hemos dibujado 7 triángulos y como cada triángulo tiene 180º, los ángulos interiores de un eneágono valdrán:
En el segundo polígono hemos dibujado 12 triángulos y como cada uno tiene 180º, los ángulos interiores de un tetradecágono valdrán:
En cualquier polígono (de más de tres lados) puedes dibujar triángulos. Para dibujar un triángulo necesitas tres lados. Con un cuadrado puedes dibujar 2 triángulos; con un pentágono 3; en un hexágono 4; en un heptágono 5, etc.
Vemos que el número de triángulos obtenidos en cada polígono es igual al número de lados menos 2. Como los grados de un triángulo valen 180º, basta con multiplicar este número por el de lados menos dos. |
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NEXO KABALISTICO ENTRE EL SALMO 119, CON EL 108 Y EL NUMERO CIRCULAR 227
No es casualidad que justo en APOCALIPSIS 1:8 NUESTRO SEÑOR HAGA REFERENCIA A QUE EL ES EL ALFA Y EL OMEGA. EL NUMERO 18 TIENE NEXO KAVALISTICO CON EL 108. LOS ESTADOS UNIDOS INCLUSO TAMBIEN TIENEN UN FUERTE NEXO CON EL NUMERO 119 EN FUNCION A SU INDEPENDENCIA.(2 DE JULIO , VERDADERA INDEPENDENCIA EN LUNA LLENA, fue el dia numero 119 desde la PRIMERA LUNA LLENA DE MARZO/MARTE). POR ESO LA FUERTE RELACION KAVALISTICA DEL 1776=48X37 en funcion al este ultimo con NEXO CON EL SOL Y LA LUNA EN CONTEXTO AL sueño de JOSE DE GENESIS (GEN DE ISIS) EN SU CAPITULO 37. ESTA TODO CODIFICADO. YHWH MANEJA TODO CON las MATEMATICAS. ESE ES EL MENSAJE QUE EL SEÑOR NOS QUIERE DAR DETRAS DEL 911/119
ALFA=1 MAS OMEGA=800 TENEMOS 801 (ANAGRAMA DE 108)
EN APOCALIPSIS 1:10 "DIA DEL SEÑOR" EN CONTEXTO A TROMPETAS E INCLUSO EN CONTEXTO A JUAN 20 EQUIVALE A JUBILEO. El PENTECOSTES (PENTA=CINCO) TIENE UN NEXO ESPIRITUAL CON EL JUBILEO/LIBERTAD/LEVITICO 25:8
NO ES CASUALIDAD LA RELACION MATEMATICA 108+119=227
Esto explica del porque el NEXO DE APOCALIPSIS 1:10 "DIA DEL SEÑOR" con JUAN 20 "RESURRECCION DE CRISTO". ES UN OBVIO NEXO CON EL JUBILEO y es por eso que aparecen las trompetas en APOCALIPSIS 1:10 E incluso con el SALMO 119 CUANDO NUESTRO SEÑOR AFIRMA SER EL ALFA Y EL OMEGA.
A.F: Con la ayuda de la Gematria ha podido descifrar aspectos oscuros del Apocalipsis. ¿Puede aclararnos su interpretación del conocido verso «Yo soy el Alfa y el Omega»?
M.S: El valor de Alfa es 1, mientras el de Omega es 800. Sumados dan 801, un «anagrama» de 1080, y número que suma «peristera», la palabra griega que significa «paloma», símbolo del Espíritu Santo. El número 1080, además, es la Gematria tanto del Espíritu Santo como del Espíritu de la Tierra (el aspecto «femenino» o «inmanente» de lo divino). Las letras del alfabeto, desde Alfa a Omega, contienen todas las posibles permutaciones y combinaciones de la «Palabra de Dios». La letra A ( el uno) representa el principio creativo masculino, mientras el Omega tiene la forma de un útero.
Apocalipsis
1:1 La revelación de Jesucristo, que Dios le dio, para manifestar a sus siervos las cosas que deben suceder pronto; y la declaró enviándola por medio de su ángel a su siervo Juan,
1:2 que ha dado testimonio de la palabra de Dios, y del testimonio de Jesucristo, y de todas las cosas que ha visto.
1:3 Bienaventurado el que lee, y los que oyen las palabras de esta profecía, y guardan las cosas en ella escritas; porque el tiempo está cerca.
1:4 Juan, a las siete iglesias que están en Asia: Gracia y paz a vosotros, del que es y que era y que ha de venir, y de los siete espíritus que están delante de su trono; (Siete espiritus son una referencia a las SIETE PALOMAS O PLEYADES/TAURO. UN OBVIO NEXO CON REFERENCIA A MARIA MAGDALENA QUE SIMBOLIZA AL ESPIRITU SANTO. Magdala significa "lugar de las palomas". EL ESPIRITU SANTO ES LA CUALIDAD FEMENINA DE YHWH.)
1:5 y de Jesucristo el testigo fiel, el primogénito de los muertos, y el soberano de los reyes de la tierra. Al que nos amó, y nos lavó de nuestros pecados con su sangre,
1:6 y nos hizo reyes y sacerdotes para Dios, su Padre; a él sea gloria e imperio por los siglos de los siglos. Amén.
1:7 He aquí que viene con las nubes, y todo ojo le verá, y los que le traspasaron; y todos los linajes de la tierra harán lamentación por él. Sí, amén.
1:8 Yo soy el Alfa y la Omega, principio y fin, dice el Señor, el que es y que era y que ha de venir, el Todopoderoso. (El alfa y el omega eran la primera y ultima letras del griego. ES OBVIO EL NEXO AQUI CON EL SALMO 119 EN UN CONTEXTO AL NUMERO 8/RESURRECCION/CIRCUNCISION/PACTO ABRAHAMICO QUE SE CUMPLIO JUSTAMENTE CUANDO CRISTO LE EXPRESO A MARIA MAGDALENA QUE EL IVA A "SU PADRE Y NUESTRO PADRE , SU DIOS Y NUESTRO DIOS") Comparar con GENESIS 17
1416. Apocalipsis 1:10: Yo estaba en el Espíritu en el día del Señor, y oí detrás de mí una gran voz como de trompeta,
43. Apocalipsis 1:16: Tenía en su diestra siete ESTRELLAS; de su boca salía una espada aguda de dos filos; y su rostro era como el sol cuando resplandece en su fuerza.
44. Apocalipsis 1:20: El misterio de las siete ESTRELLAS que has visto en mi diestra, y de los siete candeleros de oro: las siete ESTRELLAS son los ángeles de las siete iglesias, y los siete candeleros que has visto, son las siete iglesias.
LAS SIETE ESTRELLAS SON LAS SIETE PALOMAS/PLEYADES EQUIVALENTES A LAS SIETE IGLESIAS. LAS PLEYADES SIMBOLIZAN AL PODER DEL ESPIRITU SANTO SIMBOLIZADOS POR MARIA MAGDALENA, NUESTRA MADRE
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Quote:
Originally Posted by skywalker9  I always noticed 108 was the angle between points in a pentagram and thought it might have something to do with the people purifying the 5 elements. 36, 72 and 108 are all 9's. Buddhists and some other Indian systems note that the physical body has 9 doors, or nine holes, 2 eyes, 2 ears, 2 nostrils, mouth, arse, genital.
See hyperflight.com for image |
Thank you to all who replied to my question about the number 108.
I found this:
I highlighted the 12 houses and 9 planets references because this would seem to fit very well to the story of the water margin which inspired my question.
There are a number of articles I found relating the number 108 to the precession of the equinoxes as mentioned by Raphael.
The Significance of the number 108
The Indian Subcontinent rosary or set of mantra counting has 108 beads. 108 has been a sacred number in the Indian Subcontinent for a very long time. This number is explained in many different ways.
The ancient Indians were excellent mathematicians and 108 may be the product of a precise mathematical operation (e.g. 1 power 1 x 2 power 2 x 3 power 3 = 108) which was thought to have special numerological significance.
Powers of 1, 2, and 3 in math: 1 to 1st power=1; 2 to 2nd power=4 (2x2); 3 to 3rd power=27 (3x3x3). 1x4x27=108
Sanskrit alphabet: There are 54 letters in the Sanskrit alphabet. Each has masculine and feminine, shiva and shakti. 54 times 2 is 108.
Sri Yantra: On the Sri Yantra there are marmas where three lines intersect, and there are 54 such intersections. Each intersections has masculine and feminine, shiva and shakti qualities. 54 x 2 equals 108. Thus, there are 108 points that define the Sri Yantra as well as the human body.
9 times 12: Both of these numbers have been said to have spiritual significance in many traditions. 9 times 12 is 108. Also, 1 plus 8 equals 9. That 9 times 12 equals 108.
Heart Chakra: The chakras are the intersections of energy lines, and there are said to be a total of 108 energy lines converging to form the heart chakra. One of them, sushumna leads to the crown chakra, and is said to be the path to Self-realization.
Marmas: Marmas or marmastanas are like energy intersections called chakras, except have fewer energy lines converging to form them. There are said to be 108 marmas in the subtle body.
Time: Some say there are 108 feelings, with 36 related to the past, 36 related to the present, and 36 related to the future.
Astrology: There are 12 constellations, and 9 arc segments called namshas or chandrakalas. 9 times 12 equals 108. Chandra is moon, and kalas are the divisions within a whole.
Planets and Houses: In astrology, there are 12 houses and 9 planets. 12 times 9 equals 108.
Gopis of Krishna: In the Krishna tradition, there were said to be 108 gopis or maid servants of Krishna.
1, 0, and 8: 1 stands for God or higher Truth, 0 stands for emptiness or completeness in spiritual practice, and 8 stands for infinity or eternity.
Sun and Earth: The diameter of the sun is 108 times the diameter of the Earth.
Numerical scale: The 1 of 108, and the 8 of 108, when added together equals 9, which is the number of the numerical scale, i.e. 1, 2, 3 ... 10, etc., where 0 is not a number.
Smaller divisions: The number 108 is divided, such as in half, third, quarter, or twelfth, so that some malas have 54, 36, 27, or 9 beads.
Islam: The number 108 is used in Islam to refer to God.
Jain: In the Jain religion, 108 are the combined virtues of five categories of holy ones, including 12, 8, 36, 25, and 27 virtues respectively.
Sikh: The Sikh tradition has a mala of 108 knots tied in a string of wool, rather than beads.
Chinese: 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.
Stages of the soul: Said that Atman, the human soul or center goes through 108 stages on the journey.
Meru: This is a larger bead, not part of the 108. It is not tied in the sequence of the other beads. It is the quiding bead, the one that marks the beginning and end of the mala.
Dance: There are 108 forms of dance in the Indian traditions.
Pythagorean: The nine is the limit of all numbers, all others existing and coming from the same. ie: 0 to 9 is all one needs to make up an infinite amount of numbers.
We have listed below 108 Upanishads as per the list contained in the Muktikopanishad . We have arranged them in four categories according to the particular Veda to which each of them belong.
Rigveda(10): Aitareya , Atmabodha, Kaushitaki, Mudgala, Nirvana, Nadabindu, Akshamaya, Tripura, Bahvruka, Saubhagyalakshmi.
Yajurveda(50): Katha, Taittiriya , Isavasya , Brihadaranyaka, Akshi, Ekakshara, Garbha, Prnagnihotra, Svetasvatara, Sariraka, Sukarahasya, Skanda, Sarvasara, Adhyatma, Niralamba, Paingala, Mantrika, Muktika, Subala, Avadhuta, Katharudra, Brahma, Jabala, Turiyatita, Paramahamsa, Bhikshuka, Yajnavalkya, Satyayani, Amrtanada, Amrtabindu, Kshurika, Tejobindu, Dhyanabindu, Brahmavidya, YogakundalinI, Yogatattva, Yogasikha, Varaha, Advayataraka, Trisikhibrahmana, mandalabrahmana, Hamsa, Kalisantaraaa, Narayana, Tarasara, Kalagnirudra, Dakshinamurti, Pancabrahma, Rudrahrdaya, SarasvatIrahasya.
SamaVeda(16): Kena, Chandogya, Mahat, Maitrayani, Vajrasuci, Savitri, Aruneya, Kundika, Maitreyi, Samnyasa, Jabaladarsana, Yogacudaman, Avyakta, Vasudevai, Jabali, Rudrakshajabala.
Atharvaveda(32): Prasna , Mandukya, Mundaka, Atma, Surya, Narada-Parivrajakas, Parabrahma, Paramahamsa-Parivrajakas, Pasupatha-Brahma, Mahavakya, Sandilya, Krishna, Garuda, Gopalatapani, Tripadavibhuti-mahnarayana, Dattatreya, Kaivalya, NrsimhatapanI, Ramatapani, Ramarahasya, HayagrIva, Atharvasikha, Atharvasira, Ganapati, Brhajjabala, Bhasmajabala, Sarabha, Annapurna, TripuratapanI, Devi, Bhavana, SIta.
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The Significance of the number 108
We must agree that all measuring systems are merely reference frames. They give us a starting point. It doesn’t really matter if you call them farenheits or cycles. All science is based on fundamental assumptions of the mechanics of this universe. Yet, these assumptions, if correct, connect like building blocks.
Much in the same way, the number ‘108’ is just a reference frame. It is symbolic of a bigger picture: that of humility. When devotees recite 108 Hanuman Chalisas, in their minds they believe, they are proving their love for God, and that there is in fact a need to prove their love. When devotees assign a 108 names to Shri Ganesh, they are once again gauging their devotion through numbers. This, of course, may be considered unreasonable, since it suggests that 108 chants are more effective than 109 chants. How do they know this? Have they proved it? Is 108 the magic number of the universe? No, it is not! It is a reference frame. What is important is that a system is imposed to guide us through the fundamental struggles encountered in any evolutional process. Otherwise, chaos and anarchy follow and nothing gets done.
Having said that, I will show you justifications from a few subcultures in India. Obviously, I consider the Vedic rationale to be the most consistent with the fundamental laws of this universe. The others have borrowed and built, but it still smells of Vedic beginnings.
In present times, we can find many rationales for the proliferation of ‘108’ throughout our scriptures. In fact, this number seems to garner its unfair share of attention from myriad cults and faith systems around the world. I will give you a few justifications that have been brought to my attention.
JYOTISH SHASTRA {VEDIC SYSTEM**
This universe was created by the five elements: space, air, fire, water and earth. From these elements came the three attributes: Raj {birth**, Sat {protection** and Tam {destruction or death.**
The mathematical or geographical evidence proves that one circle has 360 degrees in space. Why is this circle or wheel of life considered to be of 360 degrees only? If we take a circle and start dividing it using the four elements and three attributes, all the logic can be observed.
The circle itself, is considered the first element of space, since we must consume space in drawing a circle. In this space {or circle**, the four remaining elements and three attributes create the idea of time. The circle is divisible by the product of four elements multiplied by three attributes. This involves the belief that the three attributes exist in the circle. By moving three times, each element completes its revolution.
So now we have the number 12 {3 x 4**. This division gave birth to our 12 months, and also to the 12 horas {1/2 of the day or Ahoratri**. We now have 360 degrees as well as 12 divisions. We can now further divide the wheel of time: there are 27 fixed stars (nakshatras) along with three attributes that divide the time in smaller portions. So this 27 + 3 = 30 is interpreted as 30 degrees or days of one part of the wheel (circle) or month. All of this is only half of a day. The night is yet unaccounted for. Therefore, we multiply these 30 degrees by 2. This gives us our reference of 60 seconds in a minute.
Thus the 360º x 30º = 10,800. Zero {0** is considered ‘Purna’ or complete. So we take out the last zeros and are left with 108. The idea of our total universe is represented by this number of 108. Offering 108, devotees believe that they are showing ultimate or complete respect to the Supreme.
There are many other justifications but all can be traced back to this system. A few are explained below:
SHOSHU BUDDHIST
Followers use 108 beads in their malas. They implement the following formula:
6 x 3 x 2 x3 = 108
6 senses [sight, sound, smell, taste, touch, thought]
3 aspects of time [past, present, future]
2 condition of heart [pure or impure]
3 possibilties of sentiment [like, dislike, indifference]
BUDDHA’S FOOTPRINT
All Buddhists accept the Buddha Footprint with its 108 Auspicious Illustrations. These areas are considered to have been marked on the Buddha’s left foot when his body was discovered.
BUDDHISM
108 beads on the Hindu maalaa {rosary**
108 Arhats or Holy Ones
HINDUISM
108 Gopis {consorts** of Lord Krishna
108 Holy places for Vaishnavas
108 beads on the Japa maalaa {rosary**
108 Upanishads
108 Divyadeshes - Divine or Sacred Tirtha throughout India and Nepal
108 sacred water taps in Muktinath - Nepal
TANTRA SHASTRA
108 Pitha {Sacred Places**
The story goes that Lord Shiva was in deep and incessant meditation. His asceticism was creating great heat in the universe. All existence was in peril and Lord Brahma was deeply concerned. Lord Brahma asked the Mother of the Universe, Maa Shakti, to use Her strength and wile to seduce Lord Shiva. Maa Shakti agreed and was born as Sati, daughter of Shri Daksha. Lord Shiva was so entranced by Sati’s asceticism and extraordinary beauty that he took human form and they were married. Years later, at a feast, Sati’s father insulted Lord Shiva. Sati was so humiliated that she began a deep meditation which led to her immolation. Lord Shiva was completely heart broken. He reached into the sacrificial fire and pulled out as much of His beloved’s body as he could grab. As He ascended to heaven, bits of Sati’s body fell to earth. 108 bits to be precise! In time, these places were acknowledged and worshipped.
SANATANA DHARMA
In a book by Khurana, the explanation closely mirrors the original Vedic justifications:
A circle has 360 degrees, which when multiplied by 60 gives us 21,600 minutes in a circle. 60 comes from the 60 'ghatis' which Sanatana Dharmiks believe in. One ghati is equal to 24 minutes and 60 ghatis come to 24 hours.
One ghati is divided into 60 parts or 'palas'.
So the 60 ghatis multiplied by 60 palasa comes to 3,600.
This is further multiplied by 60 (becase a pala contains 60 vipalas) which gives us 21,600.
Half of this is for the day, and the other half for the night. So, 21,600
divided by 2 gives us 10,800. For practical purposes, we use 108. Using the
number 108 helps us coordinate the rhythm of time and space & we remain in harmony with the spiritual powers of nature.
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Square times cube
Among other intrinsic and ever-unchangeable properties,
it may be hard to choose which one is sufficiently relevant.
Thus, 108 equals the sum of the first 9 multiples of 3,
viz. 0, 3, 6, 9, 12, 15, 18, 21 and 24.
This reconfirms its intimate relation with the
richly symbolic number 9, but then, so what?
Slightly more remarkable is that 108 equals the product of the
second power of 2 and the third power of 3, i.e. the first non-trivial
even and odd numbers multiplied by themselves as many times as themselves.
In figures: 108 = 2² x 3³, or 108 = 2 x 2 x 3 x 3 x 3.
This way, it unites on their own terms the polar opposites of even and odd,
the numerical counterparts of female and male, yin and yang, etc.
If nothing else, at least it's cute, is it not?
That may well be the most we can expect of number symbolism.
____________________
Much, much more info here:
source: Article on the symbolism of the number 108
And here:
photo source:
And follow the links at the bottom of the
wiki article for even more on 108...
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(inputX/Xmodvalue=1) 5843/2 =2921.5[1] 1786/4 =446.5[1] 2573/8 =321.625[1] 7189/7 =1027[1] 8213/5 =1642.6[1] 7426/1 =7426[1]  73468532/2 =36734266[1] 8932843723/4 =2233210930.75[1] it is synonymous with x/x=1 though, there are anomalies: 4156/7 =593.714285... 1123/7 =160.428571... 9336/3 =3112[7] 9663/6 =1610.5[4] compelling, nonetheless. ________________________ also, this caught my eye: The distance between the Earth and Moon is 108 times the diameter of the Moon The distance between the Earth and Sun is 108 times the diameter of the Sun The diameter of the Sun is 108 times the diameter of the Earth (wiki)
Last edited by mane; 03-06-2010 at 06:21 AM.
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Quote:
Originally Posted by skywalker9 I always noticed 108 was the angle between points in a pentagram and thought it might have something to do with the people purifying the 5 elements. 36, 72 and 108 are all 9's. Buddhists and some other Indian systems note that the physical body has 9 doors, or nine holes, 2 eyes, 2 ears, 2 nostrils, mouth, arse, genital.
See hyperflight.com for image |
Thank you to all who replied to my question about the number 108.
I found this:
I highlighted the 12 houses and 9 planets references because this would seem to fit very well to the story of the water margin which inspired my question.
There are a number of articles I found relating the number 108 to the precession of the equinoxes as mentioned by Raphael.
The Significance of the number 108
The Indian Subcontinent rosary or set of mantra counting has 108 beads. 108 has been a sacred number in the Indian Subcontinent for a very long time. This number is explained in many different ways.
The ancient Indians were excellent mathematicians and 108 may be the product of a precise mathematical operation (e.g. 1 power 1 x 2 power 2 x 3 power 3 = 108) which was thought to have special numerological significance.
Powers of 1, 2, and 3 in math: 1 to 1st power=1; 2 to 2nd power=4 (2x2); 3 to 3rd power=27 (3x3x3). 1x4x27=108
Sanskrit alphabet: There are 54 letters in the Sanskrit alphabet. Each has masculine and feminine, shiva and shakti. 54 times 2 is 108.
Sri Yantra: On the Sri Yantra there are marmas where three lines intersect, and there are 54 such intersections. Each intersections has masculine and feminine, shiva and shakti qualities. 54 x 2 equals 108. Thus, there are 108 points that define the Sri Yantra as well as the human body.
9 times 12: Both of these numbers have been said to have spiritual significance in many traditions. 9 times 12 is 108. Also, 1 plus 8 equals 9. That 9 times 12 equals 108.
Heart Chakra: The chakras are the intersections of energy lines, and there are said to be a total of 108 energy lines converging to form the heart chakra. One of them, sushumna leads to the crown chakra, and is said to be the path to Self-realization.
Marmas: Marmas or marmastanas are like energy intersections called chakras, except have fewer energy lines converging to form them. There are said to be 108 marmas in the subtle body.
Time: Some say there are 108 feelings, with 36 related to the past, 36 related to the present, and 36 related to the future.
Astrology: There are 12 constellations, and 9 arc segments called namshas or chandrakalas. 9 times 12 equals 108. Chandra is moon, and kalas are the divisions within a whole.
Planets and Houses: In astrology, there are 12 houses and 9 planets. 12 times 9 equals 108.
Gopis of Krishna: In the Krishna tradition, there were said to be 108 gopis or maid servants of Krishna.
1, 0, and 8: 1 stands for God or higher Truth, 0 stands for emptiness or completeness in spiritual practice, and 8 stands for infinity or eternity.
Sun and Earth: The diameter of the sun is 108 times the diameter of the Earth.
Numerical scale: The 1 of 108, and the 8 of 108, when added together equals 9, which is the number of the numerical scale, i.e. 1, 2, 3 ... 10, etc., where 0 is not a number.
Smaller divisions: The number 108 is divided, such as in half, third, quarter, or twelfth, so that some malas have 54, 36, 27, or 9 beads.
Islam: The number 108 is used in Islam to refer to God.
Jain: In the Jain religion, 108 are the combined virtues of five categories of holy ones, including 12, 8, 36, 25, and 27 virtues respectively.
Sikh: The Sikh tradition has a mala of 108 knots tied in a string of wool, rather than beads.
Chinese: 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.
Stages of the soul: Said that Atman, the human soul or center goes through 108 stages on the journey.
Meru: This is a larger bead, not part of the 108. It is not tied in the sequence of the other beads. It is the quiding bead, the one that marks the beginning and end of the mala.
Dance: There are 108 forms of dance in the Indian traditions.
Pythagorean: The nine is the limit of all numbers, all others existing and coming from the same. ie: 0 to 9 is all one needs to make up an infinite amount of numbers.
We have listed below 108 Upanishads as per the list contained in the Muktikopanishad . We have arranged them in four categories according to the particular Veda to which each of them belong.
Rigveda(10): Aitareya , Atmabodha, Kaushitaki, Mudgala, Nirvana, Nadabindu, Akshamaya, Tripura, Bahvruka, Saubhagyalakshmi.
Yajurveda(50): Katha, Taittiriya , Isavasya , Brihadaranyaka, Akshi, Ekakshara, Garbha, Prnagnihotra, Svetasvatara, Sariraka, Sukarahasya, Skanda, Sarvasara, Adhyatma, Niralamba, Paingala, Mantrika, Muktika, Subala, Avadhuta, Katharudra, Brahma, Jabala, Turiyatita, Paramahamsa, Bhikshuka, Yajnavalkya, Satyayani, Amrtanada, Amrtabindu, Kshurika, Tejobindu, Dhyanabindu, Brahmavidya, YogakundalinI, Yogatattva, Yogasikha, Varaha, Advayataraka, Trisikhibrahmana, mandalabrahmana, Hamsa, Kalisantaraaa, Narayana, Tarasara, Kalagnirudra, Dakshinamurti, Pancabrahma, Rudrahrdaya, SarasvatIrahasya.
SamaVeda(16): Kena, Chandogya, Mahat, Maitrayani, Vajrasuci, Savitri, Aruneya, Kundika, Maitreyi, Samnyasa, Jabaladarsana, Yogacudaman, Avyakta, Vasudevai, Jabali, Rudrakshajabala.
Atharvaveda(32): Prasna , Mandukya, Mundaka, Atma, Surya, Narada-Parivrajakas, Parabrahma, Paramahamsa-Parivrajakas, Pasupatha-Brahma, Mahavakya, Sandilya, Krishna, Garuda, Gopalatapani, Tripadavibhuti-mahnarayana, Dattatreya, Kaivalya, NrsimhatapanI, Ramatapani, Ramarahasya, HayagrIva, Atharvasikha, Atharvasira, Ganapati, Brhajjabala, Bhasmajabala, Sarabha, Annapurna, TripuratapanI, Devi, Bhavana, SIta.
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The Significance of the number 108
We must agree that all measuring systems are merely reference frames. They give us a starting point. It doesn’t really matter if you call them farenheits or cycles. All science is based on fundamental assumptions of the mechanics of this universe. Yet, these assumptions, if correct, connect like building blocks.
Much in the same way, the number ‘108’ is just a reference frame. It is symbolic of a bigger picture: that of humility. When devotees recite 108 Hanuman Chalisas, in their minds they believe, they are proving their love for God, and that there is in fact a need to prove their love. When devotees assign a 108 names to Shri Ganesh, they are once again gauging their devotion through numbers. This, of course, may be considered unreasonable, since it suggests that 108 chants are more effective than 109 chants. How do they know this? Have they proved it? Is 108 the magic number of the universe? No, it is not! It is a reference frame. What is important is that a system is imposed to guide us through the fundamental struggles encountered in any evolutional process. Otherwise, chaos and anarchy follow and nothing gets done.
Having said that, I will show you justifications from a few subcultures in India. Obviously, I consider the Vedic rationale to be the most consistent with the fundamental laws of this universe. The others have borrowed and built, but it still smells of Vedic beginnings.
In present times, we can find many rationales for the proliferation of ‘108’ throughout our scriptures. In fact, this number seems to garner its unfair share of attention from myriad cults and faith systems around the world. I will give you a few justifications that have been brought to my attention.
JYOTISH SHASTRA {VEDIC SYSTEM**
This universe was created by the five elements: space, air, fire, water and earth. From these elements came the three attributes: Raj {birth**, Sat {protection** and Tam {destruction or death.**
The mathematical or geographical evidence proves that one circle has 360 degrees in space. Why is this circle or wheel of life considered to be of 360 degrees only? If we take a circle and start dividing it using the four elements and three attributes, all the logic can be observed.
The circle itself, is considered the first element of space, since we must consume space in drawing a circle. In this space {or circle**, the four remaining elements and three attributes create the idea of time. The circle is divisible by the product of four elements multiplied by three attributes. This involves the belief that the three attributes exist in the circle. By moving three times, each element completes its revolution.
So now we have the number 12 {3 x 4**. This division gave birth to our 12 months, and also to the 12 horas {1/2 of the day or Ahoratri**. We now have 360 degrees as well as 12 divisions. We can now further divide the wheel of time: there are 27 fixed stars (nakshatras) along with three attributes that divide the time in smaller portions. So this 27 + 3 = 30 is interpreted as 30 degrees or days of one part of the wheel (circle) or month. All of this is only half of a day. The night is yet unaccounted for. Therefore, we multiply these 30 degrees by 2. This gives us our reference of 60 seconds in a minute.
Thus the 360º x 30º = 10,800. Zero {0** is considered ‘Purna’ or complete. So we take out the last zeros and are left with 108. The idea of our total universe is represented by this number of 108. Offering 108, devotees believe that they are showing ultimate or complete respect to the Supreme.
There are many other justifications but all can be traced back to this system. A few are explained below:
SHOSHU BUDDHIST
Followers use 108 beads in their malas. They implement the following formula:
6 x 3 x 2 x3 = 108
6 senses [sight, sound, smell, taste, touch, thought]
3 aspects of time [past, present, future]
2 condition of heart [pure or impure]
3 possibilties of sentiment [like, dislike, indifference]
BUDDHA’S FOOTPRINT
All Buddhists accept the Buddha Footprint with its 108 Auspicious Illustrations. These areas are considered to have been marked on the Buddha’s left foot when his body was discovered.
BUDDHISM
108 beads on the Hindu maalaa {rosary**
108 Arhats or Holy Ones
HINDUISM
108 Gopis {consorts** of Lord Krishna
108 Holy places for Vaishnavas
108 beads on the Japa maalaa {rosary**
108 Upanishads
108 Divyadeshes - Divine or Sacred Tirtha throughout India and Nepal
108 sacred water taps in Muktinath - Nepal
TANTRA SHASTRA
108 Pitha {Sacred Places**
The story goes that Lord Shiva was in deep and incessant meditation. His asceticism was creating great heat in the universe. All existence was in peril and Lord Brahma was deeply concerned. Lord Brahma asked the Mother of the Universe, Maa Shakti, to use Her strength and wile to seduce Lord Shiva. Maa Shakti agreed and was born as Sati, daughter of Shri Daksha. Lord Shiva was so entranced by Sati’s asceticism and extraordinary beauty that he took human form and they were married. Years later, at a feast, Sati’s father insulted Lord Shiva. Sati was so humiliated that she began a deep meditation which led to her immolation. Lord Shiva was completely heart broken. He reached into the sacrificial fire and pulled out as much of His beloved’s body as he could grab. As He ascended to heaven, bits of Sati’s body fell to earth. 108 bits to be precise! In time, these places were acknowledged and worshipped.
SANATANA DHARMA
In a book by Khurana, the explanation closely mirrors the original Vedic justifications:
A circle has 360 degrees, which when multiplied by 60 gives us 21,600 minutes in a circle. 60 comes from the 60 'ghatis' which Sanatana Dharmiks believe in. One ghati is equal to 24 minutes and 60 ghatis come to 24 hours.
One ghati is divided into 60 parts or 'palas'.
So the 60 ghatis multiplied by 60 palasa comes to 3,600.
This is further multiplied by 60 (becase a pala contains 60 vipalas) which gives us 21,600.
Half of this is for the day, and the other half for the night. So, 21,600
divided by 2 gives us 10,800. For practical purposes, we use 108. Using the
number 108 helps us coordinate the rhythm of time and space & we remain in harmony with the spiritual powers of nature.
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