1.
1769 in science
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The year 1769 in science and technology involved some significant events, listed below. March 4 – French astronomer Charles Messier first records the Orion Nebula, june 3 – Transit of Venus is observed from many places in order to obtain data for measuring the distance from the Earth to the Sun. The weather in Pondicherry is cloudy that day, le Gentil had also missed the 1761 transit through bad luck. November 9 – Transit of Mercury, james Cook observes this from Mercury Bay in New Zealand. Carl Wilhelm Scheele discovers a method of mass-producing phosphorus, in September he completes a full-size experimental engine at Kinneil House in Scotland. July 3 – Richard Arkwright is granted a British patent for a spinning frame able to spin thread mechanically. October 23 – Nicolas-Joseph Cugnot demonstrates a steam-powered artillery tractor in France, march 16 – Louis Antoine de Bougainville returns to Saint-Malo following a three-year circumnavigation of the world with the ships La Boudeuse and Étoile, with the loss of only seven out of 330 men
2.
1773 in science
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The year 1773 in science and technology involved some significant events. Lagrange presents his work on the equation of the Moon to the Académie française. He also publishes on the attraction of ellipsoids, carl Wilhelm Scheele and Joseph Priestley independently isolate oxygen, called by Priestley dephlogisticated air and Scheele fire air. Antoine Baumé publishes his textbook Chymie expérimentale et raisonnée in Paris, january 17 – Captain James Cook becomes the first European explorer to cross the Antarctic Circle. Spring – Tobias Furneaux explores the coast of Van Diemens Land, scottish judge James Burnett, Lord Monboddo, begins publication of Of the Origin and Progress of Language, a contribution to evolutionary ideas of the Enlightenment. Lagrange considers a functional determinant of order 3, a case of a Jacobian. October 12 – North Americas first insane asylum opens for Persons of Insane and Disordered Minds in Williamsburg, medical Society of London founded by John Coakley Lettsom. Louis-Bernard Guyton de Morveau proposes the use of acid gas for fumigation of buildings. Istanbul Technical University is established as the worlds first comprehensive institution of learning dedicated to engineering education. Copley Medal, John Walsh John Harrison receives the Longitude prize for his invention of the marine chronometer
3.
1775 in science
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The year 1775 in science and technology involved some significant events. May 25 – Joseph Priestleys account of his isolation of oxygen in the form of a gas is read to the Royal Society of London, torbern Bergmans De attractionibus electivis is published, containing the largest tables of chemical affinity ever published. Lagranges Recherches dArithmétique develops a theory of binary quadratic forms. English surgeon Percivall Pott finds the first occupational link to cancer, german physician Melchior Adam Weikard anonymously publishes the textbook Der Philosophische Arzt including the earliest description of symptoms resembling attention deficit hyperactivity disorder. February 21 – La Specola, Florences Museum of Zoology and Natural History, johan Christian Fabricius publishes his Systema entomologiæ. James Watts 1769 steam engine patent is extended to June 1800 by Act of Parliament of Great Britain, jacques-Constantin Périer operates a paddle steamer on the Seine, but it proves to be underpowered. Thomas Crapper patents a flush toilet in London, edinburgh confectioner Charles Spalding devizes improvements to the diving bell, adding a system of balance-weights. Pierre-Simon Girard, age 74, invents a water turbine, december 30 – John Arnold takes out his first patent for improvements in the construction of marine chronometers in Britain, including the first for a compensation balance
4.
1772 in architecture
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The year 1772 in architecture involved some significant architectural events and new buildings. January 27 - The Pantheon, London, designed by James Wyatt, adelphi Buildings, London, designed by Robert Adam and his brothers. Basilica of the Fourteen Holy Helpers in Bavaria, dragon House in Potsdam, by command of King Frederick the Great. Old Stone Fort, built as a Reformed Dutch church, brick Market, Newport, Rhode Island, designed by Peter Harrison
5.
Science
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Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. The formal sciences are often excluded as they do not depend on empirical observations, disciplines which use science, like engineering and medicine, may also be considered to be applied sciences. However, during the Islamic Golden Age foundations for the method were laid by Ibn al-Haytham in his Book of Optics. In the 17th and 18th centuries, scientists increasingly sought to formulate knowledge in terms of physical laws, over the course of the 19th century, the word science became increasingly associated with the scientific method itself as a disciplined way to study the natural world. It was during this time that scientific disciplines such as biology, chemistry, Science in a broad sense existed before the modern era and in many historical civilizations. Modern science is distinct in its approach and successful in its results, Science in its original sense was a word for a type of knowledge rather than a specialized word for the pursuit of such knowledge. In particular, it was the type of knowledge which people can communicate to each other, for example, knowledge about the working of natural things was gathered long before recorded history and led to the development of complex abstract thought. This is shown by the construction of calendars, techniques for making poisonous plants edible. For this reason, it is claimed these men were the first philosophers in the strict sense and they were mainly speculators or theorists, particularly interested in astronomy. In contrast, trying to use knowledge of nature to imitate nature was seen by scientists as a more appropriate interest for lower class artisans. A clear-cut distinction between formal and empirical science was made by the pre-Socratic philosopher Parmenides, although his work Peri Physeos is a poem, it may be viewed as an epistemological essay on method in natural science. Parmenides ἐὸν may refer to a system or calculus which can describe nature more precisely than natural languages. Physis may be identical to ἐὸν and he criticized the older type of study of physics as too purely speculative and lacking in self-criticism. He was particularly concerned that some of the early physicists treated nature as if it could be assumed that it had no intelligent order, explaining things merely in terms of motion and matter. The study of things had been the realm of mythology and tradition, however. Aristotle later created a less controversial systematic programme of Socratic philosophy which was teleological and he rejected many of the conclusions of earlier scientists. For example, in his physics, the sun goes around the earth, each thing has a formal cause and final cause and a role in the rational cosmic order. Motion and change is described as the actualization of potentials already in things, while the Socratics insisted that philosophy should be used to consider the practical question of the best way to live for a human being, they did not argue for any other types of applied science
6.
Technology
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Technology is the collection of techniques, skills, methods and processes used in the production of goods or services or in the accomplishment of objectives, such as scientific investigation. Technology can be the knowledge of techniques, processes, and the like, the human species use of technology began with the conversion of natural resources into simple tools. The steady progress of technology has brought weapons of ever-increasing destructive power. It has helped develop more advanced economies and has allowed the rise of a leisure class, many technological processes produce unwanted by-products known as pollution and deplete natural resources to the detriment of Earths environment. Various implementations of technology influence the values of a society and raise new questions of the ethics of technology, examples include the rise of the notion of efficiency in terms of human productivity, and the challenges of bioethics. Philosophical debates have arisen over the use of technology, with disagreements over whether technology improves the condition or worsens it. The use of the technology has changed significantly over the last 200 years. Before the 20th century, the term was uncommon in English, the term was often connected to technical education, as in the Massachusetts Institute of Technology. The term technology rose to prominence in the 20th century in connection with the Second Industrial Revolution, the terms meanings changed in the early 20th century when American social scientists, beginning with Thorstein Veblen, translated ideas from the German concept of Technik into technology. In German and other European languages, a distinction exists between technik and technologie that is absent in English, which translates both terms as technology. By the 1930s, technology referred not only to the study of the industrial arts, dictionaries and scholars have offered a variety of definitions. Ursula Franklin, in her 1989 Real World of Technology lecture, gave another definition of the concept, it is practice, the way we do things around here. The term is used to imply a specific field of technology, or to refer to high technology or just consumer electronics. Bernard Stiegler, in Technics and Time,1, defines technology in two ways, as the pursuit of life by other than life, and as organized inorganic matter. Technology can be most broadly defined as the entities, both material and immaterial, created by the application of mental and physical effort in order to some value. In this usage, technology refers to tools and machines that may be used to solve real-world problems and it is a far-reaching term that may include simple tools, such as a crowbar or wooden spoon, or more complex machines, such as a space station or particle accelerator. Tools and machines need not be material, virtual technology, such as software and business methods. W. Brian Arthur defines technology in a broad way as a means to fulfill a human purpose
7.
Joseph-Louis Lagrange
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Joseph-Louis Lagrange, born Giuseppe Lodovico Lagrangia or Giuseppe Ludovico De la Grange Tournier, was an Italian and French Enlightenment Era mathematician and astronomer. He made significant contributions to the fields of analysis, number theory, in 1787, at age 51, he moved from Berlin to Paris and became a member of the French Academy of Sciences. He remained in France until the end of his life, Lagrange was one of the creators of the calculus of variations, deriving the Euler–Lagrange equations for extrema of functionals. He also extended the method to take into account possible constraints and he proved that every natural number is a sum of four squares. His treatise Theorie des fonctions analytiques laid some of the foundations of group theory, in calculus, Lagrange developed a novel approach to interpolation and Taylor series. Born as Giuseppe Lodovico Lagrangia, Lagrange was of Italian and French descent and his mother was from the countryside of Turin. He was raised as a Roman Catholic, a career as a lawyer was planned out for Lagrange by his father, and certainly Lagrange seems to have accepted this willingly. He studied at the University of Turin and his subject was classical Latin. At first he had no enthusiasm for mathematics, finding Greek geometry rather dull. It was not until he was seventeen that he showed any taste for mathematics – his interest in the subject being first excited by a paper by Edmond Halley which he came across by accident. Alone and unaided he threw himself into mathematical studies, at the end of a years incessant toil he was already an accomplished mathematician, in that capacity, Lagrange was the first to teach calculus in an engineering school. In this Academy one of his students was François Daviet de Foncenex, Lagrange is one of the founders of the calculus of variations. Starting in 1754, he worked on the problem of tautochrone, Lagrange wrote several letters to Leonhard Euler between 1754 and 1756 describing his results. He outlined his δ-algorithm, leading to the Euler–Lagrange equations of variational calculus, Lagrange also applied his ideas to problems of classical mechanics, generalizing the results of Euler and Maupertuis. Euler was very impressed with Lagranges results, Lagrange published his method in two memoirs of the Turin Society in 1762 and 1773. Many of these are elaborate papers, the article concludes with a masterly discussion of echoes, beats, and compound sounds. Other articles in volume are on recurring series, probabilities. The next work he produced was in 1764 on the libration of the Moon, and an explanation as to why the face was always turned to the earth
8.
Three-body problem
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The three-body problem is a special case of the n-body problem. Historically, the first specific three-body problem to receive extended study was the one involving the Moon, the Earth, in an extended modern sense, a three-body problem is a class of problems in classical or quantum mechanics that model the motion of three particles. The gravitational problem of three bodies in its traditional sense dates in substance from 1687, when Isaac Newton published his Principia. The physical problem was addressed by Amerigo Vespucci and subsequently by Galileo Galilei, however the accuracy of the lunar theory was low, due to the perturbing effect of the Sun and planets on the motion of the Moon around the Earth. They submitted their competing first analyses to the Académie Royale des Sciences in 1747 and it was in connection with these researches, in Paris, in the 1740s, that the name three-body problem began to be commonly used. An account published in 1761 by Jean le Rond dAlembert indicates that the name was first used in 1747, in 1887, mathematicians Heinrich Bruns and Henri Poincaré showed that there is no general analytical solution for the three-body problem given by algebraic expressions and integrals. The motion of three bodies is generally non-repeating, except in special cases, a prominent example of the classical three-body problem is the movement of a planet with a satellite around a star. In this case, the problem is simplified to two instances of the two-body problem, however, the effect of the star on the movement of the satellite around the planet can be considered as a perturbation. While a spaceflight involving a gravity assist tends to be at least a problem, once far away from the Earth when Earths gravity becomes negligible. The general statement for the three body problem is as follows, in the circular restricted three-body problem, two massive bodies move in circular orbits around their common center of mass, and the third mass is negligible with respect to the other two. It can be useful to consider the effective potential, in 1767 Leonhard Euler found three families of periodic solutions in which the three masses are collinear at each instant. In 1772 Lagrange found a family of solutions in which the three form an equilateral triangle at each instant. Together, these form the central configurations for the three-body problem. These solutions are valid for any mass ratios, and the move on Keplerian ellipses. These five families are the only solutions for which there are explicit analytic formulae. In 1893 Meissel stated what is called the Pythagorean three-body problem. Burrau further investigated this problem in 1913, in 1967 Victor Szebehely and coworkers established eventual escape for this problem using numerical integration, while at the same time finding a nearby periodic solution. In 1911, United States scientist William Duncan MacMillan found one special solution, in 1961, Russian mathematician Sitnikov improved this solution
9.
Lagrangian point
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The Lagrange points mark positions where the combined gravitational pull of the two large masses provides precisely the centrifugal force required to orbit with them. There are five points, labeled L1 to L5, all in the orbital plane of the two large bodies. The first three are on the line connecting the two bodies, the last two, L4 and L5, each form an equilateral triangle with the two large bodies. The two latter points are stable, which implies that objects can orbit around them in a coordinate system tied to the two large bodies. Several planets have satellites near their L4 and L5 points with respect to the Sun, the three collinear Lagrange points were discovered by Leonhard Euler a few years before Lagrange discovered the remaining two. In 1772, Joseph-Louis Lagrange published an Essay on the three-body problem, in the first chapter he considered the general three-body problem. From that, in the chapter, he demonstrated two special constant-pattern solutions, the collinear and the equilateral, for any three masses, with circular orbits. The five Lagrangian points are labeled and defined as follows, The L1 point lies on the line defined by the two large masses M1 and M2, and between them. It is the most intuitively understood of the Lagrangian points, the one where the attraction of M2 partially cancels M1s gravitational attraction. Explanation An object that orbits the Sun more closely than Earth would normally have an orbital period than Earth. If the object is directly between Earth and the Sun, then Earths gravity counteracts some of the Suns pull on the object, the closer to Earth the object is, the greater this effect is. At the L1 point, the period of the object becomes exactly equal to Earths orbital period. L1 is about 1.5 million kilometers from Earth, the L2 point lies on the line through the two large masses, beyond the smaller of the two. Here, the forces of the two large masses balance the centrifugal effect on a body at L2. Explanation On the opposite side of Earth from the Sun, the period of an object would normally be greater than that of Earth. The extra pull of Earths gravity decreases the orbital period of the object, like L1, L2 is about 1.5 million kilometers from Earth. The L3 point lies on the line defined by the two masses, beyond the larger of the two. Explanation L3 in the Sun–Earth system exists on the side of the Sun
10.
Johann Heinrich Lambert
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Johann Heinrich Lambert was a Swiss polymath who made important contributions to the subjects of mathematics, physics, philosophy, astronomy and map projections. Lambert was born in 1728 into a Huguenot family in the city of Mulhouse, leaving school at 12, he continued to study in his free time whilst undertaking a series of jobs. Travelling Europe with his charges allowed him to meet established mathematicians in the German states, The Netherlands, France, on his return to Chur he published his first books and began to seek an academic post. In this stimulating and financially stable environment, he worked prodigiously until his death in 1777, Lambert was the first to introduce hyperbolic functions into trigonometry. Also, he made conjectures regarding non-Euclidean space, Lambert is credited with the first proof that π is irrational. He used a generalized continued fraction for the function tan x, euler believed but could not prove that π was irrational, and it is speculated that Aryabhata also believed this, in 500 CE. Lambert also devised theorems regarding conic sections that made the calculation of the orbits of comets simpler, Lambert devised a formula for the relationship between the angles and the area of hyperbolic triangles. These are triangles drawn on a surface, as on a saddle. Lambert showed that the angles added up to less than π, the amount of shortfall, called the defect, increases with the area. The larger the area, the smaller the sum of the angles. That is, the area of a triangle is equal to π, or 180°, minus the sum of the angles α, β. Here C denotes, in the present sense, the negative of the curvature of the surface. As the triangle gets larger or smaller, the change in a way that forbids the existence of similar hyperbolic triangles. Hence, instead of expressing the area of the triangle in terms of the lengths of its sides, as in Euclids geometry, Lambert was the first mathematician to address the general properties of map projections. In particular he was the first to discuss the properties of conformality and equal area preservation, in 1772, Lambert published seven new map projections under the title Anmerkungen und Zusätze zur Entwerfung der Land- und Himmelscharten. Further details may be found at map projections and in several texts, Lambert invented the first practical hygrometer. In 1760, he published a book on photometry, the Photometria and these results were supported by experiments involving the visual comparison of illuminations and used for the calculation of illumination. In Photometria Lambert also formulated the law of light absorption—the Beer–Lambert law) and he wrote a classic work on perspective and contributed to geometrical optics
11.
Map projection
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A map projection is a systematic transformation of the latitudes and longitudes of locations on the surface of a sphere or an ellipsoid into locations on a plane. Map projections are necessary for creating maps, all map projections distort the surface in some fashion. There is no limit to the number of map projections. More generally, the surfaces of bodies can be mapped even if they are too irregular to be modeled well with a sphere or ellipsoid. Even more generally, projections are the subject of several mathematical fields, including differential geometry. However, map projection refers specifically to a cartographic projection and these useful traits of maps motivate the development of map projections. However, Carl Friedrich Gausss Theorema Egregium proved that a spheres surface cannot be represented on a plane without distortion, the same applies to other reference surfaces used as models for the Earth. Since any map projection is a representation of one of surfaces on a plane. Every distinct map projection distorts in a distinct way, the study of map projections is the characterization of these distortions. Projection is not limited to perspective projections, such as those resulting from casting a shadow on a screen, rather, any mathematical function transforming coordinates from the curved surface to the plane is a projection. Few projections in actual use are perspective, for simplicity, most of this article assumes that the surface to be mapped is that of a sphere. In reality, the Earth and other celestial bodies are generally better modeled as oblate spheroids. These other surfaces can be mapped as well, therefore, more generally, a map projection is any method of flattening a continuous curved surface onto a plane. Many properties can be measured on the Earths surface independent of its geography, some of these properties are, Area Shape Direction Bearing Distance Scale Map projections can be constructed to preserve at least one of these properties, though only in a limited way for most. Each projection preserves or compromises or approximates basic metric properties in different ways, the purpose of the map determines which projection should form the base for the map. Because many purposes exist for maps, a diversity of projections have been created to suit those purposes, another consideration in the configuration of a projection is its compatibility with data sets to be used on the map. Data sets are geographic information, their collection depends on the datum of the Earth. Different datums assign slightly different coordinates to the location, so in large scale maps, such as those from national mapping systems
12.
Lambert conformal conic projection
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A Lambert conformal conic projection is a conic map projection used for aeronautical charts, portions of the State Plane Coordinate System, and many national and regional mapping systems. It is one of seven projections introduced by Johann Heinrich Lambert in his 1772 publication Anmerkungen und Zusätze zur Entwerfung der Land- und Himmelscharten, conceptually, the projection seats a cone over the sphere of the Earth and projects the surface conformally onto the cone. The cone is unrolled, and the parallel that was touching the sphere is assigned unit scale and that parallel is called the reference parallel or standard parallel. By scaling the map, two parallels can be assigned unit scale, with scale decreasing between the two parallels and increasing outside them. This gives the map two standard parallels, in this way, deviation from unit scale can be minimized within a region of interest that lies largely between the two standard parallels. Unlike other conic projections, no true secant form of the projection exists because using a secant cone does not yield the same scale along both standard parallels. Pilots use aeronautical charts based on LCC because a line drawn on a Lambert conformal conic projection approximates a great-circle route between endpoints for typical flight distances. The US systems of VFR sectional charts and terminal area charts are drafted on the LCC with standard parallels at 33°N and 45°N. The European Environment Agency and the INSPIRE specification for coordinate systems using this projection for conformal pan-European mapping at scales smaller or equal to 1,500,000. In Metropolitan France, the projection is Lambert-93, a Lambert conic projection using RGF93 geodetic system. The National Spatial Framework for India uses Datum WGS84 with a LCC projection and is a recommended NNRMS standard, each state has its own set of reference parameters given in the standard. The projection as used in CCS83 yields maps in which errors are limited to 1 part in 10,000. The Lambert conformal conic is one of several map projection developed by Johann Heinrich Lambert, an 18th-century Swiss mathematician, physicist, philosopher
13.
Transverse Mercator projection
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The transverse Mercator map projection is an adaptation of the standard Mercator projection. The transverse version is used in national and international mapping systems around the world. When paired with a geodetic datum, the transverse Mercator delivers high accuracy in zones less than a few degrees in east-west extent. The transverse Mercator projection is the aspect of the standard Mercator projection. For the transverse Mercator, the axis of the lies in the equatorial plane. Both projections may be modified to secant forms, which means the scale has been reduced so that the cylinder slices through the model globe, Both exist in spherical and ellipsoidal versions. Both projections are conformal, so that the point scale is independent of direction and local shapes are well preserved, since the central meridian of the transverse Mercator can be chosen at will, it may be used to construct highly accurate maps anywhere on the globe. The secant, ellipsoidal form of the transverse Mercator is the most widely applied of all projections for accurate large scale maps. In constructing a map on any projection, a sphere is normally chosen to model the Earth when the extent of the region exceeds a few hundred kilometers in length in both dimensions. For maps of regions, an ellipsoidal model must be chosen if greater accuracy is required. The spherical form of the transverse Mercator projection was one of the seven new projections presented, in 1772, Lambert did not name his projections, the name transverse Mercator dates from the second half of the nineteenth century. The principal properties of the projection are here presented in comparison with the properties of the normal projection. The ellipsoidal form of the transverse Mercator projection was developed by Carl Friedrich Gauss in 1825, the projection is known by several names, Gauss Conformal or Gauss-Krüger in Europe, the transverse Mercator in the US, or Gauss-Krüger transverse Mercator generally. The projection is conformal with a constant scale on the central meridian, the Gauss-Krüger projection is now the most widely used projection in accurate large scale mapping. The projection, as developed by Gauss and Krüger, was expressed in terms of low order power series which were assumed to diverge in the east-west direction and this was proved to be untrue by British cartographer E. H. Thompson, whose unpublished exact version of the projection, reported by L. P. Lee in 1976, near the central meridian the projection has low distortion and the shapes of Africa, western Europe, Britain, Greenland, Antarctica compare favourably with a globe. The central regions of the projections on sphere and ellipsoid are indistinguishable on the small scale projections shown here. The meridians at 90° east and west of the central meridian project to horizontal lines through the poles
14.
Lambert azimuthal equal-area projection
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The Lambert azimuthal equal-area projection is a particular mapping from a sphere to a disk. It accurately represents area in all regions of the sphere, and it is named for the Swiss mathematician Johann Heinrich Lambert, who announced it in 1772. Zenithal being synonymous with azimuthal, the projection is known as the Lambert zenithal equal-area projection. The Lambert azimuthal projection is used as a map projection in cartography and it is also used in scientific disciplines such as geology for plotting the orientations of lines in three-dimensional space. This plotting is aided by a kind of graph paper called a Schmidt net. To define the Lambert azimuthal projection, imagine a plane set tangent to the sphere at some point S on the sphere, let P be any point on the sphere other than the antipode of S. Let d be the distance between S and P in three-dimensional space, then the projection sends P to a point P′ on the plane that is a distance d from S. To make this precise, there is a unique circle centered at S, passing through P. It intersects the plane in two points, let P′ be the one that is closer to P, the antipode of S is excluded from the projection because the required circle is not unique. The case of S is degenerate, S is projected to itself, explicit formulas are required for carrying out the projection on a computer. Consider the projection centered at S = on the unit sphere, in Cartesian coordinates on the sphere and on the plane, the projection and its inverse are then described by =, =. In spherical coordinates on the sphere and polar coordinates on the disk, in cylindrical coordinates on the sphere and polar coordinates on the plane, the map and its inverse are given by =, =. The projection can be centered at other points, and defined on spheres of other than 1. As defined in the section, the Lambert azimuthal projection of the unit sphere is undefined at. It sends the rest of the sphere to the disk of radius 2 centered at the origin in the plane. It sends the point to, the equator z =0 to the circle of radius √2 centered at, the projection is a diffeomorphism between the sphere and the open disk of radius 2. It is a map, which can be seen by computing the area element of the sphere when parametrized by the inverse of the projection. In Cartesian coordinates it is d A = d X d Y and this means that measuring the area of a region on the sphere is tantamount to measuring the area of the corresponding region on the disk
15.
Daniel Rutherford
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Daniel Rutherford FRSE FRCPE FLS FSA was a Scottish physician, chemist and botanist who is most famous for the isolation of nitrogen in 1772. Rutherford was the uncle of the novelist Sir Walter Scott, the son of Professor John Rutherford and Anne Mackay, Daniel Rutherford was born in Edinburgh on 3 November 1749. He left home at the age of 16 to go to college and he was educated at Mundells School and Edinburgh University. Rutherford discovered nitrogen by the isolation of the particle in 1772, when Joseph Black was studying the properties of carbon dioxide, he found that a candle would not burn in it. Black turned this problem over to his student at the time, Rutherford kept a mouse in a space with a confined quantity of air until it died. Then, he burned a candle in the air until it went out. Afterwards, he burned phosphorus in that, until it would not burn, then the air was passed through a carbon dioxide absorbing solution. The remaining component of the air did not support combustion, Rutherford called the gas “noxious air” or “phlogisticated air”. Rutherford reported the experiment in 1772 and he and Black were convinced of the validity of the phlogiston theory, so they explained their results in terms of it. He was a professor of botany at the University of Edinburgh and he was President of the Royal College of Physicians of Edinburgh from 1796 to 1798. His pupils included Thomas Brown of Lanfine and Waterhaughs, biographical note at “Lectures and Papers of Professor Daniel Rutherford, and Diary of Mrs Harriet Rutherford”
16.
Nitrogen
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Nitrogen is a chemical element with symbol N and atomic number 7. It was first discovered and isolated by Scottish physician Daniel Rutherford in 1772, although Carl Wilhelm Scheele and Henry Cavendish had independently done so at about the same time, Rutherford is generally accorded the credit because his work was published first. Nitrogen is the lightest member of group 15 of the periodic table, the name comes from the Greek πνίγειν to choke, directly referencing nitrogens asphyxiating properties. It is an element in the universe, estimated at about seventh in total abundance in the Milky Way. At standard temperature and pressure, two atoms of the element bind to form dinitrogen, a colourless and odorless diatomic gas with the formula N2, dinitrogen forms about 78% of Earths atmosphere, making it the most abundant uncombined element. Nitrogen occurs in all organisms, primarily in amino acids, in the nucleic acids, the human body contains about 3% nitrogen by mass, the fourth most abundant element in the body after oxygen, carbon, and hydrogen. The nitrogen cycle describes movement of the element from the air, into the biosphere and organic compounds, many industrially important compounds, such as ammonia, nitric acid, organic nitrates, and cyanides, contain nitrogen. The extremely strong bond in elemental nitrogen, the second strongest bond in any diatomic molecule. Synthetically produced ammonia and nitrates are key industrial fertilisers, and fertiliser nitrates are key pollutants in the eutrophication of water systems. Apart from its use in fertilisers and energy-stores, nitrogen is a constituent of organic compounds as diverse as Kevlar used in high-strength fabric, Nitrogen is a constituent of every major pharmacological drug class, including antibiotics. Many notable nitrogen-containing drugs, such as the caffeine and morphine or the synthetic amphetamines. Nitrogen compounds have a long history, ammonium chloride having been known to Herodotus. They were well known by the Middle Ages, alchemists knew nitric acid as aqua fortis, as well as other nitrogen compounds such as ammonium salts and nitrate salts. The mixture of nitric and hydrochloric acids was known as aqua regia, celebrated for its ability to dissolve gold, the discovery of nitrogen is attributed to the Scottish physician Daniel Rutherford in 1772, who called it noxious air. Though he did not recognise it as a different chemical substance, he clearly distinguished it from Joseph Blacks fixed air. The fact that there was a component of air that does not support combustion was clear to Rutherford, Nitrogen was also studied at about the same time by Carl Wilhelm Scheele, Henry Cavendish, and Joseph Priestley, who referred to it as burnt air or phlogisticated air. Nitrogen gas was inert enough that Antoine Lavoisier referred to it as air or azote, from the Greek word άζωτικός. In an atmosphere of nitrogen, animals died and flames were extinguished
17.
Joseph Priestley
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He is usually credited with the discovery of oxygen, having isolated it in its gaseous state, although Carl Wilhelm Scheele and Antoine Lavoisier also have a claim to the discovery. However, Priestleys determination to defend phlogiston theory and to reject what would become the chemical revolution eventually left him isolated within the scientific community, Priestleys science was integral to his theology, and he consistently tried to fuse Enlightenment rationalism with Christian theism. In his metaphysical texts, Priestley attempted to combine theism, materialism, and determinism and he believed that a proper understanding of the natural world would promote human progress and eventually bring about the Christian Millennium. Priestley, who believed in the free and open exchange of ideas, advocated toleration and equal rights for religious Dissenters. He spent his last ten years in Northumberland County, Pennsylvania and these educational writings were among Priestleys most popular works. Priestley was born to an established English Dissenting family in Birstall and he was the oldest of six children born to Mary Swift and Jonas Priestley, a finisher of cloth. To ease his mothers burdens, Priestley was sent to live with his grandfather around the age of one and he returned home, five years later, after his mother died. When his father remarried in 1741, Priestley went to live with his aunt and uncle, during his youth, Priestley attended local schools where he learned Greek, Latin, and Hebrew. Around 1749, Priestley became seriously ill and believed he was dying, raised as a devout Calvinist, he believed a conversion experience was necessary for salvation, but doubted he had had one. This emotional distress eventually led him to question his upbringing, causing him to reject election. As a result, the elders of his church, the Independent Upper Chapel of Heckmondwike. Priestleys illness left him with a permanent stutter and he gave up any thoughts of entering the ministry at that time, in preparation for joining a relative in trade in Lisbon, he studied French, Italian, and German in addition to Aramaic, and Arabic. Priestley eventually decided to return to his studies and, in 1752, matriculated at Daventry. Because he had read widely, Priestley was allowed to skip the first two years of coursework. He continued his study, this, together with the liberal atmosphere of the school, shifted his theology further leftward. Abhorring dogma and religious mysticism, Rational Dissenters emphasised the rational analysis of the natural world, Priestley later wrote that the book that influenced him the most, save the Bible, was David Hartleys Observations on Man. Hartleys psychological, philosophical, and theological treatise postulated a theory of mind. Hartley aimed to construct a Christian philosophy in both religious and moral facts could be scientifically proven, a goal that would occupy Priestley for his entire life
18.
Nitrous oxide
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Nitrous oxide, commonly known as laughing gas or nitrous, is a chemical compound, an oxide of nitrogen with the formula N 2O. At room temperature, it is a colorless, odorless non-flammable gas, at elevated temperatures, nitrous oxide is a powerful oxidizer similar to molecular oxygen. Nitrous oxide has significant medical uses, especially in surgery and dentistry and its name laughing gas is due to the euphoric effects of inhaling it, a property that has led to its recreational use as a dissociative anaesthetic. It is also used as an oxidizer in rocket propellants, Nitrous oxide occurs in small amounts in the atmosphere, but has been found recently to be a major scavenger of stratospheric ozone, with impact comparable to that of CFCs. It is estimated that 30% of the N 2O in the atmosphere is the result of human activity, Nitrous oxide can be used as an oxidizer in a rocket motor. This has the advantages over other oxidisers in that it is not only non-toxic, as a secondary benefit it can be readily decomposed to form breathing air. Its high density and low storage pressure enable it to be competitive with stored high-pressure gas systems. In a 1914 patent, American rocket pioneer Robert Goddard suggested nitrous oxide, Nitrous oxide has been the oxidiser of choice in several hybrid rocket designs. The combination of nitrous oxide with hydroxyl-terminated polybutadiene fuel has been used by SpaceShipOne and it is also notably used in amateur and high power rocketry with various plastics as the fuel. Nitrous oxide can also be used in a monopropellant rocket, in the presence of a heated catalyst, N 2O will decompose exothermically into nitrogen and oxygen, at a temperature of approximately 1,070 °F. Because of the heat release, the catalytic action rapidly becomes secondary as thermal autodecomposition becomes dominant. In a vacuum thruster, this can provide a monopropellant specific impulse of as much as 180 s, while noticeably less than the Isp available from hydrazine thrusters, the decreased toxicity makes nitrous oxide an option worth investigating. Nitrous oxide is said to deflagrate somewhere around 600 °C at a pressure of 21 atmospheres, at 600 psi for example, the required ignition energy is only 6 joules, whereas N 2O at 130 psi a 2500-joule ignition energy input is insufficient. In vehicle racing, nitrous oxide allows the engine to burn more fuel by providing more oxygen than air alone, the gas itself is not flammable at a low pressure/temperature, but it delivers more oxygen than atmospheric air by breaking down at elevated temperatures. Therefore, it is mixed with another fuel that is easier to deflagrate. Nitrous oxide is a strong oxidant roughly equivalent to hydrogen peroxide, Nitrous oxide is sometimes injected into the intake manifold, whereas other systems directly inject right before the cylinder to increase power. The technique was used during World War II by Luftwaffe aircraft with the GM-1 system to boost the output of aircraft engines. Originally meant to provide the Luftwaffe standard aircraft with superior high-altitude performance, accordingly, it was only used by specialized planes like high-altitude reconnaissance aircraft, high-speed bombers, and high-altitude interceptor aircraft
19.
Antoine Lavoisier
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Antoine-Laurent de Lavoisier was a French nobleman and chemist central to the 18th-century chemical revolution and had a large influence on both the history of chemistry and the history of biology. He is widely considered in popular literature as the father of modern chemistry and it is generally accepted that Lavoisiers great accomplishments in chemistry largely stem from his changing the science from a qualitative to a quantitative one. Lavoisier is most noted for his discovery of the role oxygen plays in combustion and he recognized and named oxygen and hydrogen and opposed the phlogiston theory. Lavoisier helped construct the system, wrote the first extensive list of elements. He predicted the existence of silicon and was also the first to establish that sulfur was an element rather than a compound and he discovered that, although matter may change its form or shape, its mass always remains the same. Lavoisier was a member of a number of aristocratic councils. All of these political and economic activities enabled him to fund his scientific research, at the height of the French Revolution, he was accused by Jean-Paul Marat of selling adulterated tobaccoand of other crimes, and was eventually guillotined a year after Marats death. Antoine-Laurent Lavoisier was born to a family of the nobility in Paris on 26 August 1743. The son of an attorney at the Parliament of Paris, he inherited a fortune at the age of five with the passing of his mother. Lavoisier began his schooling at the Collège des Quatre-Nations, University of Paris in Paris in 1754 at the age of 11, in his last two years at the school, his scientific interests were aroused, and he studied chemistry, botany, astronomy, and mathematics. Lavoisier entered the school of law, where he received a degree in 1763. Lavoisier received a law degree and was admitted to the bar, however, he continued his scientific education in his spare time. Lavoisiers education was filled with the ideals of the French Enlightenment of the time and he attended lectures in the natural sciences. Lavoisiers devotion and passion for chemistry were largely influenced by Étienne Condillac and his first chemical publication appeared in 1764. From 1763 to 1767, he studied geology under Jean-Étienne Guettard, in collaboration with Guettard, Lavoisier worked on a geological survey of Alsace-Lorraine in June 1767. In 1768 Lavoisier received an appointment to the Academy of Sciences. In 1769, he worked on the first geological map of France, on behalf of the Ferme générale Lavoisier commissioned the building of a wall around Paris so that customs duties could be collected from those transporting goods into and out of the city. Lavoisier attempted to introduce reforms in the French monetary and taxation system to help the peasants, Lavoisier consolidated his social and economic position when, in 1771 at age 28, he married Marie-Anne Pierrette Paulze, the 13-year-old daughter of a senior member of the Ferme générale
20.
Phlogiston theory
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The phlogiston theory is a superseded scientific theory that postulated that a fire-like element called phlogiston is contained within combustible bodies and released during combustion. The name comes from the Ancient Greek φλογιστόν phlogistón, from φλόξ phlóx and it was first stated in 1667 by Johann Joachim Becher, and then put together more formally by Georg Ernst Stahl. The theory attempted to explain burning processes such as combustion and rusting, phlogisticated substances are substances that contain phlogiston and dephlogisticate when burned. Dephlogisticating is when the substance simply releases the phlogiston inside of it, growing plants then absorb this phlogiston, which is why air does not spontaneously combust and also why plant matter burns as well as it does. In the following quote, Becher described phlogiston as a process that explained combustion through a process that was opposite to that of oxygen. When air had become completely phlogisticated it would no longer serve to support combustion of any material, nor would a metal heated in it yield a calx, breathing was thought to take phlogiston out of the body. Joseph Blacks student Daniel Rutherford discovered nitrogen in 1772 and the pair used the theory to explain his results. The residue of air left after burning, in fact a mixture of nitrogen and carbon dioxide, was referred to as phlogisticated air. Conversely, when oxygen was first discovered, it was thought to be dephlogisticated air, capable of combining with more phlogiston and thus supporting combustion for longer than ordinary air. Empedocles had formulated the theory that there were four elements, water, earth, fire and air. Fire was thus thought of as a substance and burning was seen as a process of decomposition which applied only to compounds, however experience had shown that burning was not always accompanied by a loss of material and a better theory was needed to account for this. In 1667, Johann Joachim Becher published his book Physica subterranea, in his book, Becher eliminated fire, water, and air from the classical element model and replaced them with three forms of earth, terra lapidea, terra fluida, and terra pinguis. Terra pinguis was the element that imparted oily, sulphurous, or combustible properties, Becher believed that terra pinguis was a key feature of combustion and was released when combustible substances were burned. Becher did not have much to do with phlogiston theory as we know it now, bechers main contribution was the start of the theory itself, however much it was changed after him. Bechers idea was that combustible substances contain an ignitable matter, the terra pinguis, the term phlogiston itself was not something that Stahl invented. There is evidence that the word was used as early as 1606, the term was derived from a Greek word meaning to inflame. When the oxide was heated with a substance rich in phlogiston, such as charcoal, phlogiston was a definite substance, the same in all its combinations. Stahls first definition of phlogiston first appeared in his Zymotechnia fundamentalis and his most quoted definition was found in the treatise on chemistry entitled Fundamenta chymiae in 1723
21.
French Academy of Sciences
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The French Academy of Sciences is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at the forefront of developments in Europe in the 17th and 18th centuries. Currently headed by Sébastien Candel, it is one of the five Academies of the Institut de France, the Academy of Sciences makes its origin to Colberts plan to create a general academy. He chose a group of scholars who met on 22 December 1666 in the Kings library. The first 30 years of the Academys existence were relatively informal, in contrast to its British counterpart, the Academy was founded as an organ of government. The Academy was expected to remain apolitical, and to avoid discussion of religious, on 20 January 1699, Louis XIV gave the Company its first rules. The Academy received the name of Royal Academy of Sciences and was installed in the Louvre in Paris, following this reform, the Academy began publishing a volume each year with information on all the work done by its members and obituaries for members who had died. This reform also codified the method by which members of the Academy could receive pensions for their work, on 8 August 1793, the National Convention abolished all the academies. Almost all the old members of the previously abolished Académie were formally re-elected, among the exceptions was Dominique, comte de Cassini, who refused to take his seat. In 1816, the again renamed Royal Academy of Sciences became autonomous, while forming part of the Institute of France, in the Second Republic, the name returned to Académie des sciences. During this period, the Academy was funded by and accountable to the Ministry of Public Instruction, the Academy came to control French patent laws in the course of the eighteenth century, acting as the liaison of artisans knowledge to the public domain. As a result, academicians dominated technological activities in France, the Academy proceedings were published under the name Comptes rendus de lAcadémie des sciences. The Comptes rendus is now a series with seven titles. The publications can be found on site of the French National Library, in 1818 the French Academy of Sciences launched a competition to explain the properties of light. The civil engineer Augustin-Jean Fresnel entered this competition by submitting a new theory of light. Siméon Denis Poisson, one of the members of the judging committee, being a supporter of the particle-theory of light, he looked for a way to disprove it. The Poisson spot is not easily observed in every-day situations, so it was natural for Poisson to interpret it as an absurd result. However, the head of the committee, Dominique-François-Jean Arago, and he molded a 2-mm metallic disk to a glass plate with wax
22.
Louis-Bernard Guyton de Morveau
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Louis-Bernard Guyton, Baron de Morveau was a French chemist and politician. He is credited with producing the first systematic method of chemical nomenclature, Guyton de Morveau was born in Dijon, where he served as a lawyer, then avocat général, of the Dijon parlement. In 1773, already interested in chemistry, he proposed use of acid gas for fumigation of buildings. However, chlorine was not well characterized at that time, in 1782 he resigned this post to dedicate himself to chemistry, collaborating on the Encyclopédie Méthodique and working for industrial applications. He performed various services in this role, and founded La Société des Mines et Verreries in Saint-Bérain-sur-Dheune. He developed the first system of chemical nomenclature, in 1783, he was elected a foreign member of the Royal Swedish Academy of Sciences and in 1788 a Fellow of the Royal Society. Although a member of the wing, he voted in favor of the execution of King Louis XVI. He himself flew in a balloon during the battle of Fleurus on 26 June 1794 and he was among the founders of the École Polytechnique and the École de Mars, and was a professor of mineralogy at the Polytechnique. He became a member of the Académie des sciences in chemistry, on 20 November 1795. In 1798 he married Claudine Picardet, a widowed friend. Under the Directory, he served on the Council of Five Hundred from 1797, elected from Ille-et-Vilaine, with Hugues Maret and Jean François Durande he also published the Élémens de chymie théorique et pratique. During his lifetime, Guyton de Morveau received the cross of the Legion of Honour and was made an Officer of the Legion of Honour for service to humanity and he was made a baron of the First French Empire in 1811. Guyton de Morveau died in Paris on 2 January 1816
23.
Calcination
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Authorities differ on the meaning of calcination. The IUPAC defines it as heating to temperatures in air or oxygen. A calciner is a cylinder that rotates inside a heated furnace. The product of calcination is usually referred to in general as calcine, calcination is carried out in furnaces or reactors of various designs including shaft furnaces, rotary kilns, multiple hearth furnaces, and fluidized bed reactors. Calcination reactions usually take place at or above the decomposition temperature or the transition temperature. This temperature is defined as the temperature at which the standard Gibbs free energy for a particular calcination reaction is equal to zero. For example, in limestone calcination, a process, the chemical reaction is CaCO3 → CaO + CO2 The standard Gibbs free energy of reaction is approximated as ΔG°r =177,100 −158 T. The standard free energy of reaction is 0 in this case when the temperature, T, is equal to 1121 K, see also calcination equilibrium of calcium carbonate In some cases, calcination of a metal results in oxidation of the metal. Jean Rey noted that lead and tin when calcinated gained weight, in alchemy, calcination was believed to be one of the 12 vital processes required for the transformation of a substance. Alchemists distinguished two kinds of calcination, actual and potential, actual calcination is that brought about by actual fire, from wood, coals, or other fuel, raised to a certain temperature
24.
Central England temperature
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The monthly mean surface air temperatures, for the Midlands region of England, are given from the year 1659 to the present. This record represents the longest series of temperature observations in existence. It is a valuable dataset for meteorologists and climate scientists and it is monthly from 1659, and a daily version has been produced from 1772. The monthly means from November 1722 onwards are given to a precision of 0.1 °C and this reflects the number, accuracy, reliability and geographical spread of the temperature records that were available for the years in question. Although best efforts have made by Manley and subsequent researchers to quality control the series, there are data problems in the early years. These problems account for the precision to which the early monthly means were quoted by Manley. Parker et al. addressed this by not using data prior to 1772, before 1722, instrumental records do not overlap and Manley used a non-instrumental series from Utrecht compiled by Labrijn, to make the monthly central England temperature series complete. Between 1723 and the 1760s most observations were not from outside measurements but from indoor readings in unheated rooms. During the eighteenth and nineteenth centuries, a period which coincided with snowy winters and generally cool summers. From 1910, temperatures increased slightly until about 1950 when they flattened before a rising trend began in about 1975. Temperatures in the most recent decade were higher in all seasons than the long-term average. Taking the 355-year period for the series as a whole, Climate of the United Kingdom England and Wales Precipitation G. Manley, Central England temperatures, quarterly J. of the Royal Meteorological Society, vol. Folland, A new daily Central England Temperature series 1772-1991, Int, graphs of the series at the University of East Anglia Freely downloadable text file containing the data. Met Office Hadley Centre CET pages
25.
William Hamilton (diplomat)
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Sir William Hamilton KB, PC, FRS, FRSE was a Scottish diplomat, antiquarian, archaeologist and vulcanologist. After a short period as a Member of Parliament, he served as British Ambassador to the Kingdom of Naples from 1764 to 1800 and he studied the volcanoes Vesuvius and Etna, becoming a Fellow of the Royal Society and recipient of the Copley Medal. His second wife was Emma Hamilton, famed as Horatio Nelsons mistress and his mother was a favourite, and possibly a mistress, of the Prince of Wales and William grew up with his son George III, who would call him his foster brother. At age nine, he went to Westminster School, where he made friends of Frederick Hervey. Hamilton used to say that he was born with an ancient name, so, six weeks after his sixteenth birthday, he was commissioned into the 3rd Foot Guards as an ensign. He spent some time with the regiment in the Netherlands, in September 1757 he was present as aide-de-camp to General Henry Seymour Conway at the abortive attack on Rochefort. The following year he left the Army, after having married Catherine Barlow, the couple shared a love of music, and the marriage, which lasted until Catherines death on 25 August 1782, was a happy one. When Catherines father died in 1763 she inherited his estates in Wales, in 1761 Hamilton entered Parliament as Member for Midhurst. When he heard that the ambassador to the court of Naples, Sir James Gray, was likely to be promoted to Madrid, Hamilton expressed an interest in the position, and was duly appointed in 1764. These official duties left him plenty of time to pursue his interests in art, antiquities, Catherine, who had never enjoyed good health, began to recover in the mild climate of Naples. Hamilton began collecting Greek vases and other antiquities as soon as he arrived in Naples, obtaining them from dealers or other collectors, in 1766–67 he published a volume of engravings of his collection entitled Collection of Etruscan, Greek, and Roman antiquities from the cabinet of the Honble. Wm. Hamilton, His Britannick Maiestys envoy extraordinary at the Court of Naples, the text was written by dHancarville with contributions by Johann Winckelmann. A further three volumes were produced in 1769–76, during the his first leave in 1771 Hamilton arranged the sale of his collection to the British Museum for £8,410. Josiah Wedgwood the potter drew inspiration from the reproductions in Hamiltons volumes, during this first leave, in January 1772, Hamilton became a Knight of the Order of the Bath and the following month was elected Fellow of the Society of Antiquaries. In 1777, during his leave to England, he became a member of the Society of Dilettanti. Hamilton had bought it from a dealer and sold it to the Duchess of Portland, the cameo work on the vase again served as inspiration to Josiah Wedgwood, this time for his jasperware. The vase was bought by the British Museum. He was elected a Foreign Honorary Member of the American Academy of Arts, in 1798, as Hamilton was about to leave Naples, he packed up his art collection and a second vase collection and sent them back to England
26.
Leonhard Euler
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He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. He is also known for his work in mechanics, fluid dynamics, optics, astronomy, Euler was one of the most eminent mathematicians of the 18th century, and is held to be one of the greatest in history. He is also considered to be the most prolific mathematician of all time. His collected works fill 60 to 80 quarto volumes, more than anybody in the field and he spent most of his adult life in Saint Petersburg, Russia, and in Berlin, then the capital of Prussia. A statement attributed to Pierre-Simon Laplace expresses Eulers influence on mathematics, Read Euler, read Euler, Leonhard Euler was born on 15 April 1707, in Basel, Switzerland to Paul III Euler, a pastor of the Reformed Church, and Marguerite née Brucker, a pastors daughter. He had two sisters, Anna Maria and Maria Magdalena, and a younger brother Johann Heinrich. Soon after the birth of Leonhard, the Eulers moved from Basel to the town of Riehen, Paul Euler was a friend of the Bernoulli family, Johann Bernoulli was then regarded as Europes foremost mathematician, and would eventually be the most important influence on young Leonhard. Eulers formal education started in Basel, where he was sent to live with his maternal grandmother. In 1720, aged thirteen, he enrolled at the University of Basel, during that time, he was receiving Saturday afternoon lessons from Johann Bernoulli, who quickly discovered his new pupils incredible talent for mathematics. In 1726, Euler completed a dissertation on the propagation of sound with the title De Sono, at that time, he was unsuccessfully attempting to obtain a position at the University of Basel. In 1727, he first entered the Paris Academy Prize Problem competition, Pierre Bouguer, who became known as the father of naval architecture, won and Euler took second place. Euler later won this annual prize twelve times, around this time Johann Bernoullis two sons, Daniel and Nicolaus, were working at the Imperial Russian Academy of Sciences in Saint Petersburg. In November 1726 Euler eagerly accepted the offer, but delayed making the trip to Saint Petersburg while he applied for a physics professorship at the University of Basel. Euler arrived in Saint Petersburg on 17 May 1727 and he was promoted from his junior post in the medical department of the academy to a position in the mathematics department. He lodged with Daniel Bernoulli with whom he worked in close collaboration. Euler mastered Russian and settled life in Saint Petersburg. He also took on a job as a medic in the Russian Navy. The Academy at Saint Petersburg, established by Peter the Great, was intended to improve education in Russia, as a result, it was made especially attractive to foreign scholars like Euler
27.
Mersenne prime
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In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a number that can be written in the form Mn = 2n −1 for some integer n. They are named after Marin Mersenne, a French Minim friar, the first four Mersenne primes are 3,7,31, and 127. If n is a number then so is 2n −1. The definition is therefore unchanged when written Mp = 2p −1 where p is assumed prime, more generally, numbers of the form Mn = 2n −1 without the primality requirement are called Mersenne numbers. The smallest composite pernicious Mersenne number is 211 −1 =2047 =23 ×89, Mersenne primes Mp are also noteworthy due to their connection to perfect numbers. As of January 2016,49 Mersenne primes are known, the largest known prime number 274,207,281 −1 is a Mersenne prime. Since 1997, all newly found Mersenne primes have been discovered by the “Great Internet Mersenne Prime Search”, many fundamental questions about Mersenne primes remain unresolved. It is not even whether the set of Mersenne primes is finite or infinite. The Lenstra–Pomerance–Wagstaff conjecture asserts that there are infinitely many Mersenne primes,23 | M11,47 | M23,167 | M83,263 | M131,359 | M179,383 | M191,479 | M239, and 503 | M251. Since for these primes p, 2p +1 is congruent to 7 mod 8, so 2 is a quadratic residue mod 2p +1, since p is a prime, it must be p or 1. The first four Mersenne primes are M2 =3, M3 =7, M5 =31, a basic theorem about Mersenne numbers states that if Mp is prime, then the exponent p must also be prime. This follows from the identity 2 a b −1 = ⋅ = ⋅ and this rules out primality for Mersenne numbers with composite exponent, such as M4 =24 −1 =15 =3 ×5 = ×. Though the above examples might suggest that Mp is prime for all p, this is not the case. The evidence at hand does suggest that a randomly selected Mersenne number is more likely to be prime than an arbitrary randomly selected odd integer of similar size. Nonetheless, prime Mp appear to grow increasingly sparse as p increases, in fact, of the 2,270,720 prime numbers p up to 37,156,667, Mp is prime for only 45 of them. The lack of any simple test to determine whether a given Mersenne number is prime makes the search for Mersenne primes a difficult task, the Lucas–Lehmer primality test is an efficient primality test that greatly aids this task. The search for the largest known prime has somewhat of a cult following, consequently, a lot of computer power has been expended searching for new Mersenne primes, much of which is now done using distributed computing
28.
Marquis de Condorcet
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Unlike many of his contemporaries, he advocated a liberal economy, free and equal public instruction, constitutionalism, and equal rights for women and people of all races. His ideas and writings were said to embody the ideals of the Age of Enlightenment and rationalism and he died a mysterious death in prison after a period of flight from French Revolutionary authorities. Condorcet was born in Ribemont, and descended from the ancient family of Caritat, fatherless at a young age, he was raised by his devoutly religious mother. He was educated at the Jesuit College in Reims and at the Collège de Navarre in Paris, where he showed his intellectual ability. When he was sixteen, his analytical abilities gained the praise of Jean le Rond dAlembert and Alexis Clairaut, soon, from 1765 to 1774, he focused on science. In 1765, he published his first work on mathematics entitled Essai sur le calcul intégral and he would go on to publish more papers, and on 25 February 1769, he was elected to the Académie royale des Sciences. In 1772, he published another paper on integral calculus, soon after, he met Jacques Turgot, a French economist, and the two became friends. Turgot was to be an administrator under King Louis XV in 1772, Condorcet worked with Leonhard Euler and Benjamin Franklin. In 1774, Condorcet was appointed general of the Paris mint by Turgot. From this point on, Condorcet shifted his focus from the purely mathematical to philosophy, in the following years, he took up the defense of human rights in general, and of womens and Blacks rights in particular. He supported the ideals embodied by the newly formed United States, in 1776, Turgot was dismissed as Controller General. Consequently, Condorcet submitted his resignation as Inspector General of the Monnaie, but the request was refused, Condorcet later wrote Vie de M. Turgot, a biography which spoke fondly of Turgot and advocated Turgots economic theories. In 1785, Condorcet wrote an essay on the application of analysis of the probability of decisions made on a majority vote, the paper also outlines a generic Condorcet method, designed to simulate pair-wise elections between all candidates in an election. He disagreed strongly with the method of aggregating preferences put forth by Jean-Charles de Borda. Condorcet was one of the first to apply mathematics in the social sciences. In 1781, Condorcet wrote a pamphlet, Reflections on Negro Slavery, in 1786, Condorcet worked on ideas for the differential and integral calculus, giving a new treatment of infinitesimals – a work which was never printed. In 1789, he published Vie de Voltaire, which agreed with Voltaire in his opposition to the Church, in 1791, Condorcet along with Sophie de Grouchy, Thomas Paine, Etienne Dumont, Jacques-Pierre Brissot, and Achilles Duchastellet published a brief journal titled Le Républicain. Its main goal being the promotion of republicanism and the rejection of establishing a constitutional monarchy, the theme being that any sort of monarchy is a threat to freedom no matter who is leading, which emphasized that liberty is freedom from domination