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Kerala School Of Astronomy And Mathematics
The Kerala school of astronomy and mathematics or the Kerala school was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Tirur, Malappuram, 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 discovered a number of important mathematical 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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kerala
Kerala ( ; ) is a state on the Malabar Coast of India. It was formed on 1 November 1956, following the passage of the States Reorganisation Act, by combining Malayalam-speaking regions of the erstwhile regions of Cochin, Malabar, South Canara, and Thiruvithamkoor. Spread over , Kerala is the 21st largest Indian state by area. It is bordered by Karnataka to the north and northeast, Tamil Nadu to the east and south, and the Lakshadweep Sea to the west. With 33 million inhabitants as per the 2011 census, Kerala is the 13th-largest Indian state by population. It is divided into 14 districts with the capital being Thiruvananthapuram. Malayalam is the most widely spoken language and is also the official language of the state. The Chera dynasty was the first prominent kingdom based in Kerala. The Ay kingdom in the deep south and the Ezhimala kingdom in the north formed the other kingdoms in the early years of the Common Era (CE). The region had been a prominent spic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Osiris (journal)
''Osiris'' is an annual peer-reviewed academic journal covering research in the history of science. George Sarton oversaw the publication of fifteen issues from the establishment of the journal in 1936 until 1968. In 1985, the History of Science Society revived the journal and has published it annually ever since (though no issue appeared in 1991). It is now published by the University of Chicago Press. History Founded in 1936 by a lecturer (and later professor) at Harvard University George Sarton and by the History of Science Society, ''Osiris'' is a peer-reviewed, scientific journal dedicated to the history of science, medicine, and technology. It was founded in order to publish longer papers that were unsuitable for its partner publication, ''Isis''. See also *''Isis'' * List of history journals *History of science and technology The history of science and technology (HST) is a field of history that examines the understanding of the natural world (science) and the abilit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Otto Neugebauer
Otto Eduard Neugebauer (May 26, 1899 – February 19, 1990) was an Austrian-American mathematician and historian of science who became known for his research on the history of astronomy and the other exact sciences as they were practiced in antiquity and the Middle Ages. By studying clay tablets, he discovered that the ancient Babylonians knew much more about mathematics and astronomy than had been previously realized. The National Academy of Sciences has called Neugebauer "the most original and productive scholar of the history of the exact sciences, perhaps of the history of science, of our age." Career Neugebauer was born in Innsbruck, Austria. His father Rudolph Neugebauer was a railroad construction engineer and a collector and scholar of Oriental carpets. His parents died when he was quite young. During World War I, Neugebauer enlisted in the Austrian Army and served as an artillery lieutenant on the Italian front and then in an Italian prisoner-of-war camp alongside fell ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Google Books
Google Books (previously known as Google Book Search, Google Print, and by its code-name Project Ocean) is a service from Google Inc. that searches the full text of books and magazines that Google has scanned, converted to text using optical character recognition (OCR), and stored in its digital database.The basic Google book link is found at: https://books.google.com/ . The "advanced" interface allowing more specific searches is found at: https://books.google.com/advanced_book_search Books are provided either by publishers and authors through the Google Books Partner Program, or by Google's library partners through the Library Project. Additionally, Google has partnered with a number of magazine publishers to digitize their archives. The Publisher Program was first known as Google Print when it was introduced at the Frankfurt Book Fair in October 2004. The Google Books Library Project, which scans works in the collections of library partners and adds them to the digital inve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Limit (mathematics)
In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value. Limits are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals. The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to limit and direct limit in category theory. In formulas, a limit of a function is usually written as : \lim_ f(x) = L, (although a few authors may use "Lt" instead of "lim") and is read as "the limit of of as approaches equals ". The fact that a function approaches the limit as approaches is sometimes denoted by a right arrow (→ or \rightarrow), as in :f(x) \to L \text x \to c, which reads "f of x tends to L as x tends to c". History Grégoire de Saint-Vincent gave the first definition of limit (terminus) of a geometric series in his work ''Opus Geometricum'' (1647): "The ''terminus'' of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor Series
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series, when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the mid-18th century. The partial sum formed by the first terms of a Taylor series is a polynomial of degree that is called the th Taylor polynomial of the function. Taylor polynomials are approximations of a function, which become generally better as increases. Taylor's theorem gives quantitative estimates on the error introduced by the use of such approximations. If the Taylor series of a function is convergent, its sum is the limit of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral
In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with differentiation, integration is a fundamental, essential operation of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others. The integrals enumerated here are those termed definite integrals, which can be interpreted as the signed area of the region in the plane that is bounded by the graph of a given function between two points in the real line. Conventionally, areas above the horizontal axis of the plane are positive while areas below are negative. Integrals also refer to the concept ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derivative
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the "instantaneous rate of change", the ratio of the instantaneous change in the dependent variable to that of the independent variable. Derivatives can be generalized to functions of several real variables. In this generalization, the de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inductive Hypothesis
Mathematical induction is a method for proving that a statement ''P''(''n'') is true for every natural number ''n'', that is, that the infinitely many cases ''P''(0), ''P''(1), ''P''(2), ''P''(3), ... all hold. Informal metaphors help to explain this technique, such as falling dominoes or climbing a ladder: A proof by induction consists of two cases. The first, the base case, proves the statement for ''n'' = 0 without assuming any knowledge of other cases. The second case, the induction step, proves that ''if'' the statement holds for any given case ''n'' = ''k'', ''then'' it must also hold for the next case ''n'' = ''k'' + 1. These two steps establish that the statement holds for every natural number ''n''. The base case does not necessarily begin with ''n'' = 0, but often with ''n'' = 1, and possibly with any fixed natural number ''n'' = ''N'', establishing the truth of the statement for all natu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Induction
Mathematical induction is a method for proving that a statement ''P''(''n'') is true for every natural number ''n'', that is, that the infinitely many cases ''P''(0), ''P''(1), ''P''(2), ''P''(3), ... all hold. Informal metaphors help to explain this technique, such as falling dominoes or climbing a ladder: A proof by induction consists of two cases. The first, the base case, proves the statement for ''n'' = 0 without assuming any knowledge of other cases. The second case, the induction step, proves that ''if'' the statement holds for any given case ''n'' = ''k'', ''then'' it must also hold for the next case ''n'' = ''k'' + 1. These two steps establish that the statement holds for every natural number ''n''. The base case does not necessarily begin with ''n'' = 0, but often with ''n'' = 1, and possibly with any fixed natural number ''n'' = ''N'', establishing the truth of the statement for all natu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Series (mathematics)
In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures (such as in combinatorics) through generating functions. In addition to their ubiquity in mathematics, infinite series are also widely used in other quantitative disciplines such as physics, computer science, statistics and finance. For a long time, the idea that such a potentially infinite summation could produce a finite result was considered paradoxical. This paradox was resolved using the concept of a limit during the 17th century. Zeno's paradox of Achilles and the tortoise illustrates this counterintuitive property of infinite sums: Achilles runs after a tortoise, but when he reaches the position of the tortoise at the beginning ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
