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Bijaganita
''Bijaganita'' ( IAST: ') was treatise on algebra by the Indian mathematician Bhāskara II. It is the second volume of his main work '' Siddhānta Shiromani (''"Crown of treatises") alongside '' Lilāvati'', ''Grahaganita'' and ''Golādhyāya''. Britannica.com Contents The book is divided into six parts, mainly indeterminate equations, quadratic equations, simple equations, surds. The contents are: * Introduction * On Simple Equations * On Quadratic Equations * On Equations involving indeterminate Questions of the 1st Degree * On Equations involving indeterminate Questions of the 2nd Degree * On Equations involving Rectangles In Bijaganita Bhāskara II refined |
Bhāskara II
Bhāskara II (c. 1114–1185), also known as Bhāskarāchārya ("Bhāskara, the teacher"), and as Bhāskara II to avoid confusion with Bhāskara I, was an Indian mathematician and astronomer. From verses, in his main work, Siddhānta Shiromani (सिद्धांतशिरोमणी), it can be inferred that he was born in 1114 in Vijjadavida (Vijjalavida) and living in the Sahyadri mountain ranges of Western Ghats, believed to be the town of Patan in Chalisgaon, located in present-day Khandesh region of Maharashtra by scholars. He is the only ancient mathematician who has been immortalized on a monument. In a temple in Maharashtra, an inscription supposedly created by his grandson Changadeva, lists Bhaskaracharya's ancestral lineage for several generations before him as well as two generations after him. Colebrooke who was the first European to translate (1817) Bhaskaracharya II's mathematical classics refers to the family as Maharashtrian Brahmins residing on the ban ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indian Mathematics
Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhata, Brahmagupta, Bhaskara II, and Varāhamihira. The decimal number system in use today: "The measure of the genius of Indian civilisation, to which we owe our modern (number) system, is all the greater in that it was the only one in all history to have achieved this triumph. Some cultures succeeded, earlier than the Indian, in discovering one or at best two of the characteristics of this intellectual feat. But none of them managed to bring together into a complete and coherent system the necessary and sufficient conditions for a number-system with the same potential as our own." was first recorded in Indian mathematics. Indian mathematicians made early contributions to the study of the concept of zero as a number,: "...our decimal system, which (by t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Siddhānta Shiromani
''Siddhānta Śiromaṇi'' (Sanskrit: सिद्धान्त शिरोमणि for "Crown of treatises") is the major treatise of Indian mathematician Bhāskara II. He wrote the ''Siddhānta Śiromaṇi'' in 1150 when he was 36 years old. The work is composed in Sanskrit Language in 1450 verses. Parts Līlāvatī The name of the book comes from his daughter, Līlāvatī. It is the first volume of the ''Siddhānta Śiromaṇi''. The book contains thirteen chapters, 278 verses, mainly arithmetic and measurement. Bījagaṇita It is the second volume of ''Siddhānta Śiromaṇi''. It is divided into six parts, contains 213 verses and is devoted to algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary .... ''Gaṇitādhyāya'' and ''Golādhyāya'' ''Gaṇitādhyā ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chakravala Method
The ''chakravala'' method ( sa, चक्रवाल विधि) is a cyclic algorithm to solve indeterminate quadratic equations, including Pell's equation. It is commonly attributed to Bhāskara II, (c. 1114 – 1185 CE)Hoiberg & Ramchandani – Students' Britannica India: Bhaskaracharya II, page 200Kumar, page 23 although some attribute it to Jayadeva (c. 950 ~ 1000 CE).Plofker, page 474 Jayadeva pointed out that Brahmagupta's approach to solving equations of this type could be generalized, and he then described this general method, which was later refined by Bhāskara II in his ''Bijaganita'' treatise. He called it the Chakravala method: ''chakra'' meaning "wheel" in Sanskrit, a reference to the cyclic nature of the algorithm.Goonatilake, page 127 – 128 C.-O. Selenius held that no European performances at the time of Bhāskara, nor much later, exceeded its marvellous height of mathematical complexity. This method is also known as the cyclic method and contains traces ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sudhakar Dwivedi
Sudhakara Dvivedi (1855–1910) was an Indian scholar in Sanskrit and mathematics. Biography Sudhakara Dvivedi was born in 1855 in Khajuri, a village near Varanasi. In childhood he studied mathematics under Pandit Devakrsna. In 1883 he was appointed a librarian in the Government Sanskrit College, Varanasi where in 1898 he was appointed the teacher of mathematics and astrology Astrology is a range of divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of celestial objects. Di ... after Bapudeva Sastri retired in 1889. He was the head of mathematics department in Queen's college Benaras from where he retired in 1905 and mathematician Ganesh Prasad became the new head of department. Dvivedi wrote a number of translations, commentaries and treatises, including one on algebra which included topics such as Pellian equations, squares, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bapudeva Sastri
Bapudeva Sastri or Narasimha Deva Paranjpe (1821–1900) was an Indian mathematician. Biography He was born on 1 November 1821, to a Hindu Brahmin family of Maharashtra. He received his early education in arithmetic and algebra at the Marathi school in Nagpur. He also studied the Lilāvati and Bijaganita under ''Dhundiraja Misra''. Noting his talent, the British political agent Lancelot Wilkinson secured his admission to the Sehore Sanskrit school where he studied Siddhānta Shiromani, Euclidean Geometry and European science in general under Pandit Sevarama and Wilkinson himself. In 1842 Sastri went to Government Sanskrit College, Varanasi, where he taught rekha-ganita (Euclidean Geometry). In 1890 Sudhakar Dwivedi was appointed the teacher of mathematics and astrology after Bapudeva Sastri, retired in 1889. Scholarly works Bapudeva Sastri translated the Siddhānta Shiromani (a treatise on Hindu mathematics written in the twelfth century by Bhaskaracharya) and published it in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IAST
The International Alphabet of Sanskrit Transliteration (IAST) is a transliteration scheme that allows the lossless romanisation of Indic scripts as employed by Sanskrit and related Indic languages. It is based on a scheme that emerged during the nineteenth century from suggestions by Charles Trevelyan, William Jones, Monier Monier-Williams and other scholars, and formalised by the Transliteration Committee of the Geneva Oriental Congress, in September 1894. IAST makes it possible for the reader to read the Indic text unambiguously, exactly as if it were in the original Indic script. It is this faithfulness to the original scripts that accounts for its continuing popularity amongst scholars. Usage Scholars commonly use IAST in publications that cite textual material in Sanskrit, Pāḷi and other classical Indian languages. IAST is also used for major e-text repositories such as SARIT, Muktabodha, GRETIL, and sanskritdocuments.org. The IAST scheme represents more than a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of Algebra
Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until the 19th century, algebra consisted essentially of the theory of equations. For example, the fundamental theorem of algebra belongs to the theory of equations and is not, nowadays, considered as belonging to algebra (in fact, every proof must use the completeness of the real numbers, which is not an algebraic property). This article describes the history of the theory of equations, called here "algebra", from the origins to the emergence of algebra as a separate area of mathematics. Etymology The word "algebra" is derived from the Arabic word الجبر ''al-jabr'', and this comes from the treatise written in the year 830 by the medieval Persian mathematician, Muhammad ibn Mūsā al-Khwārizmī, whose Arabic title, '' Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala'', can be translated as ''The Compendious Book on Calcu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of Science And Technology In India
The history of science and technology in the Indian subcontinent begins with the prehistoric human activity of the Indus Valley Civilization to the early Indian states and empires. Prehistory By 5500 BCE a number of sites similar to Mehrgarh (Pakistan) had appeared, forming the basis of later chalcolithic cultures. The inhabitants of these sites maintained trading relations with Near East and Central Asia.Kenoyer, 230 Irrigation was developed in the Indus Valley Civilization by around 4500 BCE. The size and prosperity of the Indus civilization grew as a result of this innovation, which eventually led to more planned settlements making use of drainage and sewerage.Rodda & Ubertini, 279 Sophisticated irrigation and water storage systems were developed by the Indus Valley Civilization, including artificial reservoirs at Girnar dated to 3000 BCE, and an early canal irrigation system from c. 2600 BCE. Cotton was cultivated in the region by the 5th–4th millennia BCE. Sugarcane wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Social History Of India
Social organisms, including human(s), live collectively in interacting populations. This interaction is considered social whether they are aware of it or not, and whether the exchange is voluntary or not. Etymology The word "social" derives from the Latin word ''socii'' ("allies"). It is particularly derived from the Italian ''Socii'' states, historical allies of the Roman Republic (although they rebelled against Rome in the Social War of 91–87 BC). Social theorists In the view of Karl MarxMorrison, Ken. ''Marx, Durkheim, Weber. Formations of modern social thought'', human beings are intrinsically, necessarily and by definition social beings who, beyond being "gregarious creatures", cannot survive and meet their needs other than through social co-operation and association. Their social characteristics are therefore to a large extent an objectively given fact, stamped on them from birth and affirmed by socialization processes; and, according to Marx, in producing and reproducin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Timeline Of Algebra And Geometry
The following is a timeline of key developments of geometry: Before 1000 BC * ca. 2000 BC – Scotland, carved stone balls exhibit a variety of symmetries including all of the symmetries of Platonic solids. * 1800 BC – Moscow Mathematical Papyrus, findings volume of a frustum *1800 BC – Plimpton 322 contains the oldest reference to the Pythagorean triplets. * 1650 BC – Rhind Mathematical Papyrus, copy of a lost scroll from around 1850 BC, the scribe Ahmes presents one of the first known approximate values of π at 3.16, the first attempt at squaring the circle, earliest known use of a sort of cotangent, and knowledge of solving first order linear equations 1st millennium BC * 800 BC – Baudhayana, author of the Baudhayana Sulba Sutra, a Vedic Sanskrit geometric text, contains quadratic equations, and calculates the square root of 2 correct to five decimal places * ca. 600 BC – the other Vedic "Sulba Sutras" ("rule of chords" in Sanskrit) use Pythagorean triples, co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henry Thomas Colebrooke
Henry Thomas Colebrooke FRS FRSE (15 June 1765 – 10 March 1837) was an English orientalist and mathematician. He has been described as "the first great Sanskrit scholar in Europe". Biography Henry Thomas Colebrooke was born on 15 June 1765. His parents were Sir George Colebrooke, 2nd Baronet, MP for Arundel and Chairman of the East India Company from 1769, and Mary Gaynor, daughter and heir of Patrick Gaynor of Antigua. He was educated at home. In 1782 Colebrooke was appointed through his father's influence to a writership with the East India Company in Calcutta. In 1786 and three years later he was appointed assistant collector in the revenue department at Tirhut. He wrote ''Remarks on the Husbandry and Commerce of Bengal'', which was privately published in 1795, by which time he had transferred to Purnia. This opposed the East India Company's monopoly on Indian trade, advocating instead for free trade between Britain and India, which caused offence to the East Ind ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
