Non commercial web site, available to every one. Use it if you find them useful. Encouraged to copy and distribute if needed.
Like Hindus/Indians, other cultures like Babylonians and Mayans both associated numbers with God, divinity, spirituality and so on. The Mayans used 13 and the Babylonians used 60. In the Greek world, some followers of Pythagoras prayed to the first 4 numbers and thought they were the creator.
The sacred numbers of Hinduism are thought to be the bearers of cosmic powers and grandeur. Rishis have been meditating over them to find out the hidden symbolical meaning behind it.
Philosophers/Mathematicians, were open to the concept of nothingness. Mathematicians were obsessed with giant numbers, counting well into the trillions and even had different types of infinity. Nice model of number system within zero and Infinite was a remarkable achievement. Both zero and Infinite are not strictly numbers, but two ends or boundaries.
Nothingness Emptiness and Zero
Nothingness is a philosophical term that denotes the general state of nonexistence. To exist, nothingness must also be not nothing, but an empty thing of something else. Nothingness cannot exist or it is not real. There is no Nothingness.
Many cultures had a negative view of the concept of nothingness.
Emptiness means to remove everything. Applies to both physical and mental realm. Emptiness is complete inner-silence; a quiescent mind, empty of the belief that oneself is a separate entity with an independent existence.
The zero itself does not contain anything, but is not unreal absolutely. Is ZERO just a mathematical concept?
Zero, nothing, empty or void and other derived words from the root svi, means "hollow". Hollow may include nothing bounded by something. Non existance may be beyond all these.
The mathematical zero and the philosophical notion of nothingness are related but are not the same. Nothingness plays a central role very early on in Indian thought (there called sunya), and we find speculation in virtually all myths about what must have preceded the world's creation.
Zero
Zero, is a numerical or symbolic representation of emptiness. It is difficult to say whether it exists or not, whether it is a number or not. Use of ZERO was a hugely significant mathematical development, one that is fundamental to calculus, which made physics, engineering and much of modern technology possible.
The mathematical zero and the philosophical notion of nothingness or shunya are related. Nothingness plays a central role very early on in Indian thought. Before manifestation/creation, was there only void? Shunya has many references in the vedic literature (including buddhist/Jain etc) like Amarkosa, Ganita Sastraka or the Atharvaveda. Shunya also finds its references in the Bakshali Manuscript (200 AD), the Shahpur stone inscription (672 AD) of Adityasena, Bihar and the Malay inscription of Katakapur (686 AD). Pingala used the sanskrit word sunya explicitly to refer to zero. This symbol appeared as early as 224 CE. 9th-Century Chaturbhuj Temple has zero carved into its solid rock face
This number ‘shunya’ or zero is denoted by both a dot (.) and a small circle (o), because shunya identified itself with the conception of nirguna Brahma and fullness. The conception of Brahmam further lies in meditation on a particular point or circle. Shunya might have got its symbol from planets that look like dots. Similarly smallest partice (matter) has both the aspects of absence and fullness, similar to that of shunya.
It was used in mathematics if the remainder was nothing. Brahmagupta and others used small dots under numbers to show a zero placeholder, but they also viewed the zero as having a null value. Later refined zero concepts developed in India, spread to other places. Thus Zero symbol entered the Islamic world in 813 CE. After many adventures and much opposition, the symbol we use was accepted and the concept flourished, as zero took on much more than a positional meaning.
Egyptians zero documented around 1740 BCE was nfr, also meaning beautiful or good. Sumerian culture, some 5,000 years ago used, a slanted double wedge was inserted between cuneiform symbols for numbers, to indicate the absence of a number in a place. The Mayans used the number zero, as a place holder.
ONE
Eka is a symbolic representation of saguna Brahman or Brahman with qualities and form. Brahman is also called the cosmic soul or Hiranyagarbha. one also symbolizes atman, the individual soul.
One, Eka is a symbolic representation of saguna Brahman or Brahman with qualities and form. Saguna Brahman is the awakened Brahman who projects the worlds and the entire creation out of himself. He is also called the cosmic soul or Hiranyagarbha.
It is not zero that creates other numbers, but actually the number one. Just as Brahman exists everywhere in his entire creation, the number one exists in every other number.
Like saguna Brahman, one is the first to manifest and exists or hidden in every other number. As a subjective reality, one also symbolizes atman, the individual soul. Atman is Brahman in its microcosmic aspect.
ONE and Zero
The concept of zero is essential to a system that’s at the basis of modern computing: binary numbers. Modern-day digital computers operate on the principle of two possible states, ‘on’ and ‘off’. The ‘on’ state is assigned the value ‘1’, while the ‘off’ state is assigned the value ‘0’. Or, zero. In the 2nd or 3rd Centuries BCE by a musicologist named Pingala, used this.
Two
In binary system, 2 = 10. So from single state to 2 satates and generating large varieties by repeating the process.
The number two is a symbolic representation of the state of duality which we experience objectively through our minds and the senses. It also symbolizes Purusha and Prakriti (God and Nature), Brahman and Atman, the knower and the known, the subject and the object, the doer and the deed, cause and effect, the right and wrong, knowledge and ignorance, life and death, etc
Three or Trinity
The Trinity based on roles: Brahma is the creator. Vishnu is the preserver. Siva is the destroyer.
body mind spirit/soul
Triple gunas (triguna) of sattva, rajas and tamas
The Symbol of AUM consists of three curves representing the three states of consciousness. AUM has three letters.
The number three symbolizes many other aspects of creation:
Triple division of time, past, present and future;
Three worlds of heaven, earth and the hell;
Triple qualities of sattva, rajas and tamas;
Three layers of nature, light, fire and darkness;
Three states of being immanent, transcendent and the absolute;
three worlds of heaven, earth and the hell;
Three phases of life, young age, middle age and old age;
Three paths to self-realization, the path of knowledge, the path of love and the path of action;
the triple control of control of body, mind and action or thought, word and deed;
Four
Four is the smallest composite number.
4**2 = 2**4
A circle divided by 4 makes right angles and four quadrants. Because of it, four (4) is the base number of the plane (mathematics).
A solid figure with four faces as well as four vertices is a tetrahedron,[4] and 4 is the smallest possible number of faces (as well as vertices) of a polyhedron.
The god Brahma has four faces, may be indicating ability to see all 4 directions.
The aims of life (purusharthas) are four, dharma (righteousness), artha (wealth), kama (desire) and moksha.(salvation).
The stages (ashrama) in life are four: the age of studentship (brahmacharya), the age of householder (grihasta), the age of retirement (vanaprastha) and the age of ascetic (renunciation).
The Vedas or scriptures are also four in number.
There are four Vedas: Rigveda, Samaveda, Yajurveda and Atharvaveda.[37]
The four stages of life Brahmacharya (student life), Grihastha (household life), Vanaprastha (retired life) and Sannyasa (renunciation).[39]
The four primary castes or strata of society: Brahmana (priest/teacher), Kshatriya (warrior/politician), Vaishya (landowner/entrepreneur) and Shudra (servant/manual laborer).
The swastika symbol signifies good from all four directions.[41]
[42]
There are four yugas: Satya, Dvapara, Treta and Kali[43]
The symbolic meanings of the number four are linked to those of the cross and the square. "Almost from prehistoric times, the number four was employed to signify what was solid, what could be touched and felt. Its relationship to the cross (four points) made it an outstanding symbol of wholeness and universality, a symbol which drew all to itself". Where lines of latitude and longitude intersect, they divide the earth into four proportions. Throughout the world kings and chieftains have been called "lord of the four suns" or "lord of the four quarters of the earth",[81] which is understood to refer to the extent of their powers both territorially and in terms of total control of their subjects' doings.
Five
Five elements: Ether (akasa); earth; Air (vayu); Agni (fire); and Water (jalam)
The senses are five in number: skin, eyes, nose, ears and tongue.
Five organs of action or karmendriyas, hands, legs, genitals, larynx and anus.
Five qualities of Supreme Being (Saguna Brahman): truth (satyam), knowledge (jnanam), infinity (anantam), bliss (anandam) and purity (amalatvam).
Five fold manifestation of Paramasiva or Parameswara (the primal being): Brahma (creator), Vishnu (preserver), Rudra (destroyer), Maheswara (concealer) and Sadasiva (revealer).
Five aspects of Vishnu as Isvara: para (transcendent), vyuha (emanating), vibhava (incarnating), antaryami (immanent) and archavatara (consecrated image).
Five classes of beings, gods, men, gandharvas, serpents and ancestors.
Five breaths of life, prana, apana, vyana, udana and samana.
Five angas (parts) of calendar
Six
6 is the smallest positive integer which is neither a square number nor a prime number. Six is the second smallest composite number; its proper divisors are 1, 2 and 3. Since six equals the sum of its proper divisors, six is the smallest perfect number, Granville number, and -perfect number.
6 represents 6 points forming hexagon, by intersection of two equal triangles
The mind is the sixth sense organ, with six faculties: reason, emotion, thought, awareness, knowledge and intelligence, and six enemies or impurities: lust, anger, greed, pride, delusion and envy.
Seven
Highest single digit prime number, which cannot be divided by any other number other than 1 and themselves.
7 is the only Number "that can divide "Infinitely" - infinitely, or "Infinite number of times"
1/7 = 0.142857 142857 142857 ....
2/7 = 0.285714 285714 285714 ....
3/7 = 0.428571 428571 428571 ....
4/7 = 0.571428 571428 571428 ....
5/7 = 0.714285 714285 714285 ....
6/7 = 0.857142 857142 857142 ....
Seven has been popular in all cultures. May be inspired by few 7 star patterns.
- The key musical notes are seven
- Our earth is but one in a series of several planes of existence. In all there are said to be 14 planes or worlds of which six are above the earth and seven below the earth. Satya, Tapa, Janak, Mahar, Svar, and Bhuvar are above Bhurloka (earth)
- Seven planes below: atala, vitala, sutala, mahatala, tatatala, rasatala and patala.
- Sapta-puris or seven holy cities: kashipuri, kanchipuruam, mayapuri, ayodhyapuri, dwarakapuri, mathurapuri, and avantikapuri;
- seven sacred rives: Ganga, Yamuna, Godavari, Saraswathi, Narmada, Sindhu and Kaveri
- seven islands (jambu, shaka, kusha, krauncha, shalmali, pluksha and pushkara) and surrounded by seven seas (kara, ksheera, sura, ghrita, rusa, dahi and jala).
- The seven sages or saptarishis, who descended from the stars in the constellation called Ursa Major
- Seven planes of consciousness or sheaths in our bodies: physical plane (annamaya) with earth, breath plane (pranamaya) with bhuva, mental plane (manomaya) with svarga, the plane of intelligence (vignanamaya) with mahar, the plane of latent divinities with janah, the radiant plane of spiritual fire with tapo and the supreme consciousness of Atman itself with Brahma.
- Seven Power or Energy Forms:Brahmi awakening power; Vaishnavi organizing power; Maheswari concealing power; Kaumari awakening power; Varahi assimilating power; Aindri conscientious power; and Chamundi controlling power.
Egyptians mapped seven paths to heaven. Buddha took seven strides. In the Mysteries of Mithras, in Persia, there were seven stages or degrees of initiation
Eight
8 can be halved successively till it reduces to 1.
The astadikpalas are lords of the eight directions of space: Indra (eastern Lord), Varuna (western Lord), Kubera (northern Lord), Yama (souther Lord), Agni (southeastern Lord), Niruthi (southwestern Lord), Isana (northeastern Lord) and Vayu (northwestern Lord).
Eight Adityas: Mitra, Varuna, Aryaman, Amia, Bhaga, Dhatar, Indra, Vivsvant.
Eight Rudras: Bhava, Sarva, Isana, Pasupathi, Bhima, Ugra, Mahadeva and Rudra.
Eight Vasus: Dhara (the earth), Anala (the fire), Apa (waters), Anila (wind), Dhruva (north star), Soma (the moon), Prabhasa (the dawn) and Pratyusa (the light).
The science of yoga is known to have eight limbs, hence the name as ashtanga yoga or the eight limbed yoga. They are yama (control), niyama (rules), asana (postures), pranayama (breathing practice), pratyahara (withdrawal of senses), dharana (concentration), dhyana (meditation) and samadhi (state of self-absorption).
The Goddess Lakshmihas eight forms: Adi Lakshmi (primal), Dhanya Laskhmi (wealth of grains), Dhairya Laskhmi (wealth of courage), Gaja Laskhmi (welath of elephants), Santana Laskhmi (wealth of children), Vijaya Laskhmi (wealth of success). Vidya Laskhmi (wealth of knowledge) and Dhana Laskhmi (monetrary wealth).
number 9
9 = 3*3 (3 squre, smallest magic square)
9 corresponds to grahas
Satyug - consists of 172,800 years (1+7+2+8) = 18 == (1+8 = 9)
TretaYug consists of 1296000 years (1+2+9+6) = 18 = (1+8 = 9)
DwaparYug consists of 864000 years (8+4+6) = 18 = (1+8 = 9)
Kaliyug consists of 432000 years (4+3+2) = 9
The human body is considered as a city of nine gates which correspond with the nine openings (two eyes, two ears, two nostrils, navel and two excretory openings).
The nine forms of devotion : sravanam (hearing about God), kirtanam (singing the praise of God), mananam (remembering God), padaseva (serving the feet of God), archanam (worshiping God), mantram (offering prayers to God), seva (serving the cause of God), maitri (friendship with God) and saranam (surrender to God).
Ten, Dasam
First 4 numbers totals 10 (1+2+3+4=10)
Ten is the first double digit number formed by the coming together of one and zero. The zero stands for nirguna Brahman. The one stands for both Saguna Brahman and the individual Atman.
The number symbolically represents the incarnation of God and also symbolizes a self realized yogi who has experienced Brahman.
Twelve 12
12 is a composite number with four divisors (2, 3, 4 and 6).
12 Knuckles in a hand
12 Gods, 12 Disciples, 12 Tribes and the Zodiac of 12 months, rashis and so on.
Eighteen 18
18 a manifestation of 9, is a composite number, with large number of divisors being 1, 2, 3, 6 and 9. Three of these divisors (3, 6 and 9) add up to 18, hence 18 is a semi perfect number. 18 is the only number that equals twice the sum of its decimal digits.
Mahabharata has been organized into 18 parvas and Geeta added to the epic was divided into 18 chapters.
Twenty-seven
27 Nakshatras
27 is the value of the expression n^n, where n=3.
In a prime reciprocal magic square of the multiples of 1/7.
The magic constant is 27.
1/7 = 0·1 4 2 8 5 7...
2/7 = 0·2 8 5 7 1 4...
3/7 = 0·4 2 8 5 7 1...
4/7 = 0·5 7 1 4 2 8...
5/7 = 0·7 1 4 2 8 5...
6/7 = 0·8 5 7 1 4 2...
27 54 108 216 432 Harshad number series
60 and Sexagesimal system
60 is convenient for division by 2,3,4,5 and 6.
That way one can express fraction of 60 in whole numbers.
60 = 12 (Knuckles in a hand) * 5 (fingers in a hand)
The sexagesimal system of measurement is based on the number sixty. There are sixty seconds in a minute, sixty minutes in a hour. When we measure angles, we use the sexagesimal to express units in degrees, minutes and seconds. This method of measurement familiar to both the Indian and Mesopotamian cultures.
Sexagesimal system may be based in large part upon the observation of the planets, specifically Jupiter and Saturn. After every sixty years, Jupiter and Saturn will return to the same relative place in the zodiac.
The sixty years cycle of Jupiter and Saturn gives rise to another interesting number. In a sixty year period, Jupiter will complete five circuits of the zodiac and Saturn will complete two circuits. The combined individual cycles equal seven which is also the total number of visible planets plus the two luminaries.
Number 108 is LCM of 27 and 12
108 is a Harshad (means "great joy") number, which is an integer divisible by the sum of its digits (1+0+8 = 9)
The number 108 appears often in Hindu and Buddhist philosophy. 27 constallations and each one has 4 directions or 4 parts, and 27 * 4 = 108
9 corresponds to grahas and 12 to rassi and 9 * 12 = 108
54 letters in the Sanskrit alphabet. Each has masculine and feminine, 54 times 2 is 108.
1 stands for God, 0 stands for emptiness or completeness, 8 stands for infinity or eternity. (1 - Saguna Brahman; 0 - Nirguna Brahman; 8 - eternity or infinity.)
Sun is approx 108 times the diameter of the Earth.
The distance from the Sun to the Earth is approx 108 times the diameter of the Sun. Distance of the Moon from the Earth is approx 108 times the diameter of the Moon.
Silver represent the moon and atomic weight is 108.
There are a 108 marmas in the body.
Number 360
360 is a highly composite number
The smallest number divisible by every natural number from 1 to 10 except 7.
A circle is divided into 360 degrees for the purpose of angular measurement.
This choice of unit allows round angle to be divided into equal sectors measured in integer degrees rather than fractional degrees. 360 is the sum of two twin primes (179 + 181).
one year is close to 360 days, making it equal to 12 months (30*12).
Number 432
The number 432 = (2^4)*(3^3).
Equals 2 to the power of 4 multiplied by 3 to the power of 3.
432 is a Harshad number
It was consifered as magic number for astronomical calculations.
Kalacakra calendar in use, 60 year cycle starting with Prabhava, is by Pandita Somanatha of Kashmir/Himalayas, in 367 CE. Vernal equinox of 367 CE is Prabava Varsham. He further developed sexa decimal system. The earth's axis wobble that causes the precession of the equinoxes is approximately 25,920 years or 432 sixty year cycles.
Number 2520 and 252
252 is a Harshad number in base 10. Divisible by 1, 2, 3, 4, 6, 7, 9.
2520 is the smallest number divisible by all integers from 1 to 10, i.e., it is their least common multiple.
It is the product of five consecutive numbers, namely 3×4×5×6×7
2520=7*30*12 - 7 day week 30 days a month and 12 month
It is a Harshad number in all popular bases 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 and 16.
Infinity
Infinite and Zero are two boundaries.
The first unenumerable number was constructed using effectively a recursive construction. Still the highest enumerable number has not been attained.
Five different types of infinity: infinite in one direction, infinite in two directions, infinite in area, infinite everywhere and perpetually infinite.
The set of real numbers (or even complex numbers) does not include infinity. It’s not a number, but a symbol representing a particular kind of non-number. It’s either the “end” of a process that never ends (limits), or it’s a marker indicating something didn’t “converge” (series).
As a concept “infinity” is pre-historic. Indian scriptures reserve infinity, as attributes of almighty. It represents eternal time & space. Infinity make us accept of our limitations and feel humble in a good way. The Ouroboros or Lemniscate, meaning ‘ribbon’, by ancient Greeks, is an ancient symbol depicting a serpent biting its own tail. It represents the infinite immortality, continuity, and eternal return.
Letter to Numerals
There were many system to depict letters to numerals for easy remembrance of numbers as words or verses. Some like Kaṭapayādi become popular in South India, especially Kerala. Kaṭapayādi is compared with few systems
| Kaṭapayādi | Phone pad | Numerology | mnemonic system* |
| 0 | ña na - | ambersand | | s x z (ச ங ஞ ஸ ஷ) |
| 1 | ka ṭa pa ya | a b c | a i j q y | t d (ட த ) |
| 2 | kha ṭha pha ra | d e f | b k r | n (ண ந ன) |
| 3 | ga ḍa ba la | g h i | c g l s p | m (ம) |
| 4 | gha ḍha bha va | j k l | d m t | r (ர ற) |
| 5 | ṅa ṇa ma śa | m n o | e h n x | l (ல ள) |
| 6 | ca ta - ṣa | p q r s | u v w | h (ஹ) |
| 7 | cha tha - sa | t u v | o z | c k q g (க க்ஷ) |
| 8 | ja da - ha | w x y z | f p | f v w (வ ழ) |
| 9 | jha dha - - | [ ] space | | p b (ப) |
*I (author) has used this for coding in one of the project. Vowels and letters j and y are ignored. For example 36 can be mahe and 10 can be tax. Can be extended for Tamil-grantha characters given in brackets. Sililarly characters are அ, ஆ, இ, ஈ, உ, ஊ, எ, ஏ, ஐ, ஒ, ஓ, ஔ, ய, ஜ are ignored.
Kaṭapayādi notation an ancient Indian alphasyllabic numeral system Assigning more than one letter to one numeral and nullifying certain other letters as valueless. The Ka-ṭa-pa-yā-di system is not confined to India. Some Pali chronograms based on the Ka-ṭa-pa-yā-di system have been discovered in Burma.
Following verse found in Śaṅkaravarman's Sadratnamāla explains the mechanism of Kaṭapayādi system.
नञावचश्च शून्यानि संख्या: कटपयादय:।
मिश्रे तूपान्त्यहल् संख्या न च चिन्त्यो हलस्वर:॥
nanyāvacaśca śūnyāni saṃkhyāḥ kaṭapayādayaḥ
miśre tūpāntyahal saṃkhyā na ca cintyo halasvaraḥ
Translation: na (न), ña (ञ) and a (अ)-s, i.e., vowels represent zero. The nine integers are represented by consonant group beginning with ka, ṭa, pa, ya. In a conjunct consonant, the last of the consonants alone will count. A consonant without a vowel is to be ignored.
Pi or π
Pi is an irrational number. It has an exact value, but representing that value by fractions or decimals can only be done approximately. And such approximations were all that ancient mathematicians including Indians developed.
Pi = 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 (100 digits)
355/113 ≈ 3.1415929 is the good rational approximation of π, compared to 22/7 ≈ 3.14286
Since the Indus Valley script is not deciphered, difficult to say how PI was known in the subcontinent in 3000 BC. The Vedangas and Sulabasutras also mention the value of π. The oldest of them, the Baudhayayana Sulabasutra claims that the perimeter of a pit is 3 times its diameter- therefore approximating the value of π at 3. Many other texts also approximate π at the value of 3.
Astronomical calculations in the Shatapatha Brahmana (c. 6th century BCE) use a fractional approximation of 339⁄108 ≈ 3.139.
In ancient times, pi approximated to be about the square root of 10, which is 3.16227766017. Mathematician and astronomer Aryabhata in the 5th century gave the approximation of (pi = 62832/20000 = 3.1416), which is better than (22/7 ≈ 3.14286)
Madhava (1340 AD) from the Kerala school of mathematics, came up with infinite series for trigonometric functions, including an infinite series for pi. By using the first 21 terms to compute an approximation of π, he obtains a value correct to 11 decimal places (3.14159265359). The value of 3.1415926535898, correct to 13 decimals, can be attributed to Madhava or one of his followers.
The infinite series in Yuktibhasha is rapidly convergent value of pi=3.1415926539 which is correct to 9 decimal places. With the correction formula, he found an approximation of π to 13 decimal places of accuracy when n = 75.
Ancient text a couple centuries old gives value of pi in the Katapayadi system. The digits are being read from right to left.
Karanapaddhati from the 18th century:
anūnanūnnānananunnanityai
ssmāhatāścakra kalāvibhaktoḥ
caṇḍāṃśucandrādhamakuṃbhipālair
vyāsastadarddhaṃ tribhamaurvika syāt
It gives the circumference of a circle of diameter, anūnanūnnānananunnanityai (10,000,000,000) as caṇḍāṃśucandrādhamakuṃbhipālair (31,415,926,536). That is 10 digits after the decimal point.
Sadratnamala from the 19th century has a longer verse
bhadrāṃbuddhisiddhajanmagaṇitaśraddhā sma yad bhūpagīḥ
PI=314159265358979324 (17 decimals)
Popular modern version 31-digit shloka for Pi, using modified Katapayadi verses, where the digits are read from left to right.
gopi bhagya madhuvrata
srngiso dadhi sandhiga
khala jivita khatava
gala hala rasandara
...
Website maintained by: NARA
