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Līlāvatī
''Līlāvatī'' is Indian mathematician Bhāskara II's treatise on mathematics, written in 1150 AD. It is the first volume of his main work, the ''Siddhānta Shiromani'', alongside the ''Bijaganita'', the ''Grahaganita'' and the ''Golādhyāya''. Name His book on arithmetic is the source of interesting legends that assert that it was written for his daughter, Lilavati. Lilavati was Bhaskara II's daughter. Bhaskara II studied Lilavati's horoscope and predicted that she would remain both childless and unmarried. To avoid this fate, he ascertained an auspicious moment for his daughter's wedding and to alert his daughter at the correct time, he placed a cup with a small hole at the bottom of a vessel filled with water, arranged so that the cup would sink at the beginning of the propitious hour. He put the device in a room with a warning to Lilavati to not go near it. In her curiosity though, she went to look at the device and a pearl from her bridal dress accidentally dropped ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
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] |
Indeterminate Equations
In mathematics, particularly in algebra, an indeterminate equation is an equation for which there is more than one solution. For example, the equation ax + by =c is a simple indeterminate equation, as is x^2=1. Indeterminate equations cannot be solved uniquely. In fact, in some cases it might even have infinitely many solutions. Some of the prominent examples of indeterminate equations include: Univariate polynomial equation: :a_nx^n+a_x^+\dots +a_2x^2+a_1x+a_0 = 0, which has multiple solutions for the variable x in the complex plane—unless it can be rewritten in the form a_n(x-b)^n = 0. Non-degenerate conic equation: :Ax^2 + Bxy + Cy^2 +Dx + Ey + F = 0, where at least one of the given parameters A, B, and C is non-zero, and x and y are real variables. Pell's equation: :\ x^2 - Py^2 = 1, where P is a given integer that is not a square number, and in which the variables x and y are required to be integers. The equation of Pythagorean triples: :x^2+y^2=z^2, in which the vari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Science And Technology In India
After independence, Jawaharlal Nehru, the first prime minister of India, initiated reforms to promote higher education and science and technology in India. The Indian Institute of Technology (IIT)—conceived by a 22-member committee of scholars and entrepreneurs in order to promote technical education—was inaugurated on 18 August 1951 at Kharagpur in West Bengal by the Minister of Education (India), minister of education Maulana Abul Kalam Azad. More IITs were soon opened in Bombay, Madras, Kanpur and Delhi as well in the late 1950s and early 1960s along with the regional RECs (now National Institutes of Technology (NIT). Beginning in the 1960s, close ties with the Soviet Union enabled the Indian Space Research Organisation to rapidly develop the Indian space program and advance nuclear power in India even after Smiling Buddha, the first nuclear test explosion by India on 18 May 1974 at Pokhran. India accounts for about 10% of all expenditure on research and development in ... [...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] |
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] |
Kriyakramakari
Kriyakramakari (Kriyā-kramakarī) is an elaborate commentary in Sanskrit written by Sankara Variar and Narayana, two astronomer-mathematicians belonging to the Kerala school of astronomy and mathematics, on Bhaskara II's well-known textbook on mathematics Lilavati. Kriyakramakari ('Operational Techniques'), along with Yuktibhasa of Jyeshthadeva, is one of the main sources of information about the work and contributions of Sangamagrama Madhava, the founder of Kerala school of astronomy and mathematics. Also the quotations given in this treatise throw much light on the contributions of several mathematicians and astronomers who had flourished in an earlier era. There are several quotations ascribed to Govindasvami a 9th-century astronomer from Kerala. Sankara Variar (c. 1500 - 1560), the first author of Kriyakramakari, was a pupil of Nilakantha Somayaji and a temple-assistant by profession. He was a prominent member of the Kerala school of astronomy and mathematics. His ... [...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] |
Involution (mathematics)
In mathematics, an involution, involutory function, or self-inverse function is a function that is its own inverse, : for all in the domain of . Equivalently, applying twice produces the original value. General properties Any involution is a bijection. The identity map is a trivial example of an involution. Examples of nontrivial involutions include negation (x \mapsto -x), reciprocation (x \mapsto 1/x), and complex conjugation (z \mapsto \bar z) in arithmetic; reflection, half-turn rotation, and circle inversion in geometry; complementation in set theory; and reciprocal ciphers such as the ROT13 transformation and the Beaufort polyalphabetic cipher. The composition of two involutions ''f'' and ''g'' is an involution if and only if they commute: . Involutions on finite sets The number of involutions, including the identity involution, on a set with elements is given by a recurrence relation found by Heinrich August Rothe in 1800: :a_0 = a_1 = 1 and a_n = a_ + ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fraction (mathematics)
A fraction (from la, fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A ''common'', ''vulgar'', or ''simple'' fraction (examples: \tfrac and \tfrac) consists of a numerator, displayed above a line (or before a slash like ), and a non-zero denominator, displayed below (or after) that line. Numerators and denominators are also used in fractions that are not ''common'', including compound fractions, complex fractions, and mixed numerals. In positive common fractions, the numerator and denominator are natural numbers. The numerator represents a number of equal parts, and the denominator indicates how many of those parts make up a unit or a whole. The denominator cannot be zero, because zero parts can never make up a whole. For example, in the fraction , the numerator 3 indicates that the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
