Bernards Township, New Jersey
Bernards Township is a township in Somerset County, New Jersey, United States. At the 2010 United States Census, the township's population was 26,652, reflecting an increase of 2,077 from the 24,575 counted in the 2000 Census, which had in turn increased by 7,376 from the 17,199 counted in the 1990 Census. Bernards Township was formed by royal charter on May 24, 1760, as Bernardston Township from remaining portions of Northern precinct, it was incorporated as Bernards Township by an act of the New Jersey Legislature on February 21, 1798, as one of New Jersey's initial group of 104 townships. Portions of the township were taken to form Far Hills and Bernardsville. Bernards Township celebrated its 250th charter anniversary on May 24, 2010; the township was named for Sir Francis Bernard, 1st Baronet, who served as governor of the Province of New Jersey. According to the United States Census Bureau, the township had a total area of 24.061 square miles, including 23.934 square miles of land and 0.127 square miles of water.
The township is bounded by the Second Watchung Mountain in the southwest, the Dead River swamp on the south, the Great Swamp National Wildlife Refuge, Passaic River, Millington Gorge in the east. Unincorporated communities and place names located or within the township include Basking Ridge, Green Knoll, Liberty Corner, Madisonville, Mount Horeb, Somerset Mills, State Park, Stone House and White Bridge. Martinsville is an unincorporated area in Bridgewater Township, whose 08836 ZIP Code covers portions of Bernards Township; the township borders Bedminster Township and Far Hills to the west, Bernardsville to the northwest, Bridgewater Township to the southwest, Warren Township to the southeast in Somerset County and Harding Township to the northeast and Long Hill to the east in Morris County. As of the 2010 United States Census, there were 26,652 people, 9,783 households, 6,897.015 families residing in the township. The population density was 1,113.6 per square mile. There were 10,103 housing units at an average density of 422.1 per square mile.
The racial makeup of the township was 81.83% White, 1.89% Black or African American, 0.08% Native American, 13.80% Asian, 0.03% Pacific Islander, 0.55% from other races, 1.82% from two or more races. Hispanic or Latino of any race were 3.95% of the population. There were 9,783 households out of which 40.0% had children under the age of 18 living with them, 61.7% were married couples living together, 6.9% had a female householder with no husband present, 29.5% were non-families. 26.6% of all households were made up of individuals, 11.3% had someone living alone, 65 years of age or older. The average household size was 2.65 and the average family size was 3.27. In the township, the population was spread out with 28.8% under the age of 18, 4.3% from 18 to 24, 20.6% from 25 to 44, 32.9% from 45 to 64, 13.5% who were 65 years of age or older. The median age was 43.1 years. For every 100 females there were 93.5 males. For every 100 females ages 18 and older there were 88.5 males. The Census Bureau's 2006-2010 American Community Survey showed that median household income was $123,285 and the median family income was $153,906.
Males had a median income of $123,390 versus $86,272 for females. The per capita income for the borough was $67,809. About 2.1% of families and 2.9% of the population were below the poverty line, including 1.3% of those under age 18 and 8.0% of those age 65 or over. At the 2000 United States Census there were 24,575 people, 9,242 households and 6,487 families residing in the township; the population density was 1,023.8 per square mile. There were 9,485 housing units at an average density of 395.1 per square mile. The racial makeup of the township was 89.20% White, 1.44% African American, 0.05% Native American, 7.85% Asian, 0.01% Pacific Islander, 0.40% from other races, 1.05% from two or more races. Hispanic or Latino people of any race were 2.63% of the population. There were 9,242 households of which 37.6% had children under the age of 18 living with them, 63.0% were married couples living together, 5.8% had a female householder with no husband present, 29.8% were non-families. 26.4% of all households were made up of individuals and 9.2% had someone living alone, 65 years of age or older.
The average household size was 2.58 and the average family size was 3.17. Age distribution was 27.7% under the age of 18, 3.2% from 18 to 24, 31.2% from 25 to 44, 25.5% from 45 to 64, 12.5% who were 65 years of age or older. The median age was 39 years. For every 100 females, there were 94.6 males. For every 100 females age 18 and over, there were 90.0 males. The median income for a household in the township was $107,204, the median income for a family was $135,806. Males had a median income of $95,758 versus $60,865 for females; the per capita income for the township was $56,521. About 0.6% of families and 1.3% of the population were below the poverty line, including 1.2% of those under age 18 and 2.9% of those age 65 or over. The headquarters of Barnes & Noble College Booksellers, Hitachi Power Systems USA and Verizon Wireless are located in the township. Verizon Communications, which maintains its world headquarters in New York City, has located operations of its major business units in buildings that were AT&T's world headquarters.
Bernards Township operates under the township form of New Jersey municipal government. The five-membe
Battle of Long Island
The Battle of Long Island is known as the Battle of Brooklyn and the Battle of Brooklyn Heights. The victory over the Americans gave the British control of strategically important New York City, it was fought on August 27, 1776, was the first major battle of the American Revolutionary War to take place after the United States declared its independence on July 4, 1776. In troop deployment and combat, it was the largest battle of the entire war. After defeating the British in the Siege of Boston on March 17, 1776, commander-in-chief General George Washington brought the Continental Army to defend the port city of New York, located at the southern end of Manhattan Island. Washington understood that the city's harbor would provide an excellent base for the Royal Navy, so he established defenses there and waited for the British to attack. In July, the British under the command of General William Howe landed a few miles across the harbor from Manhattan on the sparsely-populated Staten Island, where they were reinforced by ships in Lower New York Bay during the next month and a half, bringing their total force to 32,000 troops.
Washington knew the difficulty in holding the city with the British fleet in control of the entrance to the harbor at the Narrows, he moved the bulk of his forces to Manhattan, believing that it would be the first target. On August 22, the British landed on the shores of Gravesend Bay in southwest Kings County, across the Narrows from Staten Island and more than a dozen miles south from the established East River crossings to Manhattan. After five days of waiting, the British attacked U. S. defenses on the Guan Heights. Unknown to the Americans, Howe had brought his main army around their rear and attacked their flank soon after; the Americans panicked, resulting in twenty percent losses through casualties and capture, although a stand by 400 Maryland and Delaware troops prevented a more substantial portion of the army from being lost. The remainder of the army retreated to the main defenses on Brooklyn Heights; the British dug in for a siege but, on the night of August 29–30, Washington evacuated the entire army to Manhattan without the loss of supplies or a single life.
Washington and the Continental Army were driven out of New York after several more defeats and forced to retreat through New Jersey and into Pennsylvania. In the first stage of the war, the British Army was trapped in the peninsular city of Boston and they abandoned it on March 17, sailing to Halifax, Nova Scotia to await reinforcements. Washington began to transfer regiments to New York City which he believed the British would next attack because of its strategic importance. Washington left Boston on April 4, arrived at New York on April 13, established headquarters at the former home of Archibald Kennedy on Broadway facing Bowling Green. Washington had sent his second in command Charles Lee ahead to New York the previous February to establish the city's defenses. Lee remained in New York City until March. Troops were in limited supply, so Washington found the defenses incomplete, but Lee had concluded that it would be impossible to hold the city with the British commanding the sea, he reasoned that the defenses should be located with the ability to inflict heavy casualties upon the British if any move was made to take and hold ground.
Barricades and redoubts were established in and around the city, the bastion of Fort Stirling across the East River in Brooklyn Heights, facing the city. Lee saw that the immediate area was cleared of Loyalists. Washington began moving troops to Brooklyn in early May, there were several thousand of them there in a short time. Three more forts were under construction on the eastern side of the East River to support Fort Stirling, which stood to the west of the hamlet of Brooklyn Heights; these new fortifications were Fort Putnam, Fort Greene, Fort Box. They lay from north to south, with Fort Putnam farthest to the north, Greene to the southwest, Box farther southwest; each of these defensive structures was surrounded by a large ditch, all connected by a line of entrenchments and a total of 36 cannons. Fort Defiance was being constructed at this time, located farther southwest, past Fort Box, near present-day Red Hook. In addition to these new forts, a mounted battery was established on Governors Island, cannons were placed at Fort George facing Bowling Green, more cannons placed at the Whitehall Dock, which sat on the East River.
Hulks were sunk at strategic locations to deter the British from entering the East River and other waterways. Washington had been authorized by Congress to recruit an army of up to 28,501 troops, but he had only 19,000 when he reached New York. Military discipline was inadequate. Petty internal conflict was common under the strain of a large number of people from different environments and temperaments in relative closeness. Commander of the artillery Henry Knox persuaded Washington to transfer 400 to 500 soldiers, who lacked muskets or guns, to crew the artillery. In early June and Greene inspected the land at the north end of Manhattan and decided to establish Fort Washington. Fort Constitution renamed Fort Lee, was planned opposite Fort Washington on the Hudson River; the forts were hoped to discourage the British ships from sailing up the Hudson River. On June 28, Washington learned that the British fleet had set sail from Halifax on June 9 and were heading toward New York. On June 29, signals were sent from men stationed on
Astronomy is a natural science that studies celestial objects and phenomena. It applies mathematics and chemistry in an effort to explain the origin of those objects and phenomena and their evolution. Objects of interest include planets, stars, nebulae and comets. More all phenomena that originate outside Earth's atmosphere are within the purview of astronomy. A related but distinct subject is physical cosmology, the study of the Universe as a whole. Astronomy is one of the oldest of the natural sciences; the early civilizations in recorded history, such as the Babylonians, Indians, Nubians, Chinese and many ancient indigenous peoples of the Americas, performed methodical observations of the night sky. Astronomy has included disciplines as diverse as astrometry, celestial navigation, observational astronomy, the making of calendars, but professional astronomy is now considered to be synonymous with astrophysics. Professional astronomy is split into theoretical branches. Observational astronomy is focused on acquiring data from observations of astronomical objects, analyzed using basic principles of physics.
Theoretical astronomy is oriented toward the development of computer or analytical models to describe astronomical objects and phenomena. The two fields complement each other, with theoretical astronomy seeking to explain observational results and observations being used to confirm theoretical results. Astronomy is one of the few sciences in which amateurs still play an active role in the discovery and observation of transient events. Amateur astronomers have made and contributed to many important astronomical discoveries, such as finding new comets. Astronomy means "law of the stars". Astronomy should not be confused with astrology, the belief system which claims that human affairs are correlated with the positions of celestial objects. Although the two fields share a common origin, they are now distinct. Both of the terms "astronomy" and "astrophysics" may be used to refer to the same subject. Based on strict dictionary definitions, "astronomy" refers to "the study of objects and matter outside the Earth's atmosphere and of their physical and chemical properties," while "astrophysics" refers to the branch of astronomy dealing with "the behavior, physical properties, dynamic processes of celestial objects and phenomena."
In some cases, as in the introduction of the introductory textbook The Physical Universe by Frank Shu, "astronomy" may be used to describe the qualitative study of the subject, whereas "astrophysics" is used to describe the physics-oriented version of the subject. However, since most modern astronomical research deals with subjects related to physics, modern astronomy could be called astrophysics; some fields, such as astrometry, are purely astronomy rather than astrophysics. Various departments in which scientists carry out research on this subject may use "astronomy" and "astrophysics" depending on whether the department is affiliated with a physics department, many professional astronomers have physics rather than astronomy degrees; some titles of the leading scientific journals in this field include The Astronomical Journal, The Astrophysical Journal, Astronomy and Astrophysics. In early historic times, astronomy only consisted of the observation and predictions of the motions of objects visible to the naked eye.
In some locations, early cultures assembled massive artifacts that had some astronomical purpose. In addition to their ceremonial uses, these observatories could be employed to determine the seasons, an important factor in knowing when to plant crops and in understanding the length of the year. Before tools such as the telescope were invented, early study of the stars was conducted using the naked eye; as civilizations developed, most notably in Mesopotamia, Persia, China and Central America, astronomical observatories were assembled and ideas on the nature of the Universe began to develop. Most early astronomy consisted of mapping the positions of the stars and planets, a science now referred to as astrometry. From these observations, early ideas about the motions of the planets were formed, the nature of the Sun and the Earth in the Universe were explored philosophically; the Earth was believed to be the center of the Universe with the Sun, the Moon and the stars rotating around it. This is known as the geocentric model of the Ptolemaic system, named after Ptolemy.
A important early development was the beginning of mathematical and scientific astronomy, which began among the Babylonians, who laid the foundations for the astronomical traditions that developed in many other civilizations. The Babylonians discovered. Following the Babylonians, significant advances in astronomy were made in ancient Greece and the Hellenistic world. Greek astronomy is characterized from the start by seeking a rational, physical explanation for celestial phenomena. In the 3rd century BC, Aristarchus of Samos estimated the size and distance of the Moon and Sun, he proposed a model of the Solar System where the Earth and planets rotated around the Sun, now called the heliocentric model. In the 2nd century BC, Hipparchus discovered precession, calculated the size and distance of the Moon and inven
Second Continental Congress
The Second Continental Congress was a convention of delegates from the Thirteen Colonies that started meeting in the spring of 1775 in Philadelphia, Pennsylvania. It succeeded the First Continental Congress, which met in Philadelphia between September 5, 1774, October 26, 1774; the Second Congress moved incrementally towards independence. It adopted the Lee Resolution which established the new country on July 2, 1776, it agreed to the United States Declaration of Independence on July 4, 1776; the Congress acted as the de facto national government of the United States by raising armies, directing strategy, appointing diplomats, making formal treaties such as the Olive Branch Petition. The Second Continental Congress came together on May 11, 1775 reconvening the First Continental Congress. Many of the 56 delegates who attended the first meeting were in attendance at the second, the delegates appointed the same president and secretary. Notable new arrivals included John Hancock of Massachusetts.
Within two weeks, Randolph was summoned back to Virginia to preside over the House of Burgesses. Henry Middleton was elected as president to replace Randolph. Hancock was elected president on May 24. Delegates from twelve of the Thirteen Colonies were present when the Second Continental Congress convened. Georgia had not participated in the First Continental Congress and did not send delegates to the Second. On May 13, 1775, Lyman Hall was admitted as a delegate from the Parish of St. John's in the Colony of Georgia, not as a delegate from the colony itself. On July 4, 1775, revolutionary Georgians held a Provincial Congress to decide how to respond to the American Revolution, that congress decided on July 8 to send delegates to the Continental Congress, they arrived on September 13. The First Continental Congress had sent entreaties to King George III to stop the Coercive Acts; the Second Continental Congress met on May 10, 1775 to plan further responses if the British government had not repealed or modified the acts.
For the first few months of the war, the Patriots carried on their struggle in an ad-hoc and uncoordinated manner. They had seized arsenals, driven out royal officials, besieged the British army in the city of Boston. On June 14, 1775, the Congress voted to create the Continental Army out of the militia units around Boston and appointed George Washington of Virginia as commanding general. On July 6, 1775, Congress approved a Declaration of Causes outlining the rationale and necessity for taking up arms in the Thirteen Colonies. On July 8, they extended the Olive Branch Petition to the British Crown as a final attempt at reconciliation. Silas Deane was sent to France as a minister of the Congress, American ports were reopened in defiance of the British Navigation Acts; the Continental Congress had no explicit legal authority to govern, but it assumed all the functions of a national government, such as appointing ambassadors, signing treaties, raising armies, appointing generals, obtaining loans from Europe, issuing paper money, disbursing funds.
The Congress had no authority to levy taxes and was required to request money and troops from the states to support the war effort. Individual states ignored these requests. Congress was moving towards declaring independence from the British Empire in 1776, but many delegates lacked the authority from their home governments to take such a drastic action. Advocates of independence moved to have reluctant colonial governments revise instructions to their delegations, or replace those governments which would not authorize independence. On May 10, 1776, Congress passed a resolution recommending that any colony with a government, not inclined toward independence should form one that was. On May 15, they adopted a more radical preamble to this resolution, drafted by John Adams, which advised throwing off oaths of allegiance and suppressing the authority of the Crown in any colonial government that still derived its authority from the Crown; that same day, the Virginia Convention instructed its delegation in Philadelphia to propose a resolution that called for a declaration of independence, the formation of foreign alliances, a confederation of the states.
The resolution of independence was delayed for several weeks, as advocates of independence consolidated support in their home governments. On June 7, 1776, Richard Henry Lee offered a resolution before the Congress declaring the colonies independent, he urged Congress to resolve "to take the most effectual measures for forming foreign Alliances" and to prepare a plan of confederation for the newly independent states. Lee argued that independence was the only way to ensure a foreign alliance, since no European monarchs would deal with America if they remained Britain's colonies. American leaders had rejected the divine right of kings in the New World, but recognized the necessity of proving their credibility in the Old World. Congress formally adopted the resolution of independence, but only after creating three overlapping committees to draft the Declaration, a Model Treaty, the Articles of Confederation; the Declaration announced the states' entry into the international
Red coat (military uniform)
Red coat or redcoat is a historical item of military clothing used though not worn, by most regiments of the British Army from the 17th to the 20th centuries. The scarlet tunic continues to be used into the 21st century, with several armed forces of the Commonwealth of Nations adopting them as their full dress and mess dress uniforms. From the mid-17th century to the 19th century, the uniform of most British soldiers included a madder red coat or coatee. From 1873 onwards, the more vivid shade of scarlet was adopted for all ranks, having been worn only by officers and all ranks of some cavalry regiments. There had been instances of red military clothing pre-dating its general adoption by the New Model Army; the uniforms of the Yeoman of the Guard and the Yeomen Warders have traditionally been in Tudor red and gold. The Gentlemen Pensioners of James I had worn red with yellow feathers. At Edgehill, the first battle of the Civil War, the King's people had worn red coats, as had at least two Parliamentary regiments".
However none of these examples constituted the national uniform that the red coat was to become. In Ireland during the reign of Elizabeth, the soldiers of the queen's Lord Lieutenant of Ireland were on occasion referred to as "red coats" by the native Irish, from the colour of their clothing; as early as 1561 the Irish named a victory over these royal troops as Cath na gCasóga Dearga meaning'The Battle of the Red Cassocks' but translated as the Battle of the Red Sagums – sagum being a cloak. Note the Irish word is casóg but the word may be translated as coat, cloak, or uniform, in the sense that all of these troops were uniformly attired in red; that the term redcoat was brought to Europe and elsewhere by Irish emigrants is evidenced by Philip O'Sullivan Beare, one of the many thousands of fugitives from Tudor and early Stuart Ireland, who mentions the'Battle of the Redcoats' event in his 1621 history of the Tudor conquest, written in Latin in Spain. He wrote of it as "that famous victory, called'of the red coats' because among others who fell in battle were four hundred soldiers brought from England and clad in the red livery of the viceroy".
O'Sullivan alludes to two other encounters in which the Irish won the day against English'red coats'. One concerns an engagement, twenty years in 1581, during the Second Desmond Rebellion, in which he says "a company of English soldiers, distinguished by their dress and arms, who were called "red coats", being sent to war by the Queen were overwhelmed near Lismore by John Fitzedmund Fitzgerald, the seneschal"; the other relates to a rout by William Burke, Lord of Bealatury in 1599 of "English recruits clad in red coats". English sources confirm. In 1584 the Lords and Council informed the Sheriffs and Justices of Lancashire who were charged with raising 200 foot for service in Ireland that they should be furnished with "a cassocke of some motley, sad grene coller, or russett". Russet was chosen. Again, in the summer of 1595, the Lord Deputy William Russell, 1st Baron Russell of Thornhaugh writing to William Cecil, 1st Baron Burghley about the relief of Enniskillen, mentions that the Irish rebel Hugh O'Neill, Earl of Tyrone had "300 shot in red coats like English soldiers" – the inference being that English soldiers in Ireland were distinguished by their red uniforms.
The Red Coat has evolved from being the British infantryman's worn uniform to a garment retained only for ceremonial purposes. Its official adoption dates from February 1645, when the Parliament of England passed the New Model Army ordinance; the new English Army was formed of 22,000 men, divided into 12 foot regiments of 600 men each, one dragoon regiment of 1000 men, the artillery, consisting of 900 guns. The infantry regiments wore coats of Venetian red with blue or yellow facings. A contemporary comment on the New Model Army dated 7 May 1645 stated "the men are Redcoats all, the whole army only are distinguished by the several facings of their coats". Outside of Ireland, the English Red Coat made its first appearance on a European continental battlefield at the Battle of the Dunes in 1658. A Protectorate army had been landed at Calais the previous year and "every man had a new red coat and a new pair of shoes"; the English name from the battle comes from the major engagement carried out by the "red-coats".
To the surprise of continental observers they stormed sand-dunes 150 feet high fighting experienced Spanish soldiers from their summits with musket fire and push of pike. The adoption and continuing use of red by most British/English soldiers after The Restoration was the result of circumstances rather than policy, including the relative cheapness of red dyes. Red was by no means universal at first, with grey and blue coats being worn. There is no known basis for the myth that red coats were favoured because they did not show blood stains. Blood does in fact show on red clothing as a black stain. Prior to 1707 colonels of regiments made their own arrangements for the manufacture of uniforms under their command; this ended when a royal warrant of 16 January 1707 established a Board of General Officers to regulate the clothing of the army. Uniforms supplied were to conform to the "sealed pattern" agreed by the board; the style of the coat tended to follow those worn by other European armies. From an early stage red coats were lined with contrast
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
New York City
The City of New York called either New York City or New York, is the most populous city in the United States. With an estimated 2017 population of 8,622,698 distributed over a land area of about 302.6 square miles, New York is the most densely populated major city in the United States. Located at the southern tip of the state of New York, the city is the center of the New York metropolitan area, the largest metropolitan area in the world by urban landmass and one of the world's most populous megacities, with an estimated 20,320,876 people in its 2017 Metropolitan Statistical Area and 23,876,155 residents in its Combined Statistical Area. A global power city, New York City has been described as the cultural and media capital of the world, exerts a significant impact upon commerce, research, education, tourism, art and sports; the city's fast pace has inspired the term New York minute. Home to the headquarters of the United Nations, New York is an important center for international diplomacy.
Situated on one of the world's largest natural harbors, New York City consists of five boroughs, each of, a separate county of the State of New York. The five boroughs – Brooklyn, Manhattan, The Bronx, Staten Island – were consolidated into a single city in 1898; the city and its metropolitan area constitute the premier gateway for legal immigration to the United States. As many as 800 languages are spoken in New York, making it the most linguistically diverse city in the world. New York City is home to more than 3.2 million residents born outside the United States, the largest foreign-born population of any city in the world. In 2017, the New York metropolitan area produced a gross metropolitan product of US$1.73 trillion. If greater New York City were a sovereign state, it would have the 12th highest GDP in the world. New York is home to the highest number of billionaires of any city in the world. New York City traces its origins to a trading post founded by colonists from the Dutch Republic in 1624 on Lower Manhattan.
The city and its surroundings came under English control in 1664 and were renamed New York after King Charles II of England granted the lands to his brother, the Duke of York. New York served as the capital of the United States from 1785 until 1790, it has been the country's largest city since 1790. The Statue of Liberty greeted millions of immigrants as they came to the U. S. by ship in the late 19th and early 20th centuries and is an international symbol of the U. S. and its ideals of liberty and peace. In the 21st century, New York has emerged as a global node of creativity and entrepreneurship, social tolerance, environmental sustainability, as a symbol of freedom and cultural diversity. Many districts and landmarks in New York City are well known, with the city having three of the world's ten most visited tourist attractions in 2013 and receiving a record 62.8 million tourists in 2017. Several sources have ranked New York the most photographed city in the world. Times Square, iconic as the world's "heart" and its "Crossroads", is the brightly illuminated hub of the Broadway Theater District, one of the world's busiest pedestrian intersections, a major center of the world's entertainment industry.
The names of many of the city's landmarks and parks are known around the world. Manhattan's real estate market is among the most expensive in the world. New York is home to the largest ethnic Chinese population outside of Asia, with multiple signature Chinatowns developing across the city. Providing continuous 24/7 service, the New York City Subway is the largest single-operator rapid transit system worldwide, with 472 rail stations. Over 120 colleges and universities are located in New York City, including Columbia University, New York University, Rockefeller University, which have been ranked among the top universities in the world. Anchored by Wall Street in the Financial District of Lower Manhattan, New York has been called both the most economically powerful city and the leading financial center of the world, the city is home to the world's two largest stock exchanges by total market capitalization, the New York Stock Exchange and NASDAQ. In 1664, the city was named in honor of the Duke of York.
James's older brother, King Charles II, had appointed the Duke proprietor of the former territory of New Netherland, including the city of New Amsterdam, which England had seized from the Dutch. During the Wisconsinan glaciation, 75,000 to 11,000 years ago, the New York City region was situated at the edge of a large ice sheet over 1,000 feet in depth; the erosive forward movement of the ice contributed to the separation of what is now Long Island and Staten Island. That action left bedrock at a shallow depth, providing a solid foundation for most of Manhattan's skyscrapers. In the precolonial era, the area of present-day New York City was inhabited by Algonquian Native Americans, including the Lenape, whose homeland, known as Lenapehoking, included Staten Island; the first documented visit into New York Harbor by a European was in 1524 by Giovanni da Verrazzano, a Florentine explorer in the service of the French crown. He named it Nouvelle Angoulême. A Spanish expedition led by captain Estêvão Gomes, a Portuguese sailing for Emperor Charles V, arrived in New York Harbor in January 1525 and charted the mouth of the Hudson River, which he named Río de San Antonio.
The Padrón Rea