Johannes Hudde
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Johannes Hudde
Johannes (van Waveren) Hudde (23 April 1628 – 15 April 1704) was a burgomaster (mayor) of Amsterdam between 1672 – 1703, a mathematician and governor of the Dutch East India Company. As a "burgemeester" of Amsterdam he ordered that the city canals should be flushed at high tide and that the polluted water of the town "secreten" should be diverted to pits outside the town instead of into the canals. He also promoted hygiene in and around the town's water supply. "Hudde's stones" were marker stones that were used to mark the summer high water level at several points in the city. They later were the foundation for the "NAP", the now Europe-wide system for measuring water levels.J.P.M KwaaHet Normal Amsterdam Peil (NAP)(Dutch) Mathematical work Hudde studied law at the University of Leiden, but turned to mathematics under the influence of his teacher Frans van Schooten. From 1654 to 1663 he worked under van Schooten. ''La Géométrie'' (1637) by René Descartes provid ...
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Amsterdam
Amsterdam ( , , , lit. ''The Dam on the River Amstel'') is the Capital of the Netherlands, capital and Municipalities of the Netherlands, most populous city of the Netherlands, with The Hague being the seat of government. It has a population of 907,976 within the city proper, 1,558,755 in the City Region of Amsterdam, urban area and 2,480,394 in the Amsterdam metropolitan area, metropolitan area. Located in the Provinces of the Netherlands, Dutch province of North Holland, Amsterdam is colloquially referred to as the "Venice of the North", for its large number of canals, now designated a World Heritage Site, UNESCO World Heritage Site. Amsterdam was founded at the mouth of the Amstel River that was dammed to control flooding; the city's name derives from the Amstel dam. Originally a small fishing village in the late 12th century, Amsterdam became a major world port during the Dutch Golden Age of the 17th century, when the Netherlands was an economic powerhouse. Amsterdam is th ...
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Maxima And Minima
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the ''local'' or ''relative'' extrema), or on the entire domain (the ''global'' or ''absolute'' extrema). Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions. As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum. Definition A real-valued function ''f'' defined on a domain ''X'' has a global (or absolute) maximum point at ''x''∗, if for all ''x'' in ''X''. Similarly, the function has a global (or absolute) minimum point at ''x''∗, if for all ''x'' in ''X''. The value of the function at a m ...
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17th-century Dutch Mathematicians
The 17th century lasted from January 1, 1601 ( MDCI), to December 31, 1700 ( MDCC). It falls into the early modern period of Europe and in that continent (whose impact on the world was increasing) was characterized by the Baroque cultural movement, the latter part of the Spanish Golden Age, the Dutch Golden Age, the French ''Grand Siècle'' dominated by Louis XIV, the Scientific Revolution, the world's first public company and megacorporation known as the Dutch East India Company, and according to some historians, the General Crisis. From the mid-17th century, European politics were increasingly dominated by the Kingdom of France of Louis XIV, where royal power was solidified domestically in the civil war of the Fronde. The semi-feudal territorial French nobility was weakened and subjugated to the power of an absolute monarchy through the reinvention of the Palace of Versailles from a hunting lodge to a gilded prison, in which a greatly expanded royal court could be more easily k ...
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1704 Deaths
Seventeen or 17 may refer to: *17 (number), the natural number following 16 and preceding 18 * one of the years 17 BC, AD 17, 1917, 2017 Literature Magazines * ''Seventeen'' (American magazine), an American magazine * ''Seventeen'' (Japanese magazine), a Japanese magazine Novels * ''Seventeen'' (Tarkington novel), a 1916 novel by Booth Tarkington *''Seventeen'' (''Sebuntiin''), a 1961 novel by Kenzaburō Ōe * ''Seventeen'' (Serafin novel), a 2004 novel by Shan Serafin Stage and screen Film * ''Seventeen'' (1916 film), an American silent comedy film *''Number Seventeen'', a 1932 film directed by Alfred Hitchcock * ''Seventeen'' (1940 film), an American comedy film *''Eric Soya's '17''' (Danish: ''Sytten''), a 1965 Danish comedy film * ''Seventeen'' (1985 film), a documentary film * ''17 Again'' (film), a 2009 film whose working title was ''17'' * ''Seventeen'' (2019 film), a Spanish drama film Television * ''Seventeen'' (TV drama), a 1994 UK dramatic short starring Chris ...
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1628 Births
Sixteen or 16 may refer to: *16 (number), the natural number following 15 and preceding 17 *one of the years 16 BC, AD 16, 1916, 2016 Films * '' Pathinaaru'' or ''Sixteen'', a 2010 Tamil film * ''Sixteen'' (1943 film), a 1943 Argentine film directed by Carlos Hugo Christensen * ''Sixteen'' (2013 Indian film), a 2013 Hindi film * ''Sixteen'' (2013 British film), a 2013 British film by director Rob Brown Music *The Sixteen, an English choir *16 (band), a sludge metal band * Sixteen (Polish band), a Polish band Albums * ''16'' (Robin album), a 2014 album by Robin * 16 (Madhouse album), a 1987 album by Madhouse * ''Sixteen'' (album), a 1983 album by Stacy Lattisaw *''Sixteen'' , a 2005 album by Shook Ones * ''16'', a 2020 album by Wejdene Songs * "16" (Sneaky Sound System song), 2009 * "Sixteen" (Thomas Rhett song), 2017 * "Sixteen" (Ellie Goulding song), 2019 *"16", by Craig David from ''Following My Intuition'', 2016 *"16", by Green Day from ''39/Smooth'', 1990 *"16", by ...
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Centaurus (journal)
''Centaurus. Journal of the European Society for the History of Science'' is a quarterly peer-reviewed academic journal covering research on the history of mathematics, science, and technology. It is the official journal of the European Society for the History of Science. The journal was established in 1950. In January 2022, Centaurus was relaunched in open-access format by the ESHS and Brepols as ''Centaurus. Journal of the European Society for the History of Science''. The editor-in-chief is Koen Vermeir (Centre national de la recherche scientifique and Paris Diderot University). Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal has a 2020 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as i ... ...
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Tangent
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. More precisely, a straight line is said to be a tangent of a curve at a point if the line passes through the point on the curve and has slope , where ''f'' is the derivative of ''f''. A similar definition applies to space curves and curves in ''n''-dimensional Euclidean space. As it passes through the point where the tangent line and the curve meet, called the point of tangency, the tangent line is "going in the same direction" as the curve, and is thus the best straight-line approximation to the curve at that point. The tangent line to a point on a differentiable curve can also be thought of as a '' tangent line approximation'', the graph of the affine function that best approximates the original function at the given point. Similarly, t ...
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Mercator Series
In mathematics, the Mercator series or Newton–Mercator series is the Taylor series for the natural logarithm: :\ln(1+x)=x-\frac+\frac-\frac+\cdots In summation notation, :\ln(1+x)=\sum_^\infty \frac x^n. The series converges to the natural logarithm (shifted by 1) whenever -1 .


History

The series was discovered independently by and . It was first published by , in his 1668 treatise ''Logarithmotechnia''.


Derivation

The series can be obtained from

History Of Group Theory
The history of group theory, a mathematical domain studying groups in their various forms, has evolved in various parallel threads. There are three historical roots of group theory: the theory of algebraic equations, number theory and geometry. Joseph Louis Lagrange, Niels Henrik Abel and Évariste Galois were early researchers in the field of group theory. Early 19th century The earliest study of groups as such probably goes back to the work of Lagrange in the late 18th century. However, this work was somewhat isolated, and 1846 publications of Augustin Louis Cauchy and Galois are more commonly referred to as the beginning of group theory. The theory did not develop in a vacuum, and so three important threads in its pre-history are developed here. Development of permutation groups One foundational root of group theory was the quest of solutions of polynomial equations of degree higher than 4. An early source occurs in the problem of forming an equation of degree ''m'' having as ...
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Infinitesimal Calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. It has two major branches, differential calculus and integral calculus; the former concerns instantaneous rates of change, and the slopes of curves, while the latter concerns accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus, and they make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Infinitesimal calculus was developed independently in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. Later work, including codifying the idea of limits, put these developments on a more solid conceptual footing. Today, calculus has widespread uses in scien ...
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Gottfried Wilhelm Leibniz
Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathematics. He wrote works on philosophy, theology, ethics, politics, law, history and philology. Leibniz also made major contributions to physics and technology, and anticipated notions that surfaced much later in probability theory, biology, medicine, geology, psychology, linguistics and computer science. In addition, he contributed to the field of library science: while serving as overseer of the Wolfenbüttel library in Germany, he devised a cataloging system that would have served as a guide for many of Europe's largest libraries. Leibniz's contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters and in unpublished manuscripts. He wrote in several languages, primarily in Latin, ...
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Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the greatest mathematicians and physicists and among the most influential scientists of all time. He was a key figure in the philosophical revolution known as the Enlightenment. His book (''Mathematical Principles of Natural Philosophy''), first published in 1687, established classical mechanics. Newton also made seminal contributions to optics, and shares credit with German mathematician Gottfried Wilhelm Leibniz for developing infinitesimal calculus. In the , Newton formulated the laws of motion and universal gravitation that formed the dominant scientific viewpoint for centuries until it was superseded by the theory of relativity. Newton used his mathematical description of gravity to derive Kepler's laws of planetary motion, account for ...
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