Virasena

Thursday, 17 January 2013

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Srimad-Bhagavatam 10.74 - The Deliverance of Sisupala at the Rajasuya Sacrifice

Krsna Book 1970 - 74 - The Deliverance of Sisupala

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India
India (ⁱ/ˈɪndiə/), officially the Republic of India (Bhārat Gaṇarājya), is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world. Bounded by the Indian Ocean on the south, the Arabian Sea on the south-west, and the Bay of Bengal on the south-east, it shares land borders with Pakistan to the west;China, Nepal, and Bhutan to the north-east; and Burma and Bangladesh to the east. In the Indian Ocean, India is in the vicinity of Sri Lanka and the Maldives; in addition, India's Andaman and Nicobar Islands share a maritime border with Thailand and Indonesia.
Home to the ancient Indus Valley Civilisation and a region of historic trade routes and vast empires, the Indian subcontinent was identified with its commercial and cultural wealth for much of its long history. Four of the world's major religions—Hinduism, Buddhism, Jainism, and Sikhism—originated here, whereas Zoroastrianism, Christianity, and Islam arrived in the 1st millennium CE and also helped shape the region's diverse culture. Gradually annexed by and brought under the administration of the British East India Company from the early 18th century and administered directly by the United Kingdom from the mid-19th century, India became an independent nation in 1947 after a struggle for independence that was marked by non-violent resistance led by Mahatma Gandhi.

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Ujjain
Ujjain pronunciation (help·info) (also known as Ujain, Ujjayini, Avanti, Avantikapuri), is an ancient city of Malwa region in central India, on the eastern bank of the Kshipra River (Hindi: क्षिप्रा), today part of the state of Madhya Pradesh. It is the administrative centre of Ujjain District and Ujjain Division.
In ancient times the city was called Ujjayini. As mentioned in the Mahabharata epic, Ujjayini was the capital of the Avanti Kingdom, and has been the Prime Meridian for Hindu geographers since the 4th century BCE. Ujjain is one of the seven sacred cities (Sapta Puri) of the Hindus, and the Kumbh Mela religious festival is held there every 12 years. It is also home to Mahakaleshwar Jyotirlinga, one of the twelve Jyotirlinga shrines to the god Shiva and is also the place where Lord Krishna got education with Balarama and Sudama from Maharshi Sandipani.

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Yantra Mantra
[[File:Sun Dial Ved S
The name is derived from Yantra, instrument, and Mantra, for formula or, in this context, calculation. Therefore jantar mantar means literally calculation instrument. Jantar Mantar is colloquially equated with the magical practices where "Mantar" refers to the incantation (or spell) and Jantar Mantar refers to questionable magical arts (astrology falling into such arts).The yantras have evocative names like, samrat yantra, jai prakash, ram yantra and niyati chakra; each of which are used to for various astronomical calculations.The primary purpose of the observatory was to compile astronomical tables, and to predict the times and movements of the sun, moon and planets.
Coordinates: 26°55′28.45711″N 75°49′27.32569″E / 26.9245714194°N 75.8242571361°E / 26.9245714194; 75.8242571361

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Achyuta Pisharati
Achyutha Pisharodi (c. 1550 at Trikkandiyur, Tirur, Kerala, India – 7 July 1621 in Kerala) was an Sanskrit grammarian, astrologer, astronomer and mathematician who studied under Jyeṣṭhadeva and was a member of Mādhava of Sañgamāgrama's Kerala school of astronomy and mathematics. He is remembered mainly for his part in the composition of his student Melpathur Narayana Bhattathiri's devotional poem, Narayaneeyam.
He discovered the technique of 'the reduction of the ecliptic'. He authored Sphuta-nirnaya , Raasi-gola-sphuta-neeti (raasi meaning zodiac, gola meaning sphere and neeti roughly meaning rule), Karanottama (1593) and a four- chapter treatise Uparagakriyakrama on lunar and solar eclipses.
Pisharati is known to have scolded and provoked an errant Narayana to take up the Brahmin's duties of prayer and religious practices. He accepted Narayana as his student. Later when Pisharoti was struck with paralysis (or rheumatism by another account), Narayana, unable to bear the pain of his dear guru, by way of Gurudakshina took the disease upon himself. As a result Pisharoti is said to have been cured, but no medicine could cure Narayana. As a last resort, Narayana went to Guruvayur and requested Thunchaththu Ramanujan Ezhuthachan, a great devotee of Guruvayoorappan, to suggest a remedy for his disease. Ramajunan Ezhuthachan advised him to compose a poetical work on the Avatars (incarnations) of Lord Vishnu beginning with that of Matsya (Fish). Narayana composed beautiful slokas in praise of Lord Guruvayurappan and recited them before the deity. He was soon cured of his disease.

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Apastamba
The Dharmasutra of Āpastamba forms a part of the larger Kalpasūtra of Āpastamba. It contains thirty praśnas, which literally means ‘questions’ or books. The subjects of this Dharmasūtra are well organized and preserved in good condition. These praśanas consist of the Śrautasūtra followed by Mantrapāṭha which is used in domestic rites and is a collection of ritual formulas, the Gṛhyasūtra which deals with domestic rituals and lastly the Śulvasūtra which are principles of geometry needed for vedic rituals.
Āpastamba is from a family of Brahmins of the Taittirīya branch Vedic school dedicated to the study of the KRISHNA Yajurveda. It is believed that the entire Kalpasūtra was written by Āpastamba, but, Kane states that there is difference of opinion among scholars regarding this issue. Kane assigns this Dharmasūtra an approximate date between 450-350 BC.
Several ancient commentaries were written on this Dharmasūtra. Among the most famous and the only one that survives is that of Haradatta. He commented on the praśnas of Āpastamba’s Gṛhyasūtra and Mantrapāṭha and Gautama’s Dharmasūtra. Haradatta belonged to South India, and Kane dates him to 1100-1300 CE.

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Aryabhata
Aryabhata (IAST: Āryabhaṭa, Sanskrit: आर्यभट) (476–550 CE) was the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His most famous works are the Āryabhaṭīya (499 CE, when he was 23 years old) and the Arya-siddhanta.
While there is a tendency to misspell his name as "Aryabhatta" by analogy with other names having the "bhatta" suffix, his name is properly spelled Aryabhata: every astronomical text spells his name thus, including Brahmagupta's references to him "in more than a hundred places by name". Furthermore, in most instances "Aryabhatta" does not fit the metre either.
Aryabhata mentions in the Aryabhatiya that it was composed 3,630 years into the Kali Yuga, when he was 23 years old. This corresponds to 499 CE, and implies that he was born in 476
Aryabhata was born in Taregna (literally, song of the stars), which is a small town in Bihar, India, about 30 km (19 mi) from Patna (then known as Pataliputra), the capital city of Bihar State. Evidences justify his birth there. In Taregna Aryabhata set up an Astronomical Observatory in the Sun Temple 6th century.

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Aryabhata II
Āryabhaṭa II (c. 920 – c. 1000) was an Indian mathematician and astronomer, and the author of the Maha-Siddhanta. The numeral II is given to him to distinguish him from the earlier and more influential Āryabhaṭa I.
Aryabhatta II's most eminent work was Mahasiddhanta. The treatise consists of eighteen chapters and was written in the form of verse in Sanskrit. The initial twelve chapters deals with topics related to mathematical astronomy and covers the topics that Indian mathematicians of that period had already worked on. The various topics that have been included in these twelve chapters are: the longitudes of the planets, lunar and solar eclipses, the estimation of eclipses, the lunar crescent, the rising and setting of the planets, association of the planets with each other and with the stars.
The next six chapters of the book includes topics such as geometry, geography and algebra, which were applied to calculate the longitudes of the planets. In about twenty verses in the treatise, he gives elaborate rules to solve the indeterminate equation: by = ax + c. These rules have been applied to a number of different cases such as when c has a positive value, when c has a negative value, when the number of the quotients is a even number, when this number of quotients is an odd number, etc.

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Bhāskara I
Bhāskara (c. 600 – c. 680) (Marathi: भास्कर commonly called Bhaskara I to avoid confusion with the 12th century mathematician Bhāskara II) was a 7th century Indian mathematician, who was apparently the first to write numbers in the Hindu-Arabic decimal system with a circle for the zero, and who gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhata's work. This commentary, Āryabhaṭīyabhāṣya, written in 629 CE, is the oldest known prose work in Sanskrit on mathematics and astronomy. He also wrote two astronomical works in the line of Aryabhata's school, the Mahābhāskarīya and the Laghubhāskarīya.
Little is known about Bhāskara's life. He was "probably a Marathi astronomer". He was born at Bori, in Parbhani district of Maharashtra state in India in 7th century.^{[citation needed]}
His astronomical education was given by his father. Bhaskara is considered the most important scholar of Aryabhata's astronomical school. He and Brahmagupta are the most renowned Indian mathematicians who made considerable contributions to the study of fractions.

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Bhāskara II
Bhāskara ( (1114–1185), also known as Bhāskara II and Bhāskarāchārya ("Bhāskara the teacher")), was an Indian mathematician and astronomer. He was born near Vijjadavida (Bijāpur in modern Karnataka). Bhāskara is alleged to have been the head of an astronomical observatory at Ujjain, the leading mathematical center of ancient India. He lived in the Sahyadri region.
Bhāskara and his works represent a significant contribution to mathematical and astronomical knowledge in the 12th century. He has been called the greatest mathematician of medieval India. His main work Siddhānta Shiromani, (Sanskrit for "Crown of treatises,") is divided into four parts called Lilāvati, Bijaganita, Grahaganita and Golādhyāya. These four sections deal with arithmetic, algebra, mathematics of the planets, and spheres respectively. He also wrote another treatise named Karan Kautoohal.
Bhāskara's work on calculus predates Newton and Leibniz by half a millennium. He is particularly known in the discovery of the principles of differential calculus and its application to astronomical problems and computations. While Newton and Leibniz have been credited with differential and integral calculus, there is strong evidence to suggest that Bhāskara was a pioneer in some of the principles of differential calculus. He was perhaps the first to conceive the differential coefficient and differential calculus.

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Brahmadeva
Brahmadeva (1060–1130) was an Indian mathematician. He was the author of Karanaprakasa, which is a commentary on Aryabhata's Aryabhatiya. Its contents deal partly with trigonometry and its applications to astronomy.He was well known and intelligent scientist.

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Brahmagupta
Brahmagupta (Sanskrit: ब्रह्मगुप्त; listen (help·info)) (598–668 CE) was an Indian mathematician and astronomer who wrote many important works on mathematics and astronomy. His best known work is the Brāhmasphuṭasiddhānta (Correctly Established Doctrine of Brahma), written in 628 in Bhinmal. Its 25 chapters contain several unprecedented mathematical results.
Brahmagupta is believed to have been born in 598 AD in Bhinmal city in the state of Rajasthan of Northwest India. In ancient times Bhillamala was the seat of power of the Gurjars. His father was Jisnugupta. He likely lived most of his life in Bhillamala (modern Bhinmal in Rajasthan) during the reign (and possibly under the patronage) of King Vyaghramukha. As a result, Brahmagupta is often referred to as Bhillamalacarya, that is, the teacher from Bhillamala. He was the head of the astronomical observatory at Ujjain, and during his tenure there wrote four texts on mathematics and astronomy: the Cadamekela in 624, the Brahmasphutasiddhanta in 628, the Khandakhadyaka in 665, and the Durkeamynarda in 672. The Brahmasphutasiddhanta (Corrected Treatise of Brahma) is arguably his most famous work. The historian al-Biruni (c. 1050) in his book Tariq al-Hind states that the Abbasid caliph al-Ma'mun had an embassy in India and from India a book was brought to Baghdad which was translated into Arabic as Sindhind. It is generally presumed that Sindhind is none other than Brahmagupta's Brahmasphuta-siddhanta.

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Gangesha Upadhyaya
Gangesha Upadhyaya (Sanskrit: गंगेश उपाध्याय, Gaṅgeśa Upādhyāya) (late 12th century) was an Indian mathematician and philosopher from the kingdom of Mithila. He established the Navya-Nyāya ("New Logic") school. His Tattvacintāmaṇi (The Jewel of Thought on the Nature of Things) also known as Pramāṇacintāmaṇi (The Jewel of Thought on the Means of Valid Knowledge) is the basic text for all later developments. The logicians of this school were primarily interested in defining their terms and concepts related to non-binary logical categories.
Gengesha was born at Karion village on the banks of the river Kamala, 19 km south-east of Darbhanga in a Brahman family. According to tradition, he was illiterate in his early years but later he acquired the knowledge of logic as a boon from the goddess Kali. His son Vardhamana Upadhyaya was also a noted philosopher of the Nyaya school.
The text is divided into four khaṇḍas (books): Pratyakṣakhaṇḍa (book on perception), Anumānakhaṇḍa (book on inference), Upamānakhaṇḍa (book on comparison) and Śabdakhaṇḍa (book on verbal testimony). The first book opens with a salutation to Shiva.

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Haribhadra
Haribhadra Suri (c.700-c.770, or 459-529, traditional) was a Svetambara mendicant Jain leader and author.
There are multiple contradictory dates assigned to his birth. These include 459, 478, and 529. However, given his familiarity with Dharmakirti, a more likely choice would be sometime after 650. In his writings, Haribhadra identifies himself as a student of Jinabhadra and Jinadatta of the Vidyadhara Kula. There are several, somewhat contradictory, accounts of his life.
The earlier of these, which dates to the 12th century, says that Haribhadra was an educated Brahmin who made the boast that he would become a pupil of anyone who stated a sentence which he could not understand. After hearing a Jain nun named Yākinī Mahattarā recite a verse that he could not understand, he was sent to her teacher Jinabhaṭa, who promised Haribhadra that he would instruct him if Haribhadra accepted initiation into Jainism. Haribhadra agreed, and took the name Yākinīputra, or "Spiritual Son of Yākinī".
The second account, which bears similarities to the story of Akalanka Digambara, also shows the state of relations between Buddhist and Jain mendicants at the time. In this story, Haribhadra was teaching two of his nephews. These nephews went to secretly study logic at a Buddhist temple, and fled after being discovered there. One of them was killed by the Buddhists, and the other died of grief later. Haribhadra engaged the monks of this monastery in a philosophical debate, and emerged victorious. He then ordered the losing monks to jump into a vat of hot oil. When Haribhadra's own teacher heard of this, he ordered Haribhadra to undertake severe penances for his unseemly display of anger and attachment. Haribhadra did so, and took the title "Virahānka", which means "having separation (or viraha, from his nephews) as a distinguishing characteristic".

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Jagannatha Samrat
Pandita Jagannatha Samrat (1652–1744) was an Indian astronomer and mathematician in the court of Jai Singh II of Amber. He learned Arabic and Persian in order to study Islamic astronomy. His works include Rekhaganita, a translation of Euclid's Elements made from Nasir al-Din al-Tusi's Arabic recension of same; Siddhantasarakaustubha, a translation of the Almagest from Arabic; and two works on astronomical instruments such as the astrolabe, Siddhanta-samrat and Yantraprakara, which also record astronomical observations made by Jagannatha.

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Jayant Narlikar
Dr. Jayant Vishnu Narlikar (born July 19, 1938) (Marathi: जयंत विष्णू नारळीकर) is an Indian cosmologist.
Narlikar is a proponent of the steady state cosmology. He developed with Sir Fred Hoyle the conformal gravity theory, commonly known as Hoyle–Narlikar theory. It synthesizes Albert Einstein’s Theory of Relativity and Mach's Principle. It proposes that the inertial mass of a particle is a function of the masses of all other particles, multiplied by a coupling constant, which is a function of cosmic epoch. In cosmologies based on this theory, the gravitational constant G decreases strongly with time.
Narlikar was born in Kolhapur, India on July 19, 1938. His father, Vishnu Vasudev Narlikar, was a mathematician who served as a professor and later as the Head of the Department of Mathematics at Banaras Hindu University, Varanasi. Jayant's mother, Sumati Narlikar, was a scholar of Sanskrit language. He studied in Kendriya Vidyalaya Banaras(till class 12) and Banaras Hindu University(12th Onwards) campus, Varanasi.

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Jyeṣṭhadeva
Jyeṣṭhadeva (Malayalam: ജ്യേഷ്ഠദേവന്‍) (c. 1500 – c. 1610) was an astronomer-mathematician of the Kerala school of astronomy and mathematics founded by Sangamagrama Madhava (c.1350 – c.1425) . He is best known as the author of Yuktibhāṣā, a commentary in Malayalam of Tantrasamgraha by Nilakantha Somayaji (1444–1544). In Yuktibhāṣā, Jyeṣṭhadeva had given complete proofs and rationale of the statements in Tantrasamgraha. This was unusual for traditional Indian mathematicians of the time. An analysis of the mathematics content of Yuktibhāṣā has prompted some scholars to call it "the first textbook of calculus". Jyeṣṭhadeva also authored Drk-karana a treatise on astronomical observations.
There are a few references to Jyeṣṭhadeva scattered across several old manuscripts. From these manuscripts, one can deduce a few bare facts about the life of Jyeṣṭhadeva. He was a Namputiri belonging to the Parangngottu family (Sanskrtised as Parakroda) born about the year 1500 CE. He was a pupil of Damodara and a younger contemporary of Nilakantha Somayaji. Achyuta Pisharati was a pupil of Jyeṣṭhadeva. In the concluding verse of his work titled Uparagakriyakrama, completed in 1592, Achyuta Pisharati has referred to Jyeṣṭhadeva as his aged benign teacher. From a few references in Drkkarana, a work believed to be of Jyeṣṭhadeva, one may conclude that Jyeṣṭhadeva lived up to about 1610 CE.

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Kātyāyana
Kātyāyana (c. 3rd century BC) was a Sanskrit grammarian, mathematician and Vedic priest who lived in ancient India.
He is known for two works:
Kātyāyana's views on the word-meaning connection tended towards naturalism. Kātyāyana believed, like Plato, that the word-meaning relationship was not a result of human convention. For Kātyāyana, word-meaning relations were siddha, given to us, eternal. Though the object a word is referring to is non-eternal, the substance of its meaning, like a lump of gold used to make different ornaments, remains undistorted, and is therefore permanent.
Realizing that each word represented a categorization, he came up with the following conundrum (following Matilal):
Clearly, this leads to infinite regress. Kātyāyana's solution to this was to restrict the universal category to that of the word itself — the basis for the use of any word is to be the very same word-universal itself."
This view may have been the nucleus of the Sphoṭa doctrine enunciated by Bhartṛhari in the 5th c., in which he elaborates the word-universal as the superposition of two structures — the meaning-universal or the semantic structure (artha-jāti) is superposed on the sound-universal or the phonological structure (śabda-jāti).

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Mahavira
Mahāvīra (Sanskrit: महावीर "Great Hero", Kannada: ಮಹಾವೀರ Mahāvīra, Malayalam: മഹാവീരൻ Mahāvīran and Tamil: அருகன் Arukaṉ) is the name most commonly used to refer to the Indian sage Vardhamāna (Sanskrit: वर्धमान; traditionally 599–527 BCE) who established what are today considered to be the central tenets of Jainism. According to Jain tradition, he was the 24th and the last Tirthankara. In Tamil, he is referred to as Arukaṉ or Arukadevan. He is also known in texts as Vira or Viraprabhu, Sanmati, Ativira,and Gnatputra. In the Buddhist Pali Canon, he is referred to as Nigantha Nātaputta and Gyatra Putta.
In a place called Kundalagrama (Vaishali district) situated close to Besadha Patti, 27 miles from Patna in modern day Bihar, India, Mahavira was born in a royal family to King Siddartha and Queen Trishala on the 13th day under the rising moon of Chaitra (12 April according to the Gregorian calendar). While still in his mother's womb it is believed he brought wealth and prosperity to the entire kingdom, which is why he was named Vardhaman. An increase of all good things, like the abundant bloom of beautiful flowers, was noticed in the kingdom after his conception. Trishala had a number of auspicious dreams before giving birth to Vardhaman (14 according to the Svetambaras and 16 according to the Digambaras), signs foretelling the advent of a great soul.He found "Nirvana" at the age of 72 in 527 BC near Rajgir, Bihar .Vardhaman's birthday is celebrated as Mahavir Jayanti, the most important religious holiday of Jains around the world.

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Mahendra Sūri
Mahendra Sūri is the 14th century Jain astronomer who wrote the Yantraraja, the first Indian treatise on the astrolabe. He was a pupil of Madana Suri.

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Manava
Manava (ca. 750 BC – 690 BC) is an author of the Indian geometric text of Sulba Sutras.
The Manava Sulbasutra is not the oldest (the one by Baudhayana is older), nor is it one of the most important, there being at least three Sulbasutras which are considered more important. Historians place his lifetime at around 750 BC.
Manava would have not have been a mathematician in the sense that we would understand it today. Nor was he a scribe who simply copied manuscripts like Ahmes. He would certainly have been a man of very considerable learning but probably not interested in mathematics for its own sake, merely interested in using it for religious purposes. Undoubtedly he wrote the Sulbasutra to provide rules for religious rites and it would appear almost a certainty that Manava himself would be a Vedic priest.
The mathematics given in the Sulbasutras is there to enable accurate construction of altars needed for sacrifices. It is clear from the writing that Manava, as well as being a priest, must have been a skilled craftsman.

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Narendra Karmarkar
Narendra K. Karmarkar (born 1957) is an Indian mathematician, who developed Karmarkar's algorithm. He is listed as an ISI highly cited researcher.
Narendra Karmarkar was born in Gwalior to a Marathi family. Karmarkar received his B.Tech in Electrical Engineering from IIT Bombay in 1978, M.S. from the California Institute of Technology and Ph.D. in Computer Science from the University of California, Berkeley. He invented a polynomial algorithm for linear programming also known as the interior point method. The algorithm is a cornerstone in the field of Linear Programming. He published his famous result in 1984 while he was working for Bell Laboratories in New Jersey. Karmarkar was a professor at the Tata Institute of Fundamental Research in Mumbai. He is currently working on a new architecture for supercomputing. Some of the ideas are published at. Fab5 conference organised by MIT center for bits and atoms.
Karmarkar received a number of awards for his algorithm, among them:
Karmarkar's algorithm solves linear programming problems in polynomial time. These problems are represented by "n" variables and "m" constraints. The previous method of solving these problems consisted of problem representation by an "x" sided solid with "y" vertices, where the solution was approached by traversing from vertex to vertex. Karmarkar's novel method approaches the solution by cutting through the above solid in its traversal. Consequently, complex optimization problems are solved much faster using the Karmarkar algorithm. A practical example of this efficiency is the solution to a complex problem in communications network optimization where the solution time was reduced from weeks to days. His algorithm thus enables faster business and policy decisions. Karmarkar's algorithm has stimulated the development of several other interior point methods, some of which are used in current codes for solving linear programs.

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Nilakantha Somayaji
Kelallur Nilakantha Somayaji (Malayalam: നീലകണ്ഠ സോമയാജി, Hindi: नीलकण्ठ सोमयाजि) (1444–1544) (also referred to as Kelallur Comatiri) was a major mathematician and astronomer of the Kerala school of astronomy and mathematics. One of his most influential works was the comprehensive astronomical treatise Tantrasamgraha completed in 1501. He had also composed an elaborate commentary on Aryabhatiya called the Aryabhatiya Bhasya. In this Bhasya, Nilakantha had discussed infinite series expansions of trigonometric functions and problems of algebra and spherical geometry. Grahapareeksakrama is a manual on making observations in astronomy based on instruments of the time.
Nilakantha Somayaji was one of the very few authors of the scholarly traditions of India who had cared to record details about his own life and times. So fortunately a few accurate particulars about Nilakantha Somayaji are known.
In one of his works titled Siddhanta-darpana and also in his own commentary on Siddhanta-darpana, Nilakantha Somayaji has stated that he was born on Kali-day 1,660,181 which works out to 14 th June 1444 CE. A contemporary reference to Nilakantha Somayaji in a Malayalam work on astrology implies that Somayaji lived to a ripe old age even to become a centenarian. Sankara Variar, a pupil of Nilakantha Somayaji, in his commentary on Tantrasamgraha titled Tantrasamgraha-vyakhya, points out that the first and last verses of Tantrasamgraha contain chronograms specifying the Kali-days of the commencement (1,680,548) and of completion (1,680,553) of Somayaji's magnum opus Tantrasamgraha. Both these days occur in 1500 CE.

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Parameshvara
Vatasseri Parameshvara Nambudiri (Malayalam: വടശ്ശേരി പരമേശ്വരന്‍) (ca.1380–1460) was a major Indian mathematician and astronomer of the Kerala school of astronomy and mathematics founded by Madhava of Sangamagrama. He was also an astrologer. Parameshvara was a proponent of observational astronomy in medieval India and he himself had made a series of eclipse observations to verify the accuracy of the computational methods then in use. Based on his eclipse observations, Parameshvara proposed several corrections to the astronomical parameters which had been in use since the times of Aryabhata. The computational scheme based on the revised set of parameters has come to be known as the Drgganita system. Parameshvara was also a prolific writer on matters relating to astronomy. At least 25 manuscripts have been identified as being authored by Parameshvara.
Parameshvara was a Hindu of Bhrgugotra following the Ashvalayanasutra of the Rgveda. Parameshvara's family name (Illam) was Vatasseri (also called Vatasreni) and his family resided in the village of Alathiyur (Sanskritised as Asvatthagrama) in Tirur, Kerala. Alathiyur is situated on the northern bank of the river Nila (river Bharathappuzha) at its mouth in Kerala. He was a grandson of a disciple of Govinda Bhattathiri (1237–1295 CE), a legendary figure in the astrological traditions of Kerala.

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Pingala
Pingala (Devanagari: पिङ्गल piṅgala) is the traditional name of the author of the Chandaḥśāstra (also Chandaḥsūtra), the earliest known Sanskrit treatise on prosody.
Little is known about Piṅgala himself. In Indian literary tradition, he is variously identified either as the younger brother of Pāṇini (4th century BCE), or as Patañjali, the author of the Mahabhashya (2nd century BCE).
The Chandaḥśāstra is a work of eight chapters in the late Sūtra style, not fully comprehensible without a commentary. It has been dated to either the final centuries BCE or the early centuries CE, at the transition between Vedic meter and the classical meter of the Sanskrit epics. This would place it close to the beginning of the Common Era, likely post-dating Mauryan times. The 10th century mathematician Halayudha wrote a commentary on the Chandaḥśāstra and expanded it.
The Chandaḥśāstra presents the first known description of a binary numeral system in connection with the systematic enumeration of meters with fixed patterns of short and long syllables. The discussion of the combinatorics of meter corresponds to the binomial theorem. Halāyudha's commentary includes a presentation of the Pascal's triangle (called meruprastāra). Pingala's work also contains the Fibonacci number, called mātrāmeru, and now known as the Gopala–Hemachandra number.

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Pāṇini
Pāṇini (Sanskrit: पाणिनि, IPA: [pɑːɳin̪i]; a patronymic meaning "descendant of Paṇi") was an Sanskrit grammarian from Pushkalavati, Gandhara - modern Charsadda, Pakistan (fl. 6th century BC).
Pāṇini is known for his Sanskrit grammar, particularly for his formulation of the 3,959 rules of Sanskrit morphology, syntax and semantics in the grammar known as Ashtadhyayi (अष्टाध्यायी Aṣṭādhyāyī, meaning "eight chapters"), the foundational text of the grammatical branch of the Vedanga, the auxiliary scholarly disciplines of Vedic religion.
The Ashtadhyayi is one of the earliest known grammars of Sanskrit, although Pāṇini refers to previous texts like the Unadisutra, Dhatupatha, and Ganapatha. It is the earliest known work on descriptive linguistics, and together with the work of his immediate predecessors (Nirukta, Nighantu, Pratishakyas) stands at the beginning of the history of linguistics itself. His theory of morphological analysis was more advanced than any equivalent Western theory before the mid 20th century, and his analysis of noun compounds still forms the basis of modern linguistic theories of compounding, which have borrowed Sanskrit terms such as bahuvrihi and dvandva.

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Sankara Variar
Sankara Variar (circa. 1500 - 1560 CE) was an astronomer-mathematician of the Kerala school of astronomy and mathematics who lived during the sixteenth century CE. His family were employed as temple-assistants in the Shiva-temple at Trkkutaveli near modern Ottapalam.
He was taught mainly by Nilakantha Somayaji (1444–1544), the author of the celebrated Tantrasamgraha and Jyesthadeva (1500–1575), the author of Yuktibhāṣā. Other teachers of Sankara Variar include Netranarayana, the patron of Nilakantha Somayaji and Chitrabhanu, the author of an astronomical treaties dated to 1530 and of a small work with solutions and proofs for algebraic equations.
The known works of Sankara Variar are the following:

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Sarvadaman Chowla
Sarvadaman D. S. Chowla (22 October 1907, London–10 December 1995, Laramie, Wyoming) was a prominent Indian mathematician, specializing in number theory.
He was born in London, since his father, Gopal Chowla, a professor of mathematics in Lahore, was then studying in Cambridge. His family returned to India, where he received his masters degree in 1928 from the Government College in Lahore. In 1931 he received his doctorate from the University of Cambridge, where he studied under J. E. Littlewood.
Chowla then returned to India, where he taught at several universities, becoming head of mathematics at Government College in 1936. During the difficulties arising from the partition of India in 1947, he left for the United States. There he visited the Institute for Advanced Study until the fall of 1949, then taught at the University of Kansas in Lawrence until moving to the University of Colorado in 1952. He moved to Penn State in 1963 as a research professor, where he remained until his retirement in 1976. He was a member of the Indian National Science Academy and received the Padma Bhushan award.

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Satyendra Nath Bose
Prof. Satyendra Nath Bose (Bengali: সত্যেন্দ্র নাথ বসু Shottendronath Boshū, IPA: [ʃot̪ːend̪ronat̪ʰ boʃu]; 1 January 1894 – 4 February 1974) was an Indian mathematician and physicist noted for his collaboration with Albert Einstein in developing a theory regarding the gaslike qualities of electromagnetic radiation. He is best known for his work on quantum mechanics in the early 1920s, providing the foundation for Bose–Einstein statistics and the theory of the Bose–Einstein condensate. He is honoured as the namesake of the boson. A Fellow of the Royal Society, he was awarded India's second highest civilian award, the Padma Vibhushan in 1954 by the Government of India.
Bose’s numerous scientific papers (published from 1918 to 1956) contributed to statistical mechanics, the electromagnetic properties of the ionosphere, the theories of X-ray crystallography and thermoluminescence, and unified field theory. Bose’s Planck’s Law and the Hypothesis of Light Quanta (1924) led Einstein to seek him out for collaboration.

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Sridhara
Sridhara (c. 870, India – c. 930 India) was an Indian mathematician. He was born in Hooghly district. His father's name was Baladevacharya and mother's name was Acchoka.

He Found that Formula :-

ax^2 + abx + c = 0
4a^2x^2 + 4a^2bx + 4ac = 0 ( Multiply by 4a )
4a2x2 + 4a2bx + 4ac + b2 = 0 + b2 { Add b^2 }
(4a^2x^2 + 4a^2bx + b^2 )+ 4ac = b^2
(2ax + b)(2ax + b)+ 4ac = b^2
(2ax + b)(2ax + b)+ 4ac - b^2= 0
(2ax + b)^2 = b2 - 4ac
( D= b^2-4ac )
(2ax + b)^2 = (√D)^2
(2ax + b)^2 - (√D)^2 = 0
(2ax + b - √D) (2ax + b + √D) = 0

(2ax + b - √D) = 0 (2ax + b + √D) = 0
2ax + b - √D = 0 2ax + b + √D = 0
x=(-b - √D)/2a x=(-b + √D)/2a
x= (-b - √(b^2-4ac))/2a x= (-b + √(b^2-4ac))/2a (∵D= b^2-4ac )
α = (-b - √(b^2-4ac))/2a β = (-b + √(b^2-4ac))/2a

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Srinivasa Ramanujan
Srīnivāsa Rāmānujan FRS pronunciation (help·info) (Tamil: ஸ்ரீநிவாச ராமானுஜன்) (22 December 1887 – 26 April 1920) was an Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series and continued fractions. Ramanujan was said to be a natural genius by the English mathematician G.H. Hardy, in the same league as mathematicians like Euler and Gauss.
Born in a poor Brahmin family, Ramanujan's introduction to formal mathematics began at age 10. He demonstrated a natural ability, and was given books on advanced trigonometry written by S. L. Loney that he mastered them by age 12, and even discovered theorems of his own, including independently re-discovering Euler's identity. He demonstrated unusual mathematical skills at school, winning accolades and awards. By 17, Ramanujan conducted his own mathematical research on Bernoulli numbers and the Euler–Mascheroni constant. Ramanujan received a scholarship to study at Government College in Kumbakonam, but lost it when he failed his non-mathematical coursework. He joined another college to pursue independent mathematical research, working as a clerk in the Accountant-General's office at the Madras Port Trust Office to support himself. In 1912–1913, he sent samples of his theorems to three academics at the University of Cambridge. G. H. Hardy, recognizing the brilliance of his work, invited Ramanujan to visit and work with him at Cambridge. He became a Fellow of the Royal Society and a Fellow of Trinity College, Cambridge, dying of illness, malnutrition and possibly liver infection in 1920 at the age of 32.

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Varāhamihira
Varāhamihira (Devanagari: वराहमिहिर) (505–587 CE), also called Varaha or Mihira, was an Indian astronomer, mathematician, and astrologer who lived in Ujjain. He is considered to be one of the nine jewels (Navaratnas) of the court of legendary ruler Vikramaditya (thought to be the Gupta emperor Chandragupta II Vikramaditya).
He was the first one to mention in his work Pancha Siddhantika that the ayanamsa, or the shifting of the equinox is 50.32 seconds.
Varahamihira's main work is the book Pañcasiddhāntikā (or Pancha-Siddhantika, "[Treatise] on the Five [Astronomical] Canons) dated ca. 575 CE gives us information about older Indian texts which are now lost. The work is a treatise on mathematical astronomy and it summarises five earlier astronomical treatises, namely the Surya Siddhanta, Romaka Siddhanta, Paulisa Siddhanta, Vasishtha Siddhanta and Paitamaha Siddhantas. It is a compendium of Vedanga Jyotisha as well as Hellenistic astronomy (including Greek, Egyptian and Roman elements). He was the first one to mention in his work Pancha Siddhantika that the ayanamsa, or the shifting of the equinox is 50.32 seconds.

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Vijay Kumar Patodi
Vijay Kumar Patodi (March 12, 1945 – December 21, 1976) was an Indian mathematician who made fundamental contributions to differential geometry and topology. He was the first mathematician to apply heat equation methods to the proof of the Index Theorem for elliptic operators.^{[citation needed]} He was a professor at Tata Institute of Fundamental Research, Mumbai (Bombay).
Patodi was a graduate of Government High School, Guna, Madhya Pradesh. He received his bachelor's degree from Vikram University, Ujjain, his master's degree from the Benaras Hindu University, and his Ph.D. from the University of Bombay under the guidance of M. S. Narasimhan and S. Ramanan at the Tata Institute of Fundamental Research.
In the two papers based on his Ph.D. thesis, "Curvature and Eigenforms of the Laplace Operator" (Journal of Differential Geometry), and "An Analytical Proof of the Riemann-Roch-Hirzebruch Formula for Kaehler Manifolds" (also Journal of Differential Geometry), Patodi made his fundamental breakthroughs.

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Yajnavalkya
Yājñavalkya (Devanagari: याज्ञवल्क्य) of Mithila was a legendary sage of Vedic India, credited with the authorship of the Shatapatha Brahmana (including the Brihadaranyaka Upanishad), besides the Yoga Yajnavalkya and the Yājñavalkya Smṛti. He is also a major figure in the Upanishads.
According to tradition, Yājñavalkya was the son of Devarāta and was the pupil of sage Vaiśampāyana. Once, Vaiśampāyana got angry with Yājñavalkya as the latter argued too much to separate some latter additions to Yajurveda in being abler than other students. The angry teacher asked his pupil Yājñavalkya to give back all the knowledge of Yajurveda that he had taught him.
As per the demands of his Guru, Yājñavalkya vomited all the knowledge that he acquired from his teacher in form of digested food. Other disciples of Vaiśampāyana took the form of partridge birds and consumed the digested knowledge (a metaphor for knowledge in its simplified form without the complexities of the whole but the simplicity of parts) because it was knowledge and they were very eager to receive the same.

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Śrīpati
Śrīpati (1019–1066) was an Indian astronomer and mathematician, the author of Dhikotidakarana (written in 1039), a work of twenty verses on solar and lunar eclipses; Dhruvamanasa (written in 1056), a work of 105 verses on calculating planetary longitudes, eclipses and planetary transits; Siddhantasekhara a major work on astronomy in 19 chapters; and Ganitatilaka, an incomplete arithmetical treatise in 125 verses based on a work by Shridhara.
Śrīpati's father was Nagadeva (sometimes written as Namadeva) and Nagadeva's father, Sripati's paternal grandfather, was Kesava. Śrīpati was a follower of the teaching of Lalla writing on astrology, astronomy and mathematics. His mathematical work was undertaken with applications to astronomy in mind, for example a study of spheres. His work on astronomy was undertaken to provide a basis for his astrology. Śrīpati was the most prominent Indian mathematicians of the 11th century.
Among Śrīpati's works are: Dhikotidakarana written in 1039, a work of twenty verses on solar and lunar eclipses; Dhruvamanasa written in 1056, a work of 105 verses on calculating planetary longitudes, eclipses and planetary transits; Siddhantasekhara a major work on astronomy in 19 chapters; and Ganitatilaka an incomplete arithmetical treatise in 125 verses based on a work by Sridhara.

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Vasanta Navarartri

One day King Dhruvasindhu went out hunting and was killed by a lion. King Yudhajit and Kin...

published: 28 Sep 2011

author: HaleyMary

Aapna Balakawa Ke -Durga Bhajan

Album : Baghwa Banal Ba Hiro Singer : Radheshyam Rasiya,Sweta Shri Music Director: Rajesh ...

published: 09 Oct 2012

author: anmolbhajan

Grupo Viracena - Parada Circense em Brazópolis

...

published: 28 Sep 2011

author: ALEXANDRACERQUEIRA

Srimad-Bhagavatam 10.74 - The Deliverance of Sisupala at the Rajasuya Sacrifice

PLAYLISTS: youtube.com youtube.com TEXT: vedabase.net AUDIO (Narration by Amal Bhakta Dāsa...

published: 19 Nov 2011

author: davidlugan

Krsna Book 1970 - 74 - The Deliverance of Sisupala

PLAYLIST: youtube.com AUDIO: amalbhakta.com Narrations may be purchased as downloads at sa...

published: 01 Feb 2012

author: davidlugan

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photo: Creative Commons / INABA Tomoaki

Emergency landing grounds Boeing 787 jets in Japan

The Guardian

16 Jan 2013

YURI KAGEYAMA. AP Business Writers= TOKYO (AP) — Boeing Co.'s 787 planes were grounded for safety checks Wednesday by two major Japanese airlines after one was forced to make an emergency landing in the latest blow for the new jet ... The 787, known as the Dreamliner, is Boeing's newest and most technologically advanced jet, and the company is counting heavily on its success ... The grounding was done voluntarily by the airlines ... The U.S ... U.S....(size: 11.1Kb)

photo: AP / BP

In this undated image released Wednesday Jan. 16, 2013, by BP petroleum company, showing the Amenas natural gas field in the eastern central region of Algeria, where Islamist militants raided and took hostages Wednesday Jan. 16, 2013.

Hostages taken at BP plant in Algeria

The Australian

16 Jan 2013

IN what could be the first spillover from France's intervention in Mali, Islamist militants attacked and occupied a natural gas complex partly operated by energy company BP in southern Algeria. Two foreigners were killed and dozens of others, including Americans, were taken hostage ... It said it was holding 41 foreigners, including seven Americans ... Recommended Coverage. Al-Qaeda seize hostages in Algeria. End of sidebar ...  . ....(size: 7.4Kb)

photo: French MoD photo

File photo of French troops at Abidjan Airport, Ivory Coast.

France set to triple size of force inside Mali

Pittsburgh Post-Gazette

16 Jan 2013

BAMAKO, Mali -- After a punishing bombing campaign failed to halt the advance of al-Qaida-linked fighters, France pledged Tuesday to triple the size of its force in Mali, sending in hundreds more troops as it prepared for a land assault to dislodge the militants occupying the country's northern half ... On Tuesday, France announced that it was increasing the number of troops from 800 to 2,500 ... "We have one objective ... On Tuesday, U.S ... ....(size: 3.6Kb)

photo: AP / Carolyn Kaster

President Barack Obama speaks in the East Room of the White House in Washington, Monday, Jan. 14, 2013

Obama unveils $500 million gun violence package

The Guardian

16 Jan 2013

JULIE PACE. Associated Press= WASHINGTON (AP) — Braced for a fight, President Barack Obama on Wednesday unveiled the most sweeping proposals for curbing gun violence in two decades, pressing a reluctant Congress to pass universal background checks and bans on military-style assault weapons and high-capacity ammunition magazines like the ones used in the Newtown, Conn., school shooting ... "And Congress must act soon." ... World news....(size: 9.2Kb)

photo: WN / Jamal Penjweny

US military in side hummer on the Ramadia road and an the duty in Ramadia present

2012 military suicides hit a record high of 349

Ohio

15 Jan 2013

WASHINGTON. Suicides in the U.S. military surged to a record 349 last year, far exceeding American combat deaths in Afghanistan, and some private experts are predicting the dark trend will grow worse this year. The Pentagon has struggled to deal with the suicides, which Defense Secretary Leon Panetta and others have called an epidemic ... Last year’s total is the highest since the Pentagon began closely tracking suicides in 2001 ... ....(size: 5.0Kb)

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Understanding ancient Indian mathematics

The Hindu

26 Dec 2011

Quite often I find that conversations, with people from various walks of life, on ancient Indian mathematics slide to “Vedic mathematics” of the “16 sutras” fame, which is supposed to endow one with magical powers of calculation ... Tall claims ... Vedic knowledge ... Virasena (8th century), Sridhara (between 850 and 950), Nemicandra (around 980 CE), Thakkura Pheru (14th century) are some more names that may be mentioned....(size: 19.3Kb)

Read 2,200-year-old Jain trilogy in Kannada soon

DNA India

16 Jul 2011

A group of Kannada scholars has brought glory to Karnataka by translating the Dhavala triology into Kannada from Sanskrit and Prakrit. The work, which began 25 years ago, is now nearing completion ... What is the Dhavala trilogy? ... The documents were preserved by Jain scholars, and were housed in the Moodbidri mutt.The work that is being translated into Kannada is believed to have been authored by Acharya Virasena 2,200 years ago ... ....(size: 2.6Kb)

Incredible treasures abound in Udayagiri

The Times of India

02 Sep 2010

An ancient land. Millennium old rock cut sculptures located in cave temples. Bisected by the Tropic of Cancer. Inscriptions in an ancient, almost-extinct language as pointers ... In Udayagiri ... Instead - under the direction of Virasena, Chandragupta’s minister for war and peace - they were painstakingly putting together an edifice that combined astronomy and sculpture, and if historians are correct, metallurgy as well ... ....(size: 3.5Kb)

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Āchārya Virasena was an 8th century Indian mathematician and Jain philosopher and scholar. He was a student of the Jain sage Elāchārya.^[1] He is also known to be a famous orator and an accomplished poet.^[2] His most reputed work is the Jain treatise Dhavala. Late Dr. Hiralal Jain places the completion of this treatise in 816 AD.^[3]

Virasena was a noted mathematician. He gave the derivation of the volume of a frustum by a sort of infinite procedure. He worked with the concept of ardhaccheda: the number of times a number could be divided by 2; effectively logarithms to base 2. He also worked with logarithms in base 3 (trakacheda) and base 4 (caturthacheda).^[4]

Virasena gave the approximate formula C = 3d + (16d+16)/113 to relate the circumference of a circle, C, to its diameter, d. For large values of d, this gives the approximation π ≈ 355/113 = 3.14159292..., which is more accurate than the approximation π ≈ 3.1416 given by Aryabhata in the Aryabhatiya.^[5]

Notes [link]

^ Indranandi. Shrutāvatāra
^ Jinasena. Ādi Purāņa
^ Nagrajji, Acharya Shri (2003). Agama and Tripitaka: Language and Literature. Concept Publishing Company. p. 530. ISBN 81-7022-730-5, 9788170227304.
^ Gupta, R. C. (2000), "History of Mathematics in India", in Hoiberg, Dale; Ramchandani, Indu, Students' Britannica India: Select essays, Popular Prakashan, p. 329, http://books.google.co.uk/books?id=-xzljvnQ1vAC&pg=PA329&lpg=PA329&dq=Virasena+logarithm#v=onepage&q=Virasena%20logarithm&f=false
^ Mishra, V.; Singh, S. L. (February 1997) [1995], "First Degree Indeterminate Analysis in Ancient India and its Application by Virasena", Indian Journal of History of Science 32 (2): 127–133

External links [link]

Singh, A. N., Lucknow University, http://www.jainworld.com/JWHindi/Books/shatkhandagama-4/02.htm Translation of part of the Dhavala.

Indian mathematics

Mathematicians

Ancient	Apastamba Baudhayana Katyayana Manava Pāṇini Pingala Yajnavalkya

Classical	Āryabhaṭa I Āryabhaṭa II Bhāskara I Bhāskara II Melpathur Narayana Bhattathiri Brahmadeva Brahmagupta Brihaddeshi Halayudha Jyeṣṭhadeva Mādhava of Sañgamāgrama Mahāvīra Mahendra Sūri Munishvara Parameshvara Achyuta Pisharati Jagannatha Samrat Nilakantha Somayaji Śrīpati Sridhara Gangesha Upadhyaya Varāhamihira Sankara Variar Virasena

Modern	Shreeram Shankar Abhyankar A. A. Krishnaswami Ayyangar Amiya Charan Banerjee Raj Chandra Bose Satyendra Nath Bose Harish-Chandra Subrahmanyan Chandrasekhar D. K. Ray-Chaudhuri Sarvadaman Chowla Narendra Karmarkar Prasanta Chandra Mahalanobis Jayant Narlikar Vijay Kumar Patodi Srinivasa Ramanujan Calyampudi Radhakrishna Rao S. N. Roy Sharadchandra Shankar Shrikhande Navin M. Singhi Mathukumalli V. Subbarao S. R. Srinivasa Varadhan

Treatises

Centers

Influences

Influenced

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