Geometry is a branch of mathematics concerned with questions of shape, relative position of figures, the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a practical way for dealing with lengths and volumes. Geometry began to see elements of formal mathematical science emerging in the West as early as the 6th century BC. By the 3rd century BC, geometry was put into an axiomatic form by Euclid, whose treatment, Euclid's Elements, set a standard for many centuries to follow. Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC. Islamic scientists expanded on them during the Middle Ages. By the early 17th century, geometry had been put on a solid analytic footing by mathematicians such as René Descartes and Pierre de Fermat. Since and into modern times, geometry has expanded into non-Euclidean geometry and manifolds, describing spaces that lie beyond the normal range of human experience.
While geometry has evolved throughout the years, there are some general concepts that are more or less fundamental to geometry. These include the concepts of points, planes, surfaces and curves, as well as the more advanced notions of manifolds and topology or metric. Geometry has applications to many fields, including art, physics, as well as to other branches of mathematics. Contemporary geometry has many subfields: Euclidean geometry is geometry in its classical sense; the mandatory educational curriculum of the majority of nations includes the study of points, planes, triangles, similarity, solid figures and analytic geometry. Euclidean geometry has applications in computer science and various branches of modern mathematics. Differential geometry uses techniques of linear algebra to study problems in geometry, it has applications in physics, including in general relativity. Topology is the field concerned with the properties of geometric objects that are unchanged by continuous mappings. In practice, this means dealing with large-scale properties of spaces, such as connectedness and compactness.
Convex geometry investigates convex shapes in the Euclidean space and its more abstract analogues using techniques of real analysis. It has close connections to convex analysis and functional analysis and important applications in number theory. Algebraic geometry studies geometry through the use of multivariate polynomials and other algebraic techniques, it has applications including cryptography and string theory. Discrete geometry is concerned with questions of relative position of simple geometric objects, such as points and circles, it shares many principles with combinatorics. Computational geometry deals with algorithms and their implementations for manipulating geometrical objects. Although being a young area of geometry, it has many applications in computer vision, image processing, computer-aided design, medical imaging, etc; the earliest recorded beginnings of geometry can be traced to ancient Mesopotamia and Egypt in the 2nd millennium BC. Early geometry was a collection of empirically discovered principles concerning lengths, angles and volumes, which were developed to meet some practical need in surveying, construction and various crafts.
The earliest known texts on geometry are the Egyptian Rhind Papyrus and Moscow Papyrus, the Babylonian clay tablets such as Plimpton 322. For example, the Moscow Papyrus gives a formula for calculating the volume of a truncated pyramid, or frustum. Clay tablets demonstrate that Babylonian astronomers implemented trapezoid procedures for computing Jupiter's position and motion within time-velocity space; these geometric procedures anticipated the Oxford Calculators, including the mean speed theorem, by 14 centuries. South of Egypt the ancient Nubians established a system of geometry including early versions of sun clocks. In the 7th century BC, the Greek mathematician Thales of Miletus used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore, he is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. Pythagoras established the Pythagorean School, credited with the first proof of the Pythagorean theorem, though the statement of the theorem has a long history.
Eudoxus developed the method of exhaustion, which allowed the calculation of areas and volumes of curvilinear figures, as well as a theory of ratios that avoided the problem of incommensurable magnitudes, which enabled subsequent geometers to make significant advances. Around 300 BC, geometry was revolutionized by Euclid, whose Elements considered the most successful and influential textbook of all time, introduced mathematical rigor through the axiomatic method and is the earliest example of the format still used in mathematics today, that of definition, axiom and proof. Although most of the contents of the Elements were known, Euclid arranged them into a single, coherent logical framework; the Elements was known to all educated people in the West until the middle of the 20th century and its contents are still taught in geometry classes today. Archimedes of Syracuse used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, gave remarkably accurate approximations of Pi.
He studied the sp
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
Mechanics is that area of science concerned with the behaviour of physical bodies when subjected to forces or displacements, the subsequent effects of the bodies on their environment. The scientific discipline has its origins in Ancient Greece with the writings of Aristotle and Archimedes. During the early modern period, scientists such as Galileo and Newton laid the foundation for what is now known as classical mechanics, it is a branch of classical physics that deals with particles that are either at rest or are moving with velocities less than the speed of light. It can be defined as a branch of science which deals with the motion of and forces on objects; the field is yet less understood in terms of quantum theory. Classical mechanics came first and quantum mechanics is a comparatively recent development. Classical mechanics originated with Isaac Newton's laws of motion in Philosophiæ Naturalis Principia Mathematica. Both are held to constitute the most certain knowledge that exists about physical nature.
Classical mechanics has often been viewed as a model for other so-called exact sciences. Essential in this respect is the extensive use of mathematics in theories, as well as the decisive role played by experiment in generating and testing them. Quantum mechanics is of a bigger scope, as it encompasses classical mechanics as a sub-discipline which applies under certain restricted circumstances. According to the correspondence principle, there is no contradiction or conflict between the two subjects, each pertains to specific situations; the correspondence principle states that the behavior of systems described by quantum theories reproduces classical physics in the limit of large quantum numbers. Quantum mechanics has superseded classical mechanics at the foundation level and is indispensable for the explanation and prediction of processes at the molecular and sub-atomic level. However, for macroscopic processes classical mechanics is able to solve problems which are unmanageably difficult in quantum mechanics and hence remains useful and well used.
Modern descriptions of such behavior begin with a careful definition of such quantities as displacement, velocity, acceleration and force. Until about 400 years ago, motion was explained from a different point of view. For example, following the ideas of Greek philosopher and scientist Aristotle, scientists reasoned that a cannonball falls down because its natural position is in the Earth. Cited as father to modern science, Galileo brought together the ideas of other great thinkers of his time and began to calculate motion in terms of distance traveled from some starting position and the time that it took, he showed that the speed of falling objects increases during the time of their fall. This acceleration is the same for heavy objects as for light ones, provided air friction is discounted; the English mathematician and physicist Isaac Newton improved this analysis by defining force and mass and relating these to acceleration. For objects traveling at speeds close to the speed of light, Newton's laws were superseded by Albert Einstein’s theory of relativity.
For atomic and subatomic particles, Newton's laws were superseded by quantum theory. For everyday phenomena, Newton's three laws of motion remain the cornerstone of dynamics, the study of what causes motion. In analogy to the distinction between quantum and classical mechanics, Einstein's general and special theories of relativity have expanded the scope of Newton and Galileo's formulation of mechanics; the differences between relativistic and Newtonian mechanics become significant and dominant as the velocity of a massive body approaches the speed of light. For instance, in Newtonian mechanics, Newton's laws of motion specify that F = ma, whereas in relativistic mechanics and Lorentz transformations, which were first discovered by Hendrik Lorentz, F = γma. Relativistic corrections are needed for quantum mechanics, although general relativity has not been integrated; the two theories remain incompatible, a hurdle which must be overcome in developing a theory of everything. The main theory of mechanics in antiquity was Aristotelian mechanics.
A developer in this tradition is Hipparchus. In the Middle Ages, Aristotle's theories were criticized and modified by a number of figures, beginning with John Philoponus in the 6th century. A central problem was that of projectile motion, discussed by Hipparchus and Philoponus. Persian Islamic polymath Ibn Sīnā published his theory of motion in The Book of Healing, he said that an impetus is imparted to a projectile by the thrower, viewed it as persistent, requiring external forces such as air resistance to dissipate it. Ibn Sina made distinction between'force' and'inclination', argued that an object gained mayl when the object is in opposition to its natural motion. So he concluded that continuation of motion is attributed to the inclination, transferred to the object, that object will be in motion until the mayl is spent, he claimed that projectile in a vacuum would not stop unless it is acted upon. This conception of motion is consistent with Newton's first law of inertia. Which states that an object in motion will stay in mo
History of steam road vehicles
The history of steam road vehicles comprises the development of vehicles powered by a steam engine for use on land and independent of rails, whether for conventional road use, such as the steam car and steam waggon, or for agricultural or heavy haulage work, such as the traction engine. The first experimental vehicles were built in the 17th and 18th century, but it was not until after Richard Trevithick had developed the use of high-pressure steam, around 1800, that mobile steam engines became a practical proposition; the first half of the 19th century saw great progress in steam vehicle design, by the 1850s it was viable to produce them on a commercial basis. This progress was dampened by legislation which limited or prohibited the use of steam powered vehicles on roads; the 1880s to the 1920s saw continuing improvements in vehicle technology and manufacturing techniques, steam road vehicles were developed for many applications. In the 20th century, the rapid development of internal combustion engine technology led to the demise of the steam engine as a source of propulsion of vehicles on a commercial basis, with few remaining in use beyond the Second World War.
Many of these vehicles were acquired by enthusiasts for preservation, numerous examples are still in existence. In the 1960s the air pollution problems in California gave rise to a brief period of interest in developing and studying steam powered vehicles as a possible means of reducing the pollution. Apart from interest by steam enthusiasts, the occasional replica vehicle, experimental technology no steam vehicles are in production at present. Early research on the steam engine before 1700 was linked to the quest for self-propelled vehicles and ships; the size reduction necessary for road transport meant an increase in steam pressure with all the attendant dangers, due to the inadequate boiler technology of the period. A strong opponent of high pressure steam was James Watt who, along with Matthew Boulton did all he could to dissuade William Murdoch from developing and patenting his steam carriage, built in model form in 1784. Ferdinand Verbiest is suggested to have built what may have been the first steam powered car in about 1672, but little concrete information on this is known to exist.
During the latter part of the 18th century, there were numerous attempts to produce self-propelled steerable vehicles. Many remained in the form of models. Progress was dogged by many problems inherent to road vehicles in general, such as suitable power-plant giving steady rotative motion, braking, adequate road surfaces and vibration-resistant bodywork, among other issues; the extreme complexity of these issues can be said to have hampered progress over more than a hundred years, as much as hostile legislation. Nicolas-Joseph Cugnot's "machine à feu pour le transport de wagons et surtout de l'artillerie" was built from 1769 in two versions for use by the French Army; this was the first steam wagon, not a toy, and, known to exist. Cugnot's fardier, a term applied to a massive two-wheeled cart for exceptionally heavy loads, was intended to be capable of transporting 4 tonnes, of travelling at up to 4 km/h; the vehicle was of tricycle layout, with two rear wheels and a steerable front wheel controlled by a tiller.
There is considerable evidence, from the period, that this vehicle ran, making it the first to do so. In 1801, Richard Trevithick constructed an experimental steam-driven vehicle, equipped with a firebox enclosed within the boiler, with one vertical cylinder, the motion of the single piston being transmitted directly to the driving wheels by means of connecting rods, it was reported as weighing 1520 kg loaded, with a speed of 14.5 km/h on the flat. During its first trip it was left unattended and "self-destructed". Trevithick soon built the London Steam Carriage that ran in London in 1803, but the venture failed to attract interest and soon folded up. In the context of Trevithick's vehicle, an English writer by the name of "Mickleham" in 1822 coined the term Steam Engine: "It exhibits in construction the most beautiful simplicity of parts, the most sagacious selection of appropriate forms, the most convenient and effective arrangement and connexion. In 1805 Oliver Evans built the "Oruktor Amphibolos", a steam-powered, flat-bottomed dredger that he modified to be self-propelled on both land and water.
It is believed to be the first amphibious vehicle, the first steam-powered road vehicle to run in the United States. However, no designs for the machine survive, the only accounts of its achievements come from Evans himself. Analysis of Evans's descriptions suggests that the 5hp engine was unlikely to have been powerful enough to move the vehicle either on land or water, that the chosen route for its demonstration would have had the benefit of gravity, river currents and tides to assist with the vehicles' progress; the dredger was not a success, after a few years lying idle, was dismantled for parts. More commercially successful for a time than Trevithick's carriage were the steam carriage services operated
A car is a wheeled motor vehicle used for transportation. Most definitions of car say they run on roads, seat one to eight people, have four tires, transport people rather than goods. Cars came into global use during the 20th century, developed economies depend on them; the year 1886 is regarded as the birth year of the modern car when German inventor Karl Benz patented his Benz Patent-Motorwagen. Cars became available in the early 20th century. One of the first cars accessible to the masses was the 1908 Model T, an American car manufactured by the Ford Motor Company. Cars were adopted in the US, where they replaced animal-drawn carriages and carts, but took much longer to be accepted in Western Europe and other parts of the world. Cars have controls for driving, passenger comfort, safety, controlling a variety of lights. Over the decades, additional features and controls have been added to vehicles, making them progressively more complex; these include rear reversing cameras, air conditioning, navigation systems, in-car entertainment.
Most cars in use in the 2010s are propelled by an internal combustion engine, fueled by the combustion of fossil fuels. Electric cars, which were invented early in the history of the car, began to become commercially available in 2008. There are benefits to car use; the costs include acquiring the vehicle, interest payments and maintenance, depreciation, driving time, parking fees and insurance. The costs to society include maintaining roads, land use, road congestion, air pollution, public health, health care, disposing of the vehicle at the end of its life. Road traffic accidents are the largest cause of injury-related deaths worldwide; the benefits include on-demand transportation, mobility and convenience. The societal benefits include economic benefits, such as job and wealth creation from the automotive industry, transportation provision, societal well-being from leisure and travel opportunities, revenue generation from the taxes. People's ability to move flexibly from place to place has far-reaching implications for the nature of societies.
There are around 1 billion cars in use worldwide. The numbers are increasing especially in China and other newly industrialized countries; the word car is believed to originate from the Latin word carrus or carrum, or the Middle English word carre. In turn, these originated from the Gaulish word karros, it referred to any wheeled horse-drawn vehicle, such as a cart, carriage, or wagon. "Motor car" is attested from 1895, is the usual formal name for cars in British English. "Autocar" is a variant, attested from 1895, but, now considered archaic. It means "self-propelled car"; the term "horseless carriage" was used by some to refer to the first cars at the time that they were being built, is attested from 1895. The word "automobile" is a classical compound derived from the Ancient Greek word autós, meaning "self", the Latin word mobilis, meaning "movable", it entered the English language from French, was first adopted by the Automobile Club of Great Britain in 1897. Over time, the word "automobile" fell out of favour in Britain, was replaced by "motor car".
"Automobile" remains chiefly North American as a formal or commercial term. An abbreviated form, "auto", was a common way to refer to cars in English, but is now considered old-fashioned; the word is still common as an adjective in American English in compound formations like "auto industry" and "auto mechanic". In Dutch and German, two languages related to English, the abbreviated form "auto" / "Auto", as well as the formal full version "automobiel" / "Automobil" are still used — in either the short form is the most regular word for "car"; the first working steam-powered vehicle was designed — and quite built — by Ferdinand Verbiest, a Flemish member of a Jesuit mission in China around 1672. It was a 65-cm-long scale-model toy for the Chinese Emperor, unable to carry a driver or a passenger, it is not known with certainty if Verbiest's model was built or run. Nicolas-Joseph Cugnot is credited with building the first full-scale, self-propelled mechanical vehicle or car in about 1769, he constructed two steam tractors for the French Army, one of, preserved in the French National Conservatory of Arts and Crafts.
His inventions were, handicapped by problems with water supply and maintaining steam pressure. In 1801, Richard Trevithick built and demonstrated his Puffing Devil road locomotive, believed by many to be the first demonstration of a steam-powered road vehicle, it was unable to maintain sufficient steam pressure for long periods and was of little practical use. The development of external combustion engines is detailed as part of the history of the car but treated separately from the development of true cars. A variety of steam-powered road vehicles were used during the first part of the 19th century, including steam cars, steam buses and steam rollers. Sentiment against them led to the Locomotive Acts of 1865. In 1807, Nicéphore Niépce and his brother Claude created what was the world's first internal combustion engine, but they chose to install it in a boat on the river Saone in France. Coincidentally, in 1807 the Swiss inventor François Isaac de Rivaz designed his own'de Rivaz internal combustion engine' and used it to develop the world's first vehicle to be powered by such an engine.
Moûtiers also called Tarentaise, is a commune in the Savoie department in the Auvergne-Rhône-Alpes region in south-eastern France. It is the access point to the Les Trois Vallées ski area and its railway station, although not on a high-speed rail line, is a seasonally important destination for TGV trains from Lyon and elsewhere. Moûtiers is located deep in the Tarentaise Valley, it is its geographic capital, between Bourg-Saint-Maurice. Several popular French ski resorts are located in its vicinity; the Isère flows through the town. Moûtiers was the capital of a Celtic tribe of Gaul, its antique name, appears on a surviving ancient Roman road map known as the Tabula Peutingeriana. In a medieval text dating from 996, Moûtiers was called Monasterium from which its names, Moustiers and Moûtiers, were derived. Moûtiers was the episcopal; the archdiocese was disbanded in 1801, re-established as the Diocese of Tarentaise. This diocese was united with the diocese of Chambéry and diocese of St-Jean-de-Maurienne to form the diocese of Chambéry, Maurienne and Tarentaise.
Today, the town has a small historic center with narrow streets surrounding Saint-Pierre cathedral. It hosted the TV display for the 1992 Winter Olympics. Saint-Pierre cathedral Grand Rue INSEE This article incorporates text from a publication now in the public domain: Herbermann, Charles, ed.. "article name needed". Catholic Encyclopedia. New York: Robert Appleton. Moûtiers on the Quid site Nearest town from Moûtiers Location of Moûtiers on a map of France Mention of Darantasia in the Tabula Peutingeriana
A notary is a person licensed by the government to perform acts in legal affairs, in particular witnessing signatures on documents. The form that the notarial profession takes varies with local legal systems. Most common law systems have what is called in the United States a notary public, a public official who notarizes legal documents and who can administer and take oaths and affirmations, among other tasks. In the United States, a signing agent known as a loan signing agent, is a notary public who specializes in notarizing mortgage and real estate documents. Although notary publics are public officials, they are not paid by the government. Documents are notarized to ensure they are properly executed. An impartial witness identifies signers to screen out impostors and to make sure they have entered into agreements knowingly and willingly. Loan documents including deeds, contracts, powers of attorney are common documents needing notarization. In the US, any person – lawyer or otherwise – may be commissioned as a notary.
Most civil law-based systems have the civil law notary, a legal professional working in civil law performing many more functions. The Worshipful Company of Scriveners use an old English term for a notary, are an association of notaries practising in central London since 1373. To "notarize" a document or event is not a term of art, its definition varies from place to place. Examples are: certificates authenticating copies and certificates as to law, such as certificates as to the capacity of a company to perform certain acts, or explaining probate law in the place. However, in civil-law jurisdictions, notaries are qualified lawyers who provide many of the same services as common-law attorneys/solicitors except any involvement in disputes to be presented before a court. Notaries are specialized in all matters relating to real estate, for example, completing title exams in order to confirm the ownership of the property, the existence of any encumbrances such as easements or mortgages. In the United States, the states of Virginia and Nevada have all passed laws allowing for online witness by notaries, using screen sharing or webcam as well as identity verification processes.
Virginia was the first state to pass legislation allowing online notarization in 2012. Texas and Nevada passed similar laws in 2017 that went into effect in July, 2018; some sites and apps include Notarize, DocVerify, NotaryCam, SIGNiX. Notarize is the first company to offer online mortgage closings, executing the first in August 2017 with United Wholesale Mortgage and Stewart Title. In the United States as of 2017 there are estimated to be over 4 million notaries employed. Civil law notary Notary public Certified copy The dictionary definition of notary at Wiktionary Media related to Notaries at Wikimedia Commons