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John Landen
John Landen (23 January 1719 – 15 January 1790) was an English mathematician. Life He was born at Peakirk, near Peterborough in Northamptonshire, on 28 January 1719. He was brought up to the business of a surveyor, and acted as land agent to Earl Fitzwilliam, from 1762 to 1788. Cultivating mathematics during his leisure hours, he became a contributor to the ''Ladies' Diary'' in 1744, published ''Mathematical Lucubrations'' in 1755, and from 1754 onwards communicated to the Royal Society valuable investigations on points connected with the fluxionary calculus. His attempt to substitute for it a purely algebraic method, expounded in book i. of ''Residual Analysis'' was further prosecuted by Lagrange. Book ii. never appeared. Landen's transformation, for expressing a hyperbolic arc in terms of two elliptic arcs, was inserted in the ''Philosophical Transactions'' for 1775, and specimens of its use were given in the first volume of his ‘Mathematical Memoirs (1780). In a pape ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Landen's Transformation
Landen's transformation is a mapping of the parameters of an elliptic integral, useful for the efficient numerical evaluation of elliptic functions. It was originally due to John Landen and independently rediscovered by Carl Friedrich Gauss. Statement The Elliptic integral#Incomplete elliptic integral of the first kind, incomplete elliptic integral of the first kind is : F(\varphi \setminus \alpha) = F(\varphi, \sin \alpha) = \int_0^\varphi \frac, where \alpha is the Angular eccentricity, modular angle. Landen's transformation states that if \alpha_0, \alpha_1, \varphi_0, \varphi_1 are such that (1 + \sin\alpha_1)(1 + \cos\alpha_0) = 2 and \tan(\varphi_1 - \varphi_0) = \cos\alpha_0 \tan \varphi_0, then :\begin F(\varphi_0 \setminus \alpha_0) &= (1 + \cos\alpha_0)^ F(\varphi_1 \setminus \alpha_1) \\ &= \tfrac(1 + \sin\alpha_1) F(\varphi_1 \setminus \alpha_1). \end Landen's transformation can similarly be expressed in terms of the elliptic modulus k = \sin\alpha and its compleme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonhard Euler
Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential discoveries in many other branches of mathematics, such as analytic number theory, complex analysis, and infinitesimal calculus. He also introduced much of modern mathematical terminology and Mathematical notation, notation, including the notion of a mathematical function. He is known for his work in mechanics, fluid dynamics, optics, astronomy, and music theory. Euler has been called a "universal genius" who "was fully equipped with almost unlimited powers of imagination, intellectual gifts and extraordinary memory". He spent most of his adult life in Saint Petersburg, Russia, and in Berlin, then the capital of Kingdom of Prussia, Prussia. Euler is credited for popularizing the Greek letter \pi (lowercase Pi (letter), pi) to denote Pi, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fellows Of The Royal Society
Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, including mathematics, engineering science, and medical science". Overview Fellowship of the Society, the oldest known scientific academy in continuous existence, is a significant honour. It has been awarded to :Fellows of the Royal Society, around 8,000 fellows, including eminent scientists Isaac Newton (1672), Benjamin Franklin (1756), Charles Babbage (1816), Michael Faraday (1824), Charles Darwin (1839), Ernest Rutherford (1903), Srinivasa Ramanujan (1918), Jagadish Chandra Bose (1920), Albert Einstein (1921), Paul Dirac (1930), Subrahmanyan Chandrasekhar (1944), Prasanta Chandra Mahalanobis (1945), Dorothy Hodgkin (1947), Alan Turing (1951), Lise Meitner (1955), Satyendra Nath Bose (1958), and Francis Crick (1959). More recently, fellow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People From Peterborough
The term "the people" refers to the public or Common people, common mass of people of a polity. As such it is a concept of human rights law, international law as well as constitutional law, particularly used for claims of popular sovereignty. In contrast, a people is any plurality of Person, persons considered as a whole. Used in politics and law, the term "a people" refers to the collective or community of an ethnic group or nation. Concepts Legal Chapter One, Article One of the Charter of the United Nations states that "peoples" have the right to self-determination. Though the mere status as peoples and the right to self-determination, as for example in the case of Declaration on the Rights of Indigenous Peoples, Indigenous peoples (''peoples'', as in all groups of indigenous people, not merely all indigenous persons as in ''indigenous people''), does not automatically provide for independence, independent sovereignty and therefore secession. Indeed, judge Ivor Jennings i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
18th-century English Mathematicians
The 18th century lasted from 1 January 1701 (represented by the Roman numerals MDCCI) to 31 December 1800 (MDCCC). During the 18th century, elements of Enlightenment thinking culminated in the Atlantic Revolutions. Revolutions began to challenge the legitimacy of monarchical and aristocratic power structures. The Industrial Revolution began mid-century, leading to radical changes in human society and the environment. The European colonization of the Americas and other parts of the world intensified and associated mass migrations of people grew in size as part of the Age of Sail. During the century, slave trading expanded across the shores of the Atlantic Ocean, while declining in Russia and China. Western historians have occasionally defined the 18th century otherwise for the purposes of their work. For example, the "short" 18th century may be defined as 1715–1789, denoting the period of time between the death of Louis XIV of France and the start of the French ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fellow Of The Royal Society
Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, including mathematics, engineering science, and medical science". Overview Fellowship of the Society, the oldest known scientific academy in continuous existence, is a significant honour. It has been awarded to :Fellows of the Royal Society, around 8,000 fellows, including eminent scientists Isaac Newton (1672), Benjamin Franklin (1756), Charles Babbage (1816), Michael Faraday (1824), Charles Darwin (1839), Ernest Rutherford (1903), Srinivasa Ramanujan (1918), Jagadish Chandra Bose (1920), Albert Einstein (1921), Paul Dirac (1930), Subrahmanyan Chandrasekhar (1944), Prasanta Chandra Mahalanobis (1945), Dorothy Hodgkin (1947), Alan Turing (1951), Lise Meitner (1955), Satyendra Nath Bose (1958), and Francis Crick (1959). More recently, fellow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Precession
Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In other words, if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis. A motion in which the second Euler angle changes is called '' nutation''. In physics, there are two types of precession: torque-free and torque-induced. In astronomy, ''precession'' refers to any of several slow changes in an astronomical body's rotational or orbital parameters. An important example is the steady change in the orientation of the axis of rotation of the Earth, known as the precession of the equinoxes. Torque-free or torque neglected Torque-free precession implies that no external moment (torque) is applied to the body. In torque-free precession, the angular momentum is a constant, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean Le Rond D'Alembert
Jean-Baptiste le Rond d'Alembert ( ; ; 16 November 1717 – 29 October 1783) was a French mathematician, mechanician, physicist, philosopher, and music theorist. Until 1759 he was, together with Denis Diderot, a co-editor of the ''Encyclopédie''. D'Alembert's formula for obtaining solutions to the wave equation is named after him. The wave equation is sometimes referred to as d'Alembert's equation, and the fundamental theorem of algebra is named after d'Alembert in French. Early years Born in Paris, d'Alembert was the natural son of the writer Claudine Guérin de Tencin and the chevalier Louis-Camus Destouches, an artillery officer. Destouches was abroad at the time of d'Alembert's birth. Days after birth his mother left him on the steps of the church. According to custom, he was named after the patron saint of the church. D'Alembert was placed in an orphanage for foundling children, but his father found him and placed him with the wife of a glazier, Madame Rousseau ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
England
England is a Countries of the United Kingdom, country that is part of the United Kingdom. It is located on the island of Great Britain, of which it covers about 62%, and List of islands of England, more than 100 smaller adjacent islands. It shares Anglo-Scottish border, a land border with Scotland to the north and England–Wales border, another land border with Wales to the west, and is otherwise surrounded by the North Sea to the east, the English Channel to the south, the Celtic Sea to the south-west, and the Irish Sea to the west. Continental Europe lies to the south-east, and Ireland to the west. At the 2021 United Kingdom census, 2021 census, the population was 56,490,048. London is both List of urban areas in the United Kingdom, the largest city and the Capital city, capital. The area now called England was first inhabited by modern humans during the Upper Paleolithic. It takes its name from the Angles (tribe), Angles, a Germanic peoples, Germanic tribe who settled du ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph Louis Lagrange
Joseph-Louis Lagrange (born Giuseppe Luigi LagrangiaJoseph-Louis Lagrange, comte de l’Empire ''Encyclopædia Britannica'' or Giuseppe Ludovico De la Grange Tournier; 25 January 1736 – 10 April 1813), also reported as Giuseppe Luigi Lagrange or Lagrangia, was an Italian and naturalized French , physicist and astronomer. He made significa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, recognising excellence in science, supporting outstanding science, providing scientific advice for policy, education and public engagement and fostering international and global co-operation. Founded on 28 November 1660, it was granted a royal charter by Charles II of England, King Charles II and is the oldest continuously existing scientific academy in the world. The society is governed by its Council, which is chaired by the society's president, according to a set of statutes and standing orders. The members of Council and the president are elected from and by its Fellows, the basic members of the society, who are themselves elected by existing Fellows. , there are about 1,700 fellows, allowed to use the postnominal title FRS (Fellow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
