Paris is the capital and most populous city of France, with an area of 105 square kilometres and an official estimated population of 2,140,526 residents as of 1 January 2019. Since the 17th century, Paris has been one of Europe's major centres of finance, commerce, fashion and the arts; the City of Paris is the centre and seat of government of the Île-de-France, or Paris Region, which has an estimated official 2019 population of 12,213,364, or about 18 percent of the population of France. The Paris Region had a GDP of €681 billion in 2016, accounting for 31 percent of the GDP of France, was the 5th largest region by GDP in the world. According to the Economist Intelligence Unit Worldwide Cost of Living Survey in 2018, Paris was the second most expensive city in the world, after Singapore, ahead of Zurich, Hong Kong and Geneva. Another source ranked Paris as most expensive, on a par with Singapore and Hong-Kong, in 2018; the city is a major rail and air-transport hub served by two international airports: Paris-Charles de Gaulle and Paris-Orly.
Opened in 1900, the city's subway system, the Paris Métro, serves 5.23 million passengers daily, is the second busiest metro system in Europe after Moscow Metro. Gare du Nord is the 24th busiest railway station in the world, the first located outside Japan, with 262 million passengers in 2015. Paris is known for its museums and architectural landmarks: the Louvre was the most visited art museum in the world in 2018, with 10.2 million visitors. The Musée d'Orsay and Musée de l'Orangerie are noted for their collections of French Impressionist art, the Pompidou Centre Musée National d'Art Moderne has the largest collection of modern and contemporary art in Europe; the historical district along the Seine in the city centre is classified as a UNESCO Heritage Site. Popular landmarks in the centre of the city include the Cathedral of Notre Dame de Paris and the Gothic royal chapel of Sainte-Chapelle, both on the Île de la Cité. Paris received 23 million visitors in 2017, measured by hotel stays, with the largest numbers of foreign visitors coming from the United States, the UK, Germany and China.
It was ranked as the third most visited travel destination in the world in 2017, after Bangkok and London. The football club Paris Saint-Germain and the rugby union club Stade Français are based in Paris; the 80,000-seat Stade de France, built for the 1998 FIFA World Cup, is located just north of Paris in the neighbouring commune of Saint-Denis. Paris hosts the annual French Open Grand Slam tennis tournament on the red clay of Roland Garros. Paris will host the 2024 Summer Olympics; the 1938 and 1998 FIFA World Cups, the 2007 Rugby World Cup, the 1960, 1984, 2016 UEFA European Championships were held in the city and, every July, the Tour de France bicycle race finishes there. The name "Paris" is derived from the Celtic Parisii tribe; the city's name is not related to the Paris of Greek mythology. Paris is referred to as the City of Light, both because of its leading role during the Age of Enlightenment and more because Paris was one of the first large European cities to use gas street lighting on a grand scale on its boulevards and monuments.
Gas lights were installed on the Place du Carousel, Rue de Rivoli and Place Vendome in 1829. By 1857, the Grand boulevards were lit. By the 1860s, the boulevards and streets of Paris were illuminated by 56,000 gas lamps. Since the late 19th century, Paris has been known as Panam in French slang. Inhabitants are known in French as Parisiens, they are pejoratively called Parigots. The Parisii, a sub-tribe of the Celtic Senones, inhabited the Paris area from around the middle of the 3rd century BC. One of the area's major north–south trade routes crossed the Seine on the île de la Cité; the Parisii minted their own coins for that purpose. The Romans began their settlement on Paris' Left Bank; the Roman town was called Lutetia. It became a prosperous city with a forum, temples, an amphitheatre. By the end of the Western Roman Empire, the town was known as Parisius, a Latin name that would become Paris in French. Christianity was introduced in the middle of the 3rd century AD by Saint Denis, the first Bishop of Paris: according to legend, when he refused to renounce his faith before the Roman occupiers, he was beheaded on the hill which became known as Mons Martyrum "Montmartre", from where he walked headless to the north of the city.
Clovis the Frank, the first king of the Merovingian dynasty, made the city his capital from 508. As the Frankish domination of Gaul began, there was a gradual immigration by the Franks to Paris and the Parisian Francien dialects were born. Fortification of the Île-de-la-Citie failed to avert sacking by Vikings in 845, but Paris' strategic importance—with its bridges prevent
Louis Vicat French engineer. He graduated from École Polytechnique 1804 and École des Ponts et Chaussées 1806. Vicat developed his own; the first building using the modern mortar is the bridge of Souillac erected in 1818. The material was superseded by Portland cement, he invented the Vicat needle, still in use for determination of setting time of concretes and cements. His son, Joseph Vicat, founded Vicat Cement, today a large international cement manufacturing company, he was a member of the French Academy of Sciences and his name is one of the 72 names inscribed on the Eiffel Tower. Vicat was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1855. Guy Coriono 250 ans de l'École des Ponts et Chaussées en cent portraits. 222 pp. Presses de l'École Nationale des Ponts et Chaussées, Paris, ISBN 2-85978-271-0. Antoine Picon L'art de l'Ingénieur. Constructeur, inventeur. 598 pp. Editions du Centre Pompidou, Paris, ISBN 2-85850-911-5
Alexandre Gustave Eiffel was a French civil engineer. A graduate of École Centrale Paris, he made his name building various bridges for the French railway network, most famously the Garabit viaduct, he is best known for the world-famous Eiffel Tower, built for the 1889 Universal Exposition in Paris, his contribution to building the Statue of Liberty in New York. After his retirement from engineering, Eiffel focused on research into meteorology and aerodynamics, making significant contributions in both fields. Gustave Eiffel was born in Burgundy, France, in the city of Dijon, Côte-d'Or, the first child of Catherine-Mélanie and Alexandre Bönickhausen, he was a descendant of Jean-René Bönickhausen, who had emigrated from the German town of Marmagen and settled in Paris at the beginning of the 18th century. The family adopted the name Eiffel as a reference to the Eifel mountains in the region from which they had come. Although the family always used the name Eiffel, Gustave's name was registered at birth as Bonickhausen dit Eiffel, was not changed to Eiffel until 1880.
At the time of Gustave's birth, his father, an ex-soldier, was working as an administrator for the French Army. Due to his mother's business commitments, Gustave spent his childhood living with his grandmother, but remained close to his mother, to remain an influential figure until her death in 1878, his father, did not play a big part in young Eiffel's early life. The business was successful enough for Catherine Eiffel to sell it in 1843 and retire on the proceeds. Eiffel was not a studious child, thought his classes at the Lycée Royal in Dijon boring and a waste of time, although in his last two years, influenced by his teachers for history and literature, he began to study and he gained his baccalauréats in humanities and science. An important part in his education was played by his uncle, Jean-Baptiste Mollerat, who had invented a process for distilling vinegar and had a large chemical works near Dijon, one of his uncle's friends, the chemist Michel Perret. Both men spent a lot of time with the young Eiffel, teaching him about everything from chemistry and mining to theology and philosophy.
Eiffel went on to attend the Collège Sainte-Barbe in Paris, to prepare for the difficult entrance exams set by engineering colleges in France, qualified for entry to two of the most prestigious schools – École polytechnique and École Centrale des Arts et Manufactures – and entered the latter. During his second year he chose to specialize in chemistry, graduated ranking at 13th place out of 80 candidates in 1855; this is what is thought to be one of the things that led young Eiffel into his career of engineering. This was the year that Paris hosted the second World's Fair, Eiffel was bought a season ticket by his mother. After graduation, Eiffel had hoped to find work in his uncle's workshop in Dijon, but a family dispute made this impossible. After a few months working as an unpaid assistant to his brother-in-law, who managed a foundry, Eiffel approached the railway engineer Charles Nepveu, who gave Eiffel his first paid job as his private secretary. However, shortly afterwards Nepveu's company went bankrupt, but Nepveu found Eiffel a job designing a 22 m sheet iron bridge for the Saint Germaine railway.
Some of Nepveu's businesses were acquired by the Compagnie Belge de Matériels de Chemin de Fer: Nepveu was appointed the managing director of the two factories in Paris, offered Eiffel a job as head of the research department. In 1857 Nepveu negotiated a contract to build a railway bridge over the river Garonne at Bordeaux, connecting the Paris-Bordeaux line to the lines running to Sète and Bayonne, which involved the construction of a 500 m iron girder bridge supported by six pairs of masonry piers on the river bed; these were constructed with the aid of compressed air caissons and hydraulic rams, both innovative techniques at the time. Eiffel was given the responsibility of assembling the metalwork and took over the management of the entire project from Nepveu, who resigned in March 1860. Following the completion of the project on schedule Eiffel was appointed as the principal engineer of the Compagnie Belge, his work had gained the attention of several people who were to give him work, including Stanislas de la Roche Toulay, who had prepared the design for the metalwork of the Bordeaux bridge, Jean Baptiste Krantz and Wilhelm Nordling.
Further promotion within the company followed, but the business began to decline, in 1865 Eiffel, seeing no future there and set up as an independent consulting engineer. He was working independently on the construction of two railway stations, at Toulouse and Agen, in 1866 he was given a contract to oversee the construction of 33 locomotives for the Egyptian government, a profitable but undemanding job in the course of which he visited Egypt, where he visited the Suez Canal, being constructed by Ferdinand de Lesseps. At the same time he was employed by Jean-Baptiste Kranz to assist him in the design of the exhibition hall for the Exposition Universelle, to be held in 1867. Eiffel's principal job was to draw up the arch girders of the Galerie des Machines. In order to carry out this work and Henri Treca, the director of the Conservatoire des Arts et Metiers, conducted valuable research on the structural properties of cast iron, definitively establishing the modulus of elasticity applicable to compound castings.
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France the French Republic, is a country whose territory consists of metropolitan France in Western Europe and several overseas regions and territories. The metropolitan area of France extends from the Mediterranean Sea to the English Channel and the North Sea, from the Rhine to the Atlantic Ocean, it is bordered by Belgium and Germany to the northeast and Italy to the east, Andorra and Spain to the south. The overseas territories include French Guiana in South America and several islands in the Atlantic and Indian oceans; the country's 18 integral regions span a combined area of 643,801 square kilometres and a total population of 67.3 million. France, a sovereign state, is a unitary semi-presidential republic with its capital in Paris, the country's largest city and main cultural and commercial centre. Other major urban areas include Lyon, Toulouse, Bordeaux and Nice. During the Iron Age, what is now metropolitan France was inhabited by a Celtic people. Rome annexed the area in 51 BC, holding it until the arrival of Germanic Franks in 476, who formed the Kingdom of Francia.
The Treaty of Verdun of 843 partitioned Francia into Middle Francia and West Francia. West Francia which became the Kingdom of France in 987 emerged as a major European power in the Late Middle Ages following its victory in the Hundred Years' War. During the Renaissance, French culture flourished and a global colonial empire was established, which by the 20th century would become the second largest in the world; the 16th century was dominated by religious civil wars between Protestants. France became Europe's dominant cultural and military power in the 17th century under Louis XIV. In the late 18th century, the French Revolution overthrew the absolute monarchy, established one of modern history's earliest republics, saw the drafting of the Declaration of the Rights of Man and of the Citizen, which expresses the nation's ideals to this day. In the 19th century, Napoleon established the First French Empire, his subsequent Napoleonic Wars shaped the course of continental Europe. Following the collapse of the Empire, France endured a tumultuous succession of governments culminating with the establishment of the French Third Republic in 1870.
France was a major participant in World War I, from which it emerged victorious, was one of the Allies in World War II, but came under occupation by the Axis powers in 1940. Following liberation in 1944, a Fourth Republic was established and dissolved in the course of the Algerian War; the Fifth Republic, led by Charles de Gaulle, remains today. Algeria and nearly all the other colonies became independent in the 1960s and retained close economic and military connections with France. France has long been a global centre of art and philosophy, it hosts the world's fourth-largest number of UNESCO World Heritage Sites and is the leading tourist destination, receiving around 83 million foreign visitors annually. France is a developed country with the world's sixth-largest economy by nominal GDP, tenth-largest by purchasing power parity. In terms of aggregate household wealth, it ranks fourth in the world. France performs well in international rankings of education, health care, life expectancy, human development.
France is considered a great power in global affairs, being one of the five permanent members of the United Nations Security Council with the power to veto and an official nuclear-weapon state. It is a leading member state of the European Union and the Eurozone, a member of the Group of 7, North Atlantic Treaty Organization, Organisation for Economic Co-operation and Development, the World Trade Organization, La Francophonie. Applied to the whole Frankish Empire, the name "France" comes from the Latin "Francia", or "country of the Franks". Modern France is still named today "Francia" in Italian and Spanish, "Frankreich" in German and "Frankrijk" in Dutch, all of which have more or less the same historical meaning. There are various theories as to the origin of the name Frank. Following the precedents of Edward Gibbon and Jacob Grimm, the name of the Franks has been linked with the word frank in English, it has been suggested that the meaning of "free" was adopted because, after the conquest of Gaul, only Franks were free of taxation.
Another theory is that it is derived from the Proto-Germanic word frankon, which translates as javelin or lance as the throwing axe of the Franks was known as a francisca. However, it has been determined that these weapons were named because of their use by the Franks, not the other way around; the oldest traces of human life in what is now France date from 1.8 million years ago. Over the ensuing millennia, Humans were confronted by a harsh and variable climate, marked by several glacial eras. Early hominids led a nomadic hunter-gatherer life. France has a large number of decorated caves from the upper Palaeolithic era, including one of the most famous and best preserved, Lascaux. At the end of the last glacial period, the climate became milder. After strong demographic and agricultural development between the 4th and 3rd millennia, metallurgy appeared at the end of the 3rd millennium working gold and bronze, iron. France has numerous megalithic sites from the Neolithic period, including the exceptiona
Gabriel Lamé was a French mathematician who contributed to the theory of partial differential equations by the use of curvilinear coordinates, the mathematical theory of elasticity. Lamé was born in today's département of Indre-et-Loire, he became well known for his general theory of curvilinear coordinates and his notation and study of classes of ellipse-like curves, now known as Lamé curves or superellipses, defined by the equation: | x a | n + | y b | n = 1 where n is any positive real number. He is known for his running time analysis of the Euclidean algorithm, marking the beginning of computational complexity theory. Using Fibonacci numbers, he proved that when finding the greatest common divisor of integers a and b, the algorithm runs in no more than 5k steps, where k is the number of digits of b, he proved a special case of Fermat's last theorem. He thought that he found a complete proof for the theorem, but his proof was flawed; the Lamé functions are part of the theory of ellipsoidal harmonics.
He worked on a wide variety of different topics. Problems in the engineering tasks he undertook led him to study mathematical questions. For example his work on the stability of vaults and on the design of suspension bridges led him to work on elasticity theory. In fact this was not a passing interest, for Lamé made substantial contributions to this topic. Another example is his work on the conduction of heat which led him to his theory of curvilinear coordinates. Curvilinear coordinates proved a powerful tool in Lamé's hands, he used them to transform Laplace's equation into ellipsoidal coordinates and so separate the variables and solve the resulting equation. His most significant contribution to engineering was to define the stresses and capabilities of a press fit joint, such as that seen in a dowel pin in a housing. In 1854, he was elected a foreign member of the Royal Swedish Academy of Sciences. Lamé died in Paris in 1870, his name is one of the 72 names inscribed on the Eiffel Tower. 1818: Examen des différentes méthodes employées pour résoudre les problèmes de géométrie 1840: Cours de physique de l'Ecole Polytechnique.
Tome premier, Propriétés générales des corps—Théorie physique de la chaleur 1840: Cours de physique de l'Ecole Polytechnique. Tome deuxième, Acoustique—Théorie physique de la lumière 1840: Cours de physique de l'Ecole Polytechnique. Tome troisième, Electricité-Magnétisme-Courants électriques-Radiations 1852: Leçons sur la théorie mathématique de l'élasticité des corps solides 1857: Leçons sur les fonctions inverses des transcendantes et les surfaces isothermes 1859: Leçons sur les coordonnées curvilignes et leurs diverses applications 1861: Leçons sur la théorie analytique de la chaleur Lamé crater Piet Hein Lamé's special quartic Julius Plücker Stefan problem Super ellipse Lamé parameters Superellipse Lamé's Oval / Superellipse O'Connor, John J..
The Trocadéro, site of the Palais de Chaillot, is an area of Paris, France, in the 16th arrondissement, across the Seine from the Eiffel Tower. It is the name of the 1878 palace, demolished in 1937 to make way for the Palais de Chaillot; the hill of the Trocadéro is the hill of a former village. The place was named in honour of the Battle of Trocadero, in which the fortified Isla del Trocadero, in southern Spain, was captured by French forces led by the Duc d'Angoulême, son of the future King of France, Charles X, on August 31, 1823. France had intervened on behalf of King Ferdinand VII of Spain, whose rule was contested by a liberal rebellion. After the battle, the autocratic Spanish Bourbon Ferdinand VII was restored to the throne of Spain. François-René de Chateaubriand said "To stride across the lands of Spain at one go, to succeed there, where Bonaparte had failed, to triumph on that same soil where the arms of the fantastic man suffered reverses, to do in six months what he couldn't do in seven years, prodigious!"Nowadays the square is named Place du Trocadéro et du 11 Novembre, although it is simply called the Place du Trocadéro.
The hill of Chaillot was first arranged for the 1867 World's Fair. For the 1878 World's Fair, the Palais du Trocadéro was built here; the palace's form was that of a large concert hall with two towers. The architect was Gabriel Davioud; the concert hall contained a large organ built by Aristide Cavaillé-Coll. The organ was inaugurated during the 1878 World Fair with a concert in which Charles Marie Widor played the premiere of his Symphony for Organ No. 6. The building proved unpopular, but the cost expended in its construction delayed its replacement for nearly fifty years. Below the building in the space left by former underground quarries, a large aquarium was built to contain fish of French rivers, it was renovated in 1937 but closed again for renovation from 1985 until May 22, 2006. The space between the palais and the Seine is set with gardens, designed by Jean-Charles Alphand, an array of fountains. Within its garden, the old palace contained two large animal statues, of a rhinoceros and an elephant, which were removed and stored during the demolition of the old Trocadero palace, have been located next to the entrance of the Musée d'Orsay since 1986.
For the Exposition Internationale of 1937, the old Palais du Trocadéro was demolished and rebuilt as the Palais de Chaillot which now tops the hill. It was designed in classicizing "moderne" style by architects Louis-Hippolyte Boileau, Jacques Carlu and Léon Azéma. Like the old palais, the Palais de Chaillot features two wings shaped to form a wide arc. However, unlike the old palais, the wings are independent buildings and there is no central element to connect them: instead, a wide esplanade leaves an open view from the place du Trocadéro to the Eiffel Tower and beyond; the buildings are decorated with quotations by Paul Valéry, sculptural groups at the attic level by Raymond Delamarre, Carlo Sarrabezolles and Alfred Bottiau. The eight gilded figures on the terrace of the Rights of Man are attributed to the sculptors Alexandre Descatoire, Marcel Gimond, Jean Paris dit Pryas, Paul Cornet, Lucien Brasseur, Robert Couturier, Paul Niclausse, Félix-Alexandre Desruelles; the buildings now house a number of museums: the Musée national de la Marine and the Musée de l'Homme in the southern wing.
The Cité de l'Architecture et du Patrimoine, including the Musée national des Monuments Français, in the eastern wing, from which one enters the Théâtre national de Chaillot, a theater below the esplanade. It was on the front terrace of the palace that Adolf Hitler was pictured during his short tour of the city in 1940, with the Eiffel Tower in the background; this became an iconic image of the Second World War. It is in the Palais de Chaillot that the United Nations General Assembly adopted the Universal Declaration of Human Rights on December 10, 1948; this event is now commemorated by a stone, the esplanade is known as the esplanade des droits de l'homme. The Palais de Chaillot was the initial headquarters of NATO, while the "Palais de l'OTAN" was being built; the Jardins du Trocadéro occupy the open space bounded to the northwest by the wings of the Palais de Chaillot and to the southeast by the Seine and the Pont d'Iéna. The present garden has an area of 93,930 square metres and was created for the Exposition Internationale des Arts et Techniques dans la Vie Moderne, on the design of architect Roger-Henri Expert.
The entire site was the garden of the old Palais du Trocadéro, laid out by Jean-Charles Alphand. Five avenues originate in the Trocadéro: the Avenue Henri-Martin, which links the Trocadéro with the Porte de la Muette and passes in front of the Lycée Janson de Sailly. There is a large municipal
Gaspard de Prony
Baron Gaspard Clair François Marie Riche de Prony was a French mathematician and engineer, who worked on hydraulics. He was born at Chamelet, Beaujolais and died in Asnières-sur-Seine, France, he was Engineer-in-Chief of the École Nationale des Ponts et Chaussées. In 1791, de Prony embarked on the task of producing logarithmic and trigonometric tables for the French Cadastre; the effort was sanctioned by the French National Assembly, after the French Revolution wanted to bring uniformity to the multiple measurements and standards used throughout the nation. In particular, his tables were intended for precise land surveys, as part of a greater cadastre effort; the tables were vast, with values calculated to between twenty-nine decimal places. Inspired by Adam Smith's Wealth of Nations, de Prony divided up the labor into three levels, bragging that he "could manufacture logarithms as as one manufactures pins."The first level consisted of five or six high-ranking mathematicians with sophisticated analytical skills, including Adrien-Marie Legendre and Lazare Carnot.
This group chose the analytical formulas most suited to evaluation by numerical methods, specified the number of decimals and the numerical range the tables were to cover. The second group of lesser mathematicians, seven or eight in number, combined analytical and computational skills, this group calculated the pivotal values using the formulas provided and the sets of starting differences, they prepared templates for the human computers, the first worked row of calculations, as well as the instructions for the computers to carry the sequence to completion. The third group consisted of sixty to eighty human computers; these had no more than a rudimentary knowledge of arithmetic and carried out the most laborious and repetitive part of the process. Many were out-of-work hairdressers, with the guillotining of the aristocracy, the hairdressing trade, which had tended the elaborate hairstyles of the elite, was in recession. At the bottom were about ninety "computers" who were not trained in mathematics, but who followed the instructions."Due to a lack of funding from inflation following the French revolution, the tables were never published in full.
The first excerpt of the table was published a century later. According to Prony, the project was to leave "nothing to desire with respect to exactitude" and to be "the most vast... monument to calculation executed or conceived." The tables were not used for their original purpose of bringing consistent standards for measurement, as the entire cadastre project saw delays in establishing both new measurement units as well as budget cuts. In particular, these tables, which were designed for the decimal division of circles and time, turned out to be obsolete after the French had changed their measurement system. Moreover, there was no practical use for the full extent of de Prony's calculation's accuracy. Hence, these tables became more of artifacts and monuments to Enlightenment rather than objects of practical use. By the turn of the 19th century, there was a shift in the meaning of calculation; the talented mathematicians and other intellectuals who produced creative and abstract ideas were regarded separately from those who were able to perform tedious and repetitive computations.
Before the 19th century, calculation was regarded as a task for the academics, while afterwards, calculations were associated with unskilled laborers. This was accompanied by a shift in gender roles as well, as women, who were underrepresented in mathematics at the time, were hired to perform extensive computations for the tables as well as other computational government projects until the end of World War II; this shift in the interpretation of calculation was due to de Prony's calculation project during the French Revolution. This project was able to unite people from many different walks of life as well as mathematical abilities and hence changed the meaning of calculation from intelligence into unskilled labor. Prony was able to have artisans work along with mathematicians to perform the calculations. Prony noted a few interesting observations about this new dynamic. First, it was fascinating to see. Second, he realized that the ones with the least intellectual ability were able to perform these computations with astonishingly few errors.
Prony saw this entire system as a collection of human computers working together as a whole - a machine governed by hierarchical principles of the division of labor. In fact, Prony may have begun to amend his notion of intelligence, which he began to use to evaluate the system as a whole, rather than evaluating the intelligence of its constituents. Charles Babbage, credited with inventing the first mechanical computer, referred in detail to de Prony's project and was seized by the idea that the labours of the unskilled computers could be taken over by machinery. One of de Prony's important scientific inventions was the "brake" which he invented in 1821 to measure the performance of machines and engines, he was first to propose using a reversible pendulum to measure gravity, independently invented in 1817 by Henry Kater and became known as the Kater's pendulum. He created a method of converting sinusoidal and exponential curves into a systems of linear equations. Prony estimation is used extensively in signal processing and finite element modelling of non linear materials.
Prony was a member, president, of the French Academy of Science. He was elected a foreign member of the Royal Swedish Academy of Sciences in 1810, his name is one of