The spread of Santana Dharma and its people throughout te world is proven by Archeological finds, Astronomy,Cultural similarities, Etymological similarities between Sanskrit ,Tamil and the languages of the world and now DNA.
I have been writing on this for quite some time with authentic sources.
Brahmins of Australia ,Transcript of a newspaper article 13 September 1947.The Morning Tribune
The land mass we know of the world was not the same before thousands of years and the Sanatana Dharma dates more than thousands of years.
The remains of the Sanatana Dharma is found around the world so also the traces of the Communities of India, then called Bharatavarsha.
Brahmins, Kshatriyas, Vaisyas and Sudras of the Vedic period migrated and their lineage ids found even now in all parts of the world.
In Sri Lanka, Burma, Vietnam, Cambodia, Laos, Korea,Japan,China, Middle east, Europe, Russia, Arctic, Africa, Latin America, Central America,, US, New Zealand and Australia.
A study has shown that people migrated from India to Australia. (AP)
Read my posts on each of these.
Now there is evidence that the Brahmins of the Vedic period were a part of the group that migrated to Australia and their traces are found in Australia.
The 1947 Report by the Secretary of the Australian labour party that the racial purity of the Brahmins will be preserved in Australia confirms the Brahmin presence in Australia.
And the DNA evidence is provided below.
Sydney – People from the Indian sub-continent migrated to Australia and mixed with Aborigines 4 000 years ago, bringing the dingo dog with them, according to a study published on Tuesday.
The continent was thought to have been isolated from other populations until Europeans landed at the end of the 1700s.
But researchers at the Max Planck Institute for Evolutionary Anthropology in Leipzig, Germany, reported “evidence of substantial gene flow between Indian populations and Australia about 4 000 years ago”.
They analysed genetic variation from across the genome from Australian Aborigines, New Guineans, Southeast Asians, and Indians.
“Long before Europeans settled in Australia humans had migrated from the Indian subcontinent to Australia and mixed with Australian Aborigines,” the study said.
It found “substantial gene flow from India to Australia 4 230 years ago i e… well before European contact”, it said.
“Interestingly, this date also coincides with many changes in the archaeological record of Australia, which include a sudden change in plant processing and stone tool technologies… and the first appearance of the dingo in the fossil record,” said researcher Irina Pugach.
“Since we detect inflow of genes from India into Australia at around the same time, it is likely that these changes were related to this migration,” she added.
A study of the Sanatana Dharma and Tamil throws some interesting questions.
The Vedic Dharma seems, it has been held, to have originated in the North of Vindhyas, Sarasvati valley.
Shiva as a Yogi.
Recent studies, excavations of archeological sites relating to Hinduism, Sanatana Dharma around the world, from Australia to South America,Europe, Africa, Russia,China and information on the practices of the aborigines in various parts of the world,indicates that the Sanatana Dharma was prevalent in one form or another in all these places,
Western scholars used this to invent the Aryan Invasion Theory, that is a Group called Aryans, invaded India thought the Khyber Pass in the Northern part of India and had influenced the thought processes of the people living in India.
This Theory, deliberately floated by the British mainly, to subjugate India , now stands discredited.
Please read my detailed Post on The Aryan Invasion Theory, Myth.
The Aryan theory could not explain the references to the Sanatana Dharma in Tamil Literature, South India.
Tamil language dates back to thousands of years and the Vedas quote them and they, in turn quote Tamil.
The oldest Tamil site has been found in Pallavaram, Chennai .(dated around a Million years.)
‘Archaeologists have discovered India’s oldest stone-age tools, up to 1.5 million years old, at a prehistoric site near Chennai. The discovery may change existing ideas about the earliest arrival of human ancestors from Africa ‘.
Lord Krishna participated in the Tail Sangam as an Invitee.
Please refer my Post on this.
He married a Pandyan Princess and had a daughter through her, and got his daughter arrived to a Pandyan Prince , gave her a dowry of one hundred Yadava families to provide her and her children with Milk and Curds.
The Chera King Perunchotru Udiyan Neduncheralaathan participated in the Mahabharata War as the provider of food to both the Kaurava and Pandava armies.
He had Tharpana performed for those who died in the War.
Now comes the curious part.
Lord Rama ‘s ancestor Satyavrata Manu migrated fro the Dravida Desa(South of Vindhya Mountains) with his sons and his son Ikshvaku founded the Ikshvaku founded the dynasty, named after him, Lord Rama Belongs to this dynasty.
Shiva and His son Ganesha left, during the Great Flood, the time when Satyavrata Manu migrated to North, through the Middle east, traveling through europe, Africa,South America, North America((US), Central America, finally landing in the Arctic, where the Rig Veda was composed.
Please refer my Post on this.
Then they returned to India, then called the Bharata varsha and this entry was used to be denoted as the entry of the Aryans.
The Artifacts, archeological finds, cultural similarities, Languages of the found around the world indicates this.
Please read my posts on this.
Now Six avatars of Vishnu are from the South.
Matsya is from the Ocean and as such we can not ascribe a location on the earth.
Kurma is in the Ocean again, but there is a Temple where Kurma avatar took place.
Later Avatars from Lord Rama are from the North of Vindhyas.
Now Shiva is not mentioned in the Vedas excepting in the Sri Rudram,
‘Nama sivaaya cha, Siva dharayacha’
No special Sukthas directly addressed to Shiva are found.
Shiva means Auspiciousnees , as he etymology goes.
There is not much reference in the North of Vindhyas of Shiva as much as Vishnu or Rama, Krishna.
Shiva is considered to be Chief deity among the Tamils, though the early Tamil Literature has Gods assigned for each landmass as Murugan, Krishna, Kotravai(Durga)Varuna and Indra.
But Shiva is taken as the First Siddha, followed by Agastya and others.
The Thirumandiram of Thirumoolar contains the Yoga thoughts, Advatita and Tantric practices that are unique.
And this is much earlier to Ramayana and Agastya is referred to have founded Tamil , being handed over by Lord Shiva.
Ravana entered into a treaty with a Pandya King.
Many of the Tamil practices were incorporated by Apasthamba in the Vedic rituals, like the Mangalya Sutra.
Though there are common factors between the Sanatana Dharma and the Tamils, yet there is a uniqueness in Tamil practices, which are, curiously enough, not against the Vedic practices but reinforces them.
Many of the Avatars of Shiva have not been reported in the Literature of the North of the Vindhyas, though Puranas, mention Shiva avatars in the South,
Shiva is described as Piravaa Yaakaip Periyon,The Eldest, though Unborn.
He is considered as the First Guru, Adi Shiva, the First Siddha, the First Yogi.
The sixty-four avatars of Shiva in Madurai are not mentioned in the North.
The Agamas which came later to Vedas specified rules for the construction of Temples, though Temple worship is not mentioned in the Vedas.
Tamil Kings followed this and one finds ancient temples, both for Vishnu and Shiva in the South in the Agama style.
These temples, though the Agamas started with out the authority of the Vedas gained currency and helped Hinduism.
Considering all these facts, I tend to think the worship of Shiva in the South preceded the Sanatana Dharma of the North.
And one may note that the Rig Veda was composed in the Arctic.
Sanatan Dharma in the south, Dravida seems to have preced the Sanatan Dharma fro the North of the Vindhyas.
Vedic mathematics and science are ancient Indian systems of knowledge that have been passed down through generations. These systems originated in the Vedas, which are a collection of ancient Indian scriptures. Vedic mathematics is a system of mathematical calculations based on 16 sutras, or word-formulas, and 13 sub-sutras, or corollaries. This system is known for its simplicity and efficiency, as it allows for faster calculations and mental math techniques.
Vedic science, on the other hand, is a system of knowledge that encompasses a wide range of subjects, including astronomy, astrology, medicine, and philosophy. It is based on the principles of the Vedas and the Upanishads, which are ancient Indian texts that contain philosophical and spiritual teachings.
One of the key principles of Vedic science is the idea of interconnectedness between all things, known as the principle of unity. This principle suggests that everything in the universe is connected and that there is a fundamental unity underlying all of existence.
Another important principle of Vedic science is the idea of balance, or the principle of equilibrium. This principle suggests that in order for an individual or society to achieve health and well-being, there must be a balance between different aspects of life, such as work and rest, or physical and spiritual pursuits.
Overall, Vedic mathematics and science offer unique insights into ancient Indian knowledge systems and can provide useful tools and perspectives for modern-day learning and living.
Before I write on what Kerala Calculus is, I feel it is necessary to remind us Indians of the fact that our continued ignorance, indifference reluctance to learn our highly scientific texts have resulted in the Myth of Aryan Invasion Theory by the Eurocentric colonialists gained currency and it has taken a lot of efforts to deny the theory which attempted to deny India its glorious past.
There are other insidious attempts too.
That the scientificancient texts are vague, they do not really talk about science and people use it, after the modern science discovers something,Indians say that the facts were mentioned in the Hindu Texts.
And another ingenious attempt to deny India its rich scientific heritage is by stating that the data referred to in the tests were not used by the ancient Indians !
The only way one can counter these arguments is for us to study the original texts and bring into light the scientific thoughts found in our Texts.
I am trying to instill a sense of pride in our heritage by posting articles on various astounding facts in out texts, our stupendous Temples Astronomy.
It is for the specialists to delve deep into the Texts and reveal what they contain.
Unfortunately those who know Sanskrit are not generally aware of advanced modern Scientific Theories and those familiar with modern concepts do not know Sanskrit.
My request is that both the groups must get familiar with what they do not know or get together to highlight the highly advanced scientific nature of Hindu Thought.
I shall continue to post articles giving general directions.
Now to Calculus.
‘
Calculus is the mathematical study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. It has two major branches, differential calculus (concerning rates of change and slopes of curves),and integral calculus (concerning accumulation of quantities and the areas under and between curves); these two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Generally, modern calculus is considered to have been developed in the 17th century by Isaac Newton and Gottfried Leibniz. Today, calculus has widespread uses in science, engineering and economics and can solve many problems that algebra alone cannot.
Calculus is a part of modern mathematics education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has historically been called “the calculus of infinitesimals”, or “infinitesimal calculus”. The word “calculus” comes from Latin (calculus) and refers to a small stone used for counting. More generally, calculus (plural calculi) refers to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus, calculus of variations, lambda calculus, and process calculus.”
The Kerala Calculus.
The Kerala school of astronomy and mathematics was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Kerala, India, which included among its members: Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar. The school flourished between the 14th and 16th centuries and the original discoveries of the school seems to have ended with Narayana Bhattathiri (1559–1632). In attempting to solve astronomical problems, the Kerala school independently created a number of important mathematics concepts. Their most important results—series expansion for trigonometric functions—were described in Sanskrit verse in a book by Neelakanta called Tantrasangraha, and again in a commentary on this work, called Tantrasangraha-vakhya, of unknown authorship. The theorems were stated without proof, but proofs for the series for sine, cosine, and inverse tangent were provided a century later in the work Yuktibhasa (c. 1500 – c. 1610), written in Malayalam, by Jyesthadeva, and also in a commentary on Tantrasangraha.
Their work, completed two centuries before the invention of calculus in Europe, provided what is now considered the first example of a power series (apart from geometric series). However, they did not formulate a systematic theory of differentiation and integration, nor is there any direct evidence of their results being transmitted outside Kerala ..
The Kerala school has made a number of contributions to the fields of infinite series and calculus. These include the following (infinite) geometric series:
This formula, however, was already known in the work of the 10th century Iraqi mathematician Alhazen (the Latinized form of the name Ibn al-Haytham) (965-1039).[8]
The Kerala school made intuitive use of mathematical induction, though the inductive hypothesis was not yet formulated or employed in proofs. They used this to discover a semi-rigorous proof of the result:
for large n. This result was also known to Alhazen.
They applied ideas from (what was to become) differential and integral calculus to obtain (Taylor-Maclaurin) infinite series for , , and .TheTantrasangraha-vakhya gives the series in verse, which when translated to mathematical notation, can be written as:
where
where, for , the series reduce to the standard power series for these trigonometric functions, for example:
and
(The Kerala school did not use the “factorial” symbolism.)
The Kerala school made use of the rectification (computation of length) of the arc of a circle to give a proof of these results. (The later method of Leibniz, using quadrature (i.e.computation of area under the arc of the circle), was not yet developed.) They also made use of the series expansion of to obtain an infinite series expression (later known as Gregory series) for :
Their rational approximation of the error for the finite sum of their series are of particular interest. For example, the error, , (for n odd, and i = 1, 2, 3) for the series:
where
They manipulated the terms, using the partial fraction expansion of : to obtain a more rapidly converging series for :[1]
They used the improved series to derive a rational expression, for correct up to nine decimal places, i.e.. They made use of an intuitive notion of a limit to compute these results. The Kerala school mathematicians also gave a semi-rigorous method of differentiation of some trigonometric functions, though the notion of a function, or of exponential or logarithmic functions, was not yet formulated.
The works of the Kerala school were first written up for the Western world by Englishman C. M. Whish in 1835, though there exists another work, namely Kala Sankalita by J. Warren from 1825 which briefly mentions the discovery of infinite series by Kerala astronomers. According to Whish, the Kerala mathematicians had “laid the foundation for a complete system of fluxions” and these works abounded “with fluxional forms and series to be found in no work of foreign countries.” However, Whish’s results were almost completely neglected, until over a century later, when the discoveries of the Kerala school were investigated again by C. Rajagopal and his associates. Their work includes commentaries on the proofs of the arctan series in Yuktibhasa given in two papers, a commentary on the Yuktibhasa’s proof of the sine and cosine seriesand two papers that provide the Sanskrit verses of the Tantrasangrahavakhya for the series for arctan, sin, and cosine (with English translation and commentary)..
The following notes by westerners would justify what I had written at the beginning of the Post.
“
(Bressoud 2002, p. 12) Quote: “There is no evidence that the Indian work on series was known beyond India, or even outside Kerala, until the nineteenth century. Gold and Pingree assert [4] that by the time these series were rediscovered in Europe, they had, for all practical purposes, been lost to India. The expansions of the sine, cosine, and arc tangent had been passed down through several generations of disciples, but they remained sterile observations for which no one could find much use.”
Jump up^Plofker 2001, p. 293 Quote: “It is not unusual to encounter in discussions of Indian mathematics such assertions as that “the concept of differentiation was understood [in India] from the time of Manjula (… in the 10th century)” [Joseph 1991, 300], or that “we may consider Madhava to have been the founder of mathematical analysis” (Joseph 1991, 293), or that Bhaskara II may claim to be “the precursor of Newton and Leibniz in the discovery of the principle of the differential calculus” (Bag 1979, 294). … The points of resemblance, particularly between early European calculus and the Keralese work on power series, have even inspired suggestions of a possible transmission of mathematical ideas from the Malabar coast in or after the 15th century to the Latin scholarly world (e.g., in (Bag 1979, 285)). … It should be borne in mind, however, that such an emphasis on the similarity of Sanskrit (or Malayalam) and Latin mathematics risks diminishing our ability fully to see and comprehend the former. To speak of the Indian “discovery of the principle of the differential calculus” somewhat obscures the fact that Indian techniques for expressing changes in the Sine by means of the Cosine or vice versa, as in the examples we have seen, remained within that specific trigonometric context. The differential “principle” was not generalized to arbitrary functions—in fact, the explicit notion of an arbitrary function, not to mention that of its derivative or an algorithm for taking the derivative, is irrelevant here”
Jump up^Pingree 1992, p. 562 Quote: “One example I can give you relates to the Indian Mādhava’s demonstration, in about 1400 A.D., of the infinite power series of trigonometrical functions using geometrical and algebraic arguments. When this was first described in English by Charles Whish, in the 1830s, it was heralded as the Indians’ discovery of the calculus. This claim and Mādhava’s achievements were ignored by Western historians, presumably at first because they could not admit that an Indian discovered the calculus, but later because no one read anymore the Transactions of the Royal Asiatic Society, in which Whish’s article was published. The matter resurfaced in the 1950s, and now we have the Sanskrit texts properly edited, and we understand the clever way that Mādhava derived the series without the calculus; but many historians still find it impossible to conceive of the problem and its solution in terms of anything other than the calculus and proclaim that the calculus is what Mādhava found. In this case the elegance and brilliance of Mādhava’s mathematics are being distorted as they are buried under the current mathematical solution to a problem to which he discovered an alternate and powerful solution.”
‘If the Tamils have been mentioned in the Vedas, is The Tamil Sangam mentioned in the Vedas , Ramayana and Mahabharata?’
The answer is that the Vedas or the Ithihasas do not mention the Tamil Sangam, though the Tamil Classical Poetry of the Tamil Sangams mention the Vedas, Ramayana and the Mahabharata.
Toddler Krishna.
I shall provide the answer to the question at the end of the Post.
To understand the Vedic references to other communities, one has to understand the Tribal Groups during the Rig Vedic period.
What were they and where were they?
‘
five major tribal groups mentioned in Rig Veda : Yadus, TurvaSas, Anus, Druhyus and Purus. Tthe TRkSis are not included because they are referred to as people beyond the Vedic Aryan realm.
It is emphasised however that the Rig Veda hymns are composed under the patronage of Purus, who alone among the five named above are Aryas or Aryans, as is meant in the text. Only the PUrus are addressed as “Arya” in the Rig Veda. The other four may or may not have been of the same racial stock but, to the Rigvedic people and the composers of Rig Veda hymns, they are considered and termed as non-Aryans or “an-Arya”.
‘
Rig Veda hymns include in mention and references : with Aryas – the Purus – on one part, and the other part comprising of Yadus, TurvaSas, Anus and Druhyus,
But there are two distinct words by which the Rig Veda refers to these others :
II 11.18, 19; 12.10; 13.9: 15.9; 20.8;
III. 29.9; 34.6, 9; 49.2
IV. 16.9, 10, 12; 28.3, 4; 38.1;
V. 4.6; 7.10; 14.4; 29.10; 30.9; 31.5, 7; 70.3;
VI. 14.3; 16.15; 18.3; 23.2; 24.8; 29.6; 31.4; 45.24;
VII. 5.6; 6.3; 19.4;
VIII. 6.14; 14.14; 39.8; 50.8; 70.11; 76.11; 77.3; 98.6;
IX. 41.2; 47.2; 88.4; 92.5;
X. 22.8; 47.4; 48.2; 49.3; 55.8; 73.5; 83.3, 6;
95.7; 99.7, 8; 105.7, 11; 170.2.
There are two distinct aspects that differentiates the DAsas and Dasyus :
The term DAsa clearly refers to other tribes (ie. non-PUru tribes)
while the term Dasyu refers to their priestly classes (ie. non-Vedic priestly classes).
[This is apart from the fact that both the terms are freely used to refer to the atmospheric demons as much as to human enemies to whom they basically refer.]
a. According to IV. 28.4, the Dasyus are a section among the DAsas.
b. The Dasyus are referred to in terms which clearly show
that the cause of hostility is religious in nature :
Not one of these abusive terms are used even once in reference to Dasas.
c. The family-wise pattern of references to them also shows
that the Dasyus are priestly rivals while the DAsas are secular rivals.
The Dasyus are referred to by all the nine priestly families of RSis,
but never by the non-priestly family of RSis (the Bharatas).
The DAsas are referred to by the Bharatas (X.69.6; 102.3) also but not by the most purely ritualistic family of RSis, the KaSyapas, nor in the purely ritualistic of MaNDalas, the MaNDala IX.
d. The Dasyus, being priestly entities, do not figure as powerful persons or persons to be feared, but the DAsas, being secular entities (tribes, tribal warriors, kings, etc.) do figure as powerful persons or persons to be feared:
In three references (VIII.5.31; 46.32; 51.9), the DAsas are rich patrons.
In seven references, the DAsas are powerful enemies from whose fury and powerful weapons the composers ask the Gods for protection (I.104.2; VIII.24.27; X.22.8; 54.1; 69.6; 102.3) or from whom the Gods rescue the RSis (I.158.5).
In three others, the word DAsa refers to powerful atmospheric demons who hold the celestial waters in their thrall (I.32.11; V.30.5; VIII.96.18).
In contrast, Dasyus never figure as rich or powerful enemies. They are depicted as sly enemies who incite others into acts of boldness (VI.24.8).
e. While both DAsas and Dasyus are referred to as enemies of the Aryas, it is only the DAsas, and never the Dasyus, who are sometimes bracketed together with the Aryas.
Seven verses refer to both Aryas and DAsas as enemies (VI.22.10; 33.3; 60.6; VII.83.1; X.38.3; 69.6; 83.1; 102.3) and one verse refers to both Aryas and DAsas together in friendly terms (VIII.51.9).
This is because both, the word DAsa and the word Arya, refer to broad secular or tribal entities, while the word Dasyu refers to priestly entities : thus, one would generally say “both Christians and Muslims”, or “both padres and mullahs”, but not “both Christians and mullahs” or “both Muslims and padres”.
2. The second difference is in the degree of hostility towards the two.
The Dasyus are clearly regarded with uncompromising hostility,
while that towards the DAsas is relatively mild and tempered :
a. The word Dasyu has a purely hostile connotation even when it occurs in the name or title of heroes :
Trasadasyu = “tormentor of the Dasyus”.
DasyavevRka = “a wolf towards the Dasyus”.
It is clear , then, that the Tamils who were living South od the Vindhyas are the people being referred to as Dasyus.
This is confirmed by the information that Sage Viswamitra banished his sons to the Dasyu Region for disobeying him.
Apasthamba, a descendant of these excommunicated sons of Viswamitra complied the Apasthamba Sutra which incorporated the Tamils’ customs like Mangalya Sutra for marriages.
Lord Krishna married a Pandyan Princess and had a child through her;he had her married to a Pandyan prince.
Please read my Post on this.
Yadu families, after the Dwaraka deluge migrated to the South.
The connection between the Yadus and the other Vedic tribes, though frowned upon, continued.
The system of worship by the Dravidas, called by the Purus as Dasyus, was differnt.Tthey had Lord Shiva as the First Siddha and were more inclined towards the worship of Reality without Form.
Reference to this may be found in Thirumoolar’s Thirumandiram, where Formless worship is emphasized and one may find reference to passages ridiculing the idolatry practices.
However Tamils, at a later period worshiped various Gods.
They divided the lands into five, assigning Gods to each land.
Kurinji-Mountainous Region- Murugan, Subrahmanya.
Mullai-Forest areas, Maayon, Krishna,
Martham,Coplands-Indra..
Neydhal , Seashore, Varuna and
Palai, Desert, Kotravai, Durga.
And these Tamil Kings fought with the Vedic tribes of the North and have won many a battle.
Ravana, belonging to Vedic people (though many people dispute this,he was a Vedic scholar) was defeated by a Pandya King and signed a peace treaty with him.
Even Krishna and Arjuna fought with the southern tribes.
No wonder the people of the North viewed the people of the South as Hostile, Dasyus and did not refer to the Tamil Sangam.
I am continuing my research in this area as I am sure the there would be a reference to the Tamil Sangams.
The present post is with the resources available to me now.
* Please read my Post Rama’s Ancestor Manu a Dravida.
Great Grand Father, Grand Father, Father, Self and son!
For Guru reference,
Adi Shankaracharya never mentions himself directly in his works.
‘Sri Govinda Bhagavatpaada Sishya,’
Disciple of the Noble Govinda Bhagavatpaada”
This system has been in place from the early period of the Vedas.
The founders of the Humanity, as far as Hindu Texts go, are the Saptha Rshi, the Seven Sages , after whom the lineage is from.
And they are referred to in introducing oneself.
This system is called the Gotra.
This is patrilineal.
Then there is Pravara.
”
a Pravara (Sanskrit for “most excellent”) is a particular Brahmin’s descent from a rishi (sage) who belonged to their gotra (clan). In vedic ritual, the importance of the pravara appears to be in its use by the ritualist for extolling his ancestry and proclaiming, “as a descendant of worthy ancestors, I am a fit and proper person to do the act I am performing.” Generally, there are either three or five pravaras. The sacred thread yajnopavita worn on upanayana has close and essential connection with the concept of pravaras related to Brahmin gotra system. While tying the knots of sacred thread, an oath is taken in the name of each one of these three or five of the most excellent rishis belonging to one’s gotra.
The full affiliation of a brāhamana consists of (1)gotra, (2)sutra (of Kalpa), (3)shakha, (4)pravaras .
(Example 🙂 A brahmana named ‘Rama’ introduces himself as follows : I am ‘Rama’, of Shrivatsa gotra, of Āpastamba sutra, of Taittiriya shākha of Yajurveda, of five pravaras named Bhārgava, Chyāvana, Āpnavan, Aurva and Jāmdagnya (This example is based upon the example given by Pattābhirām Shastri in the introduction to Vedārtha-Pārijata, cf. ref.).’
It may be noted in the Pravara,three or Five Rishis are mentioned.
For example, Kasyapa, Apasthara, Naithruva’
This is different from Kasyapa Gotra.
There is another Pravara for Kasyapa Gotra as well.
Kasyapa, Aavatsaara, Daivala.
The same with the other Rishis.
Sometimes three Rishis are mentioned and at times Five.
Why?
One view is that these references are to the excellent ancestors from the Gotra.
My view is that , if that be case the first Rishi should always be the founder.
But , as in Nythruva Kasyapa, Kasyapa does not appear as the First Rishi but it is Naithruva.
Reason is that many Rishis have more than one wife and many children through each of them.
Kasyapa had more than one wife.
The Prajapati Daksha gave his thirteen daughters (Aditi, Diti, Kadru, Danu, Arishta, Surasa, Surabhi, Vinata, Tamra, Krodhavasha,Idā, Vishva and Muni in marriage to Kashyapa.
Though the Father is one, mother differs.
To identify and emphasize the differentitae, the three or Five Rishis are mentioned.
Traditionally the first wife’s son carries the Father’s name as Gotra and the others the son of the Second or third wife and but to make the reference correct the founder is mentioned later in the Pravara.
The pravara identifies the association of a person with two, three (or sometimes five) of the above-mentioned rishis. It also signifies the Sutras contributed to different Vedas by those rishis.
For example, Kashyapa Gothram has 3 rishis associated with it viz. Kashyap, Nidruva and Avatsara
In a court case “Madhavrao vs Raghavendrarao” which involved a Deshastha Brahmin couple, the German scholar Max Mueller’s definition of gotra as descending from eight sages and then branching out to several families was thrown out by reputed judges of a Bombay High Court. The court called the idea of Brahmin families descending from an unbroken line of common ancestors as indicated by the names of their respective gotras and pravaras impossible to accept. The court consulted relevant Hindu texts and stressed the need for Hindu society and law to keep up with the times emphasizing that notions of good social behavior and the general ideology of the Hindu society had changed. The court also said that the mass of material in the Hindu texts is so vast and full of contradictions that it is almost an impossible task to reduce it to order and coherence.
Brahmins of Australia ,Transcript of a newspaper article 13 September 1947.The Morning Tribune
A study has shown that people migrated from India to Australia. (AP)
for <img class="mwe-math-fallback-image-inline tex" src="
for large n. This result was also known to Alhazen.
, 
, and 
.TheTantrasangraha-vakhya gives the series in verse, which when translated to mathematical notation, can be written as:
where 
where, for 
, the series reduce to the standard power series for these trigonometric functions, for example:
and
(The Kerala school did not use the “factorial” symbolism.)
:
, (for n odd, and i = 1, 2, 3) for the series:
to obtain a more rapidly converging series for 
for 
. They made use of an intuitive notion of a limit to compute these results. The Kerala school mathematicians also gave a semi-rigorous method of differentiation of some trigonometric functions, though the notion of a function, or of exponential or logarithmic functions, was not yet formulated.
![https://upload.wikimedia.org/math/1/1/2/112f97d0a5732861bb9297b7d2c3e631.png"](https://upload.wikimedia.org/math/1/1/2/112f97d0a5732861bb9297b7d2c3e631.png"){kind=link}
You must be logged in to post a comment.