Washington, D. C. formally the District of Columbia and referred to as Washington or D. C. is the capital of the United States. Founded after the American Revolution as the seat of government of the newly independent country, Washington was named after George Washington, first President of the United States and Founding Father; as the seat of the United States federal government and several international organizations, Washington is an important world political capital. The city is one of the most visited cities in the world, with more than 20 million tourists annually; the signing of the Residence Act on July 16, 1790, approved the creation of a capital district located along the Potomac River on the country's East Coast. The U. S. Constitution provided for a federal district under the exclusive jurisdiction of the U. S. Congress, the District is therefore not a part of any state; the states of Maryland and Virginia each donated land to form the federal district, which included the pre-existing settlements of Georgetown and Alexandria.
The City of Washington was founded in 1791 to serve as the new national capital. In 1846, Congress returned the land ceded by Virginia. Washington had an estimated population of 702,455 as of July 2018, making it the 20th most populous city in the United States. Commuters from the surrounding Maryland and Virginia suburbs raise the city's daytime population to more than one million during the workweek. Washington's metropolitan area, the country's sixth largest, had a 2017 estimated population of 6.2 million residents. All three branches of the U. S. federal government are centered in the District: Congress and the U. S. Supreme Court. Washington is home to many national monuments, museums situated on or around the National Mall; the city hosts 177 foreign embassies as well as the headquarters of many international organizations, trade unions, non-profit, lobbying groups, professional associations, including the World Bank Group, the International Monetary Fund, the Organization of American States, AARP, the National Geographic Society, the Human Rights Campaign, the International Finance Corporation, the American Red Cross.
A locally elected mayor and a 13‑member council have governed the District since 1973. However, Congress may overturn local laws. D. C. residents elect a non-voting, at-large congressional delegate to the House of Representatives, but the District has no representation in the Senate. The District receives three electoral votes in presidential elections as permitted by the Twenty-third Amendment to the United States Constitution, ratified in 1961. Various tribes of the Algonquian-speaking Piscataway people inhabited the lands around the Potomac River when Europeans first visited the area in the early 17th century. One group known as the Nacotchtank maintained settlements around the Anacostia River within the present-day District of Columbia. Conflicts with European colonists and neighboring tribes forced the relocation of the Piscataway people, some of whom established a new settlement in 1699 near Point of Rocks, Maryland. In his Federalist No. 43, published January 23, 1788, James Madison argued that the new federal government would need authority over a national capital to provide for its own maintenance and safety.
Five years earlier, a band of unpaid soldiers besieged Congress while its members were meeting in Philadelphia. Known as the Pennsylvania Mutiny of 1783, the event emphasized the need for the national government not to rely on any state for its own security. Article One, Section Eight, of the Constitution permits the establishment of a "District as may, by cession of particular states, the acceptance of Congress, become the seat of the government of the United States". However, the Constitution does not specify a location for the capital. In what is now known as the Compromise of 1790, Alexander Hamilton, Thomas Jefferson came to an agreement that the federal government would pay each state's remaining Revolutionary War debts in exchange for establishing the new national capital in the southern United States. On July 9, 1790, Congress passed the Residence Act, which approved the creation of a national capital on the Potomac River; the exact location was to be selected by President George Washington, who signed the bill into law on July 16.
Formed from land donated by the states of Maryland and Virginia, the initial shape of the federal district was a square measuring 10 miles on each side, totaling 100 square miles. Two pre-existing settlements were included in the territory: the port of Georgetown, founded in 1751, the city of Alexandria, founded in 1749. During 1791–92, Andrew Ellicott and several assistants, including a free African American astronomer named Benjamin Banneker, surveyed the borders of the federal district and placed boundary stones at every mile point. Many of the stones are still standing. A new federal city was constructed on the north bank of the Potomac, to the east of Georgetown. On September 9, 1791, the three commissioners overseeing the capital's construction named the city in honor of President Washington; the federal district was named Columbia, a poetic name for the United States in use at that time. Congress held its first session in Washington on November 17, 1800. Congress passed the District of Columbia Organic Act of 1801 that organized the District and placed the entire territory under the exclusive control of the federal
The L'Enfant Plan for the city of Washington is the urban plan developed in 1791 by Major Pierre Charles L'Enfant for George Washington, the first President of the United States. Major L'Enfant was a French engineer who served in the Continental Army during the American Revolutionary War. In 1789, discussions were underway regarding a new federal capital city for the United States, L'Enfant wrote to President Washington asking to be commissioned to plan the city. However, any decision on the capital was put on hold until July 1790 when Congress passed the Residence Act; the legislation specified that the new capital should be situated on the Potomac River, at some location between the Eastern Branch and the Conococheague Creek near Hagerstown, Maryland. The Residence Act gave authority to President Washington to appoint three commissioners to oversee the survey of the federal district and provide public buildings to accommodate the Federal government in 1800. In 1791, President Washington appointed L'Enfant to plan the new "Federal City", under the supervision of three commissioners whom Washington had earlier appointed to oversee the planning and development of the territory that became the "District of Columbia".
Included in the new district were the riverport towns of Georgetown and Alexandria, Virginia. Thomas Jefferson, serving as President Washington's Secretary of State, worked with Washington in the overall planning of the nation's capital. Jefferson sent L'Enfant a letter outlining his task, to provide a drawing of suitable sites for the federal city and the public buildings. Jefferson had modest ideas for the Capital. However, L'Enfant saw the task as far more grandiose, believing that he was devising the city plan and designing the buildings. L'Enfant began his work from Suter's Fountain Inn. Washington arrived on March 28 to meet with L'Enfant and the Commissioners for several days. On June 22, L'Enfant presented his first plan for the federal city to the President. On August 19, he appended a new map to a letter. President Washington retained a copy of one of L'Enfant's plans, showed it to the Congress, gave it to the three Commissioners. In November 1791, L'Enfant secured the lease of quarries at Wigginton Island and southeast along Aquia Creek to supply well-regarded "Aquia Creek sandstone" for the foundation of the "Congress House".
However, his temperament and his insistence that his city design be realized as a whole brought him into conflict with the Commissioners, who wanted to direct the limited funds into construction of the Federal buildings, they had Jefferson's support in the matter. L'Enfant's "Plan of the city intended for the permanent seat of the government of the United States..." encompassed an area bounded by the Potomac River, the Eastern Branch, the base of the escarpment of the Atlantic Seaboard Fall Line, Rock Creek. His plan specified locations for two buildings, the "Congress House" and the "President's House"; the "Congress House" would be built on "Jenkins Hill", which L'Enfant described as a "pedestal awaiting a monument". The "President's House" would be situated on a ridge parallel to the Potomac River north of the mouth of Tiber Creek, which L'Enfant proposed to canalize. L'Enfant envisioned the "President's House" to have monumental architecture. Reflecting his grandiose visions, he specified that the "President's House" would be five times the size of the building, constructed then becoming the largest residence constructed in America.
Emphasizing the importance of the new nation's legislature, the "Congress House" would be located on a longitude designated as 0:0. The plan specified. To form the grid, some streets would travel in an east–west direction, while others would travel in a north-south direction. Broader diagonal "grand avenues" named after the states of the Union, crossed the north/south-east/west grid; these "grand avenues" intersected with the north–south and east–west streets at circles and rectangular plazas that would honor notable Americans and provide open space. The plan identified some of the circles and rectangular plazas as numbered "reservations"; the plan's legends identified uses for other open spaces. Other legends specified the widths of grand streets. A prominent geometric feature of L'Enfant's plan was a large right triangle whose hypotenuse was a wide avenue connecting the "President's House"and the "Congress House". To complete the triangle, a line projecting due south from the center of the President's house intersected at a right angle a line projecting due west from the center of the Congress house.
A 400 feet -wide garden-lined "grand avenue" containing a "public walk" would travel for about 1 mile along the east–west line. L'Enfant chose the west end of this "grand avenue" to be the location of a future equestrian statue of George Washington for which the Continental Congress had voted in 1783. (Although the planned "grand avenue" became the portion of the National Mall, now between the Capitol's grounds and the Washington Monument, neither the avenue nor Washington's equestrian statue were constructed (see: National M
Painting is the practice of applying paint, color or other medium to a solid surface. The medium is applied to the base with a brush, but other implements, such as knives and airbrushes, can be used; the final work is called a painting. Painting is an important form in the visual arts, bringing in elements such as drawing, composition, narration, or abstraction. Paintings can be naturalistic and representational, abstract, symbolistic, emotive, or political in nature. A portion of the history of painting in both Eastern and Western art is dominated by religious art. Examples of this kind of painting range from artwork depicting mythological figures on pottery, to Biblical scenes Sistine Chapel ceiling, to scenes from the life of Buddha or other images of Eastern religious origin. In art, the term painting describes the result of the action; the support for paintings includes such surfaces as walls, canvas, glass, pottery, leaf and concrete, the painting may incorporate multiple other materials including sand, paper, gold leaf, as well as objects.
Color, made up of hue and value, dispersed over a surface is the essence of painting, just as pitch and rhythm are the essence of music. Color is subjective, but has observable psychological effects, although these can differ from one culture to the next. Black is associated with mourning in the West; some painters, theoreticians and scientists, including Goethe and Newton, have written their own color theory. Moreover, the use of language is only an abstraction for a color equivalent; the word "red", for example, can cover a wide range of variations from the pure red of the visible spectrum of light. There is not a formalized register of different colors in the way that there is agreement on different notes in music, such as F or C♯. For a painter, color is not divided into basic and derived colors. Painters deal with pigments, so "blue" for a painter can be any of the blues: phthalocyanine blue, Prussian blue, Cobalt blue, so on. Psychological and symbolical meanings of color are not speaking, means of painting.
Colors only add to the potential, derived context of meanings, because of this, the perception of a painting is subjective. The analogy with music is quite clear—sound in music is analogous to "light" in painting, "shades" to dynamics, "coloration" is to painting as the specific timbre of musical instruments is to music; these elements do not form a melody of themselves. Modern artists have extended the practice of painting to include, as one example, which began with Cubism and is not painting in the strict sense; some modern painters incorporate different materials such as sand, straw or wood for their texture. Examples of this are the works of Anselm Kiefer. There is a growing community of artists who use computers to "paint" color onto a digital "canvas" using programs such as Adobe Photoshop, Corel Painter, many others; these images can be printed onto traditional canvas. Jean Metzinger's mosaic-like Divisionist technique had its parallel in literature. I make a kind of chromatic versification and for syllables I use strokes which, variable in quantity, cannot differ in dimension without modifying the rhythm of a pictorial phraseology destined to translate the diverse emotions aroused by nature.
Rhythm, for artists such as Piet Mondrian, is important in painting as it is in music. If one defines rhythm as "a pause incorporated into a sequence" there can be rhythm in paintings; these pauses allow creative force to intervene and add new creations—form, coloration. The distribution of form, or any kind of information is of crucial importance in the given work of art, it directly affects the aesthetic value of that work; this is because the aesthetic value is functionality dependent, i.e. the freedom of perception is perceived as beauty. Free flow of energy, in art as well as in other forms of "techne", directly contributes to the aesthetic value. Music was important to the birth of abstract art, since music is abstract by nature—it does not try to represent the exterior world, but expresses in an immediate way the inner feelings of the soul. Wassily Kandinsky used musical terms to identify his works. Kandinsky theorized that "music is the ultimate teacher," and subsequently embarked upon the first seven of his ten Compositions.
Hearing tones and chords as he painted, Kandinsky theorized that, yellow is the color of middle C on a brassy trumpet. In 1871 the young Kandinsky learned to play the cello. Kandinsky's stage design for a performance of Mussorgsky's "Pictures at an Exhibition" illustrates his "synaesthetic" concept of a universal correspondence of forms and musical sounds. Music d
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
The Axe historique is a line of monuments and thoroughfares that extends from the centre of Paris, France, to the west. It is known as the Voie Triomphale; the Axe Historique began with the creation of the Champs Élysées, designed in the 17th century to create a vista to the west, extending the central axis of the gardens to the royal Palace of the Tuileries. Today the Tuileries Gardens remain, preserving their wide central pathway, though the palace was burned down during the Paris Commune, 1871. Between the Tuileries gardens and the Champs Élysées extension a jumble of buildings remained on the site of Place de la Concorde until early in the reign of Louis XV, for whom the square was at first named; the garden axis could open through a grand gateway into the new royal square. To the east, the Tuileries Palace faced the Place du Carrousel. There, by order of Napoleon, the Arc de Triomphe du Carrousel was centered on the palace. Long-standing plans to link the entrance court of the "Vieux Louvre", as the disused palace was called, with the court of the Tuileries, by sweeping away the intervening buildings came to fruition in the early 19th century.
The older axis extending from the courtyard of the Louvre is skewed to the rest of what has become the Axe historique, but the Arc du Carrousel, at the fulcrum between the two, serves to disguise the discontinuity. To the west, the completion of the Arc de Triomphe in 1836 on the Place de l'Étoile at the western end of the Champs Élysées formed the far point of this line of perspective, which now starts at the equestrian statue of Louis XIV placed by I. M. Pei adjacent to his Pyramide du Louvre in the Cour Napoléon of the Musée du Louvre; the axis was extended again westwards along the Avenue de la Grande Armée, past the city boundary of Paris to La Défense. This was a large junction, named for a statue commemorating the defence of Paris in the Franco-Prussian War. In the 1950s, the area around La Défense was marked out to become a new business district, high-rise office buildings were built along the avenue; the axis found itself extended yet again, with ambitious projects for the western extremity of the modern plaza.
It was not until the 1980s, under president François Mitterrand, that a project was initiated, with a modern 20th century version of the Arc de Triomphe. This is the work of Danish architect Johann Otto von Spreckelsen, La Grande Arche de la Fraternité, a monument to humanity and humanitarian ideals rather than militaristic victories, it was inaugurated in 1989. The network of railway lines and road tunnels beneath the elevated plaza of La Défense prevented the pillars supporting the arch from being in line with the axis: it is out of line, bending the axis should it be extended further to the west. From the roof of the Grande Arche, a second axis can be seen: the Tour Montparnasse stands behind the Eiffel Tower; the Seine-Arche project is extending the historical axis to the West through the city of Nanterre, but with a slight curve. Entry on greatbuildings.com
Mathematics includes the study of such topics as quantity, structure and change. Mathematicians use patterns to formulate new conjectures; when mathematical structures are good models of real phenomena mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back; the research required to solve mathematical problems can take years or centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano, David Hilbert, others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.
Mathematics is essential in many fields, including natural science, medicine and the social sciences. Applied mathematics has led to new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics without having any application in mind, but practical applications for what began as pure mathematics are discovered later; the history of mathematics can be seen as an ever-increasing series of abstractions. The first abstraction, shared by many animals, was that of numbers: the realization that a collection of two apples and a collection of two oranges have something in common, namely quantity of their members; as evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have recognized how to count abstract quantities, like time – days, years. Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic and geometry for taxation and other financial calculations, for building and construction, for astronomy.
The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry, it is in Babylonian mathematics that elementary arithmetic first appear in the archaeological record. The Babylonians possessed a place-value system, used a sexagesimal numeral system, still in use today for measuring angles and time. Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom and proof, his textbook Elements is considered the most successful and influential textbook of all time. The greatest mathematician of antiquity is held to be Archimedes of Syracuse, he developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.
Other notable achievements of Greek mathematics are conic sections, trigonometry (Hipparchus of Nicaea, the beginnings of algebra. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics. Other notable developments of Indian mathematics include the modern definition of sine and cosine, an early form of infinite series. During the Golden Age of Islam during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics; the most notable achievement of Islamic mathematics was the development of algebra. Other notable achievements of the Islamic period are advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarismi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe.
The development of calculus by Newton and Leibniz in the 17th century revolutionized mathematics. Leonhard Euler was the most notable mathematician of the 18th century, contributing numerous theorems and discoveries; the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, differential geometry, matrix theory, number theory, statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show that any axiomatic system, consistent will contain unprovable propositions. Mathematics has since been extended, there has been a fruitful interaction between mathematics and science, to