Branches of Mathematics

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• 
  

• 
  Barcelona
  Barcelona (English /bɑrsɨˈloʊnə/, Catalan: [bərsəˈɫonə], Spanish: [barθeˈlona]) is the capital of Catalonia and the second largest city in Spain, after Madrid, with a population of 1,621,537 within its administrative limits on a land area of 101.4 km² (39 sq mi). The urban area of Barcelona extends beyond the administrative city limits with a population of between 4,200,000 and 4,500,000 within an area of 803 km² (310 sq mi), being the sixth-most populous urban area in the European Union after Paris, London, the Ruhr, Madrid and Milan. About five million people live in the Barcelona metropolitan area. It is also Europe's largest metropolis on the Mediterranean Sea. It is the main component of an administrative area of Greater Barcelona, with a population of 3,218,071 in an area of 636 km² (density 5,060 hab/km²). It is located on the Mediterranean coast between the mouths of the rivers Llobregat and Besòs and is bounded to the west by the Serra de Collserola ridge (512 m/1,680 ft).
  Founded as a Roman city, Barcelona became the capital of the County of Barcelona. After merging with the Kingdom of Aragon, Barcelona became one of the most important cities of the Crown of Aragon. Besieged several times during its history, Barcelona has a rich cultural heritage and is today an important cultural centre and a major tourist destination. Particularly renowned are the architectural works of Antoni Gaudí and Lluís Domènech i Montaner, which have been designated UNESCO World Heritage Sites. The headquarters of the Union for the Mediterranean is located in Barcelona. The city is known for hosting the 1992 Summer Olympics as well as world-class conferences and expositions, including the 1888 Exposición Universal de Barcelona, the 1929 Barcelona International Exposition (Expo 1929), the 2004 Universal Forum of Cultures, and the 2004 World Urban Forum.
  
  wn.com/Barcelona
• 
  Hectare
  The hectare ( /ˈhɛktɛər/ or /ˈhɛktɑr/; symbol ha) is a metric unit of area defined as 10,000 square metres (100 m by 100 m), and primarily used in the measurement of land. In 1795, when the metric system was introduced, the 'are' was defined as being 100 square metres and the hectare ('hecto-' + 'are') was thus 100 'ares' or 1/100 km². A hectare of land is about 2.47 acres.
  When the metric system was further rationalised in 1960, resulting in the International System of Units (SI), the are was not included as a recognised unit. The hectare is one of the non-SI units accepted for use with the SI units.
  The metric system of measure was first given a legal basis in 1795 by the French Revolutionary government. The law of 18 Germinal, Year III (7 April 1795) defined five units of measure:
  Although the law defined the length of the metre, there was no practical way of accurately measuring the metre (and hence the are) until 1799 when the first standard metre was manufactured and adopted.
  The standard metre remained in the custody of successive French governments until 1875 when, under the Convention of the Metre, its supervision passed into international control under the auspices of the General Conference on Weights and Measures (GCPM). At the first meeting of the GCPM in 1889 when a new standard metre, manufactured by Johnson Matthey & Co of London was adopted, the are and hectare were automatically redefined.
  
  wn.com/Hectare
• 
  History of the metre
  In the aftermath of the French Revolution (1789), the old units of measure that were associated with the ancien régime were replaced by new units. The livre was replaced by the decimal franc, and a new unit of length was introduced which became known as the metre. Although there was initially considerable resistance to the adoption of the new metric system in France (including an official reversion to the mesures usuelles ["normal units"] for a period), the metre gained following in continental Europe during the mid nineteenth century, particularly in scientific usage, and was officially adopted as an international measurement unit by the Metre Convention of 1875.
  The standard measures of length in Europe diverged from one another following the fall of Charlemagne's Empire: while measures could be standardized within a given jurisdiction (which was often little more than a single market town), they were numerous varieties of measure between regions. Indeed, as the measures were often used as the basis for taxation (of cloth, for example), the use of a certain measure was associated with the sovereignty of a given ruler and often dictated by law.
  
  wn.com/History_of_the_metre
• 
  Kilometre
  The kilometre (American spelling: kilometer; SI symbol: km) is a unit of length in the metric system, equal to one thousand metres (kilo- being the SI prefix for 1000). It is now the measurement unit used officially for expressing distances between geographical places on land in most of the world; notable exceptions are the United States and the United Kingdom where the statute mile is the official unit used.
  k (pronounced kay) is occasionally used in some English-speaking countries as an alternative for the word kilometre in everyday writing and speech. A slang term for the kilometre in the U.S. military is klick.
  There are two common pronunciations for the word:
  The former pronunciation follows the general pattern in English whereby SI units of measurement are pronounced with the stress on the first syllable, and the pronunciation of the actual base unit does not change irresepective of the prefix. It is generally preferred by the British Broadcasting Corporation (BBC) and the Australian Broadcasting Corporation (ABC).
  
  wn.com/Kilometre
• 
  Montjuïc
  Coordinates: 41°21′51″N 2°09′29″E / 41.36417°N 2.15806°E / 41.36417; 2.15806
  Montjuïc (Catalan pronunciation: [muɲʒuˈik], alternatively spelled Montjuich) is a hill located in Barcelona, Catalonia, Spain.
  Montjuïc is translated as 'Jew Hill' in medieval Catalan, or is perhaps related to the Latin phrase Mons Jovicus ('hill of Jupiter'). The name is found in several locations in the Catalan Countries: the Catalan cities of Girona and Barcelona both have a Montjuïc, as does the island of Minorca. When written in a Spanish rather than Catalan context it is generally spelled Montjuich (this is old Catalan spelling before the orthographic reforms of Pompeu Fabra).
  Barcelona's Montjuïc is a broad shallow hill with a relatively flat top overlooking the harbour, to the southwest of the city centre. The eastern side of the hill is almost a sheer cliff, giving it a commanding view over the city's harbour immediately below. The top of the hill (a height of 184,8 m) was the site of several fortifications, the latest of which (the Castell de Montjuïc) remains today. The fortress largely dates from the 17th century, with 18th century additions. In 1842, the garrison (loyal to the Madrid government) shelled parts of the city. It served as a prison, often holding political prisoners, until the time of General Franco. The castle was also the site of numerous executions. In 1897, an incident popularly known as Els processos de Montjuïc prompted the execution of anarchist supporters, which then led to a severe repression of the workers' struggle for their rights. On different occasions during the Spanish Civil War, both Nationalists and Republicans were executed there, each at the time when the site was held by their opponents. The Catalan nationalist leader Lluís Companys i Jover was also executed there in 1940, having been extradited to the Franco government by the Nazis.
  
  wn.com/Montjuïc
• 
  North Pole
  Coordinates: 90°N 0°W / 90°N 0°W / 90; -0
  The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is, subject to the caveats explained below, defined as the point in the Northern Hemisphere where the Earth's axis of rotation meets its surface. It should not be confused with the North Magnetic Pole.
  The North Pole is the northernmost point on Earth, lying diametrically opposite the South Pole. It defines geodetic latitude 90° North, as well as the direction of true north. At the North Pole all directions point south; all lines of longitude converge there, so its longitude can be defined as any degree value.
  While the South Pole lies on a continental land mass, the North Pole is located in the middle of the Arctic Ocean amid waters that are almost permanently covered with constantly shifting sea ice. This makes it impractical to construct a permanent station at the North Pole (unlike the South Pole). However, the Soviet Union, and later Russia, have constructed a number of manned drifting stations on a generally annual basis since 1937, some of which have passed over or very close to the Pole. In recent years, a number of studies have predicted that the North Pole may become seasonally ice-free due to Arctic shrinkage, with timescales varying from next year to fifty years or more.
  
  wn.com/North_Pole
• 
  Paris meridian
  The Paris meridian is a meridian line running through the Paris Observatory in Paris, France—now longitude 2°20′14.025″ east. It was a long-standing rival to the Greenwich meridian as the prime meridian of the world, as was the Antwerp meridian in Antwerp, Belgium.
  In the year 1634, France ruled by Louis XIII and Cardinal Richelieu decided that Ferro's meridian should be used as the reference on maps, since this island is the most western position of the Old World. It was also thought to be exactly 20 degrees west of Paris.
  A French astronomer, Abbé Jean Picard, measured the length of a degree of longitude and computed from it the size of the Earth during 1669-1670. In 1666, Louis XIV of France had authorized the building of an observatory in Paris to measure longitude. On Midsummer's Day 1667, members of the Academy of Sciences traced the future building's outline on a plot outside town near the Port Royal abbey, with Picard's meridian exactly bisecting the site north-south. French cartographers would use it as their prime meridian for more than 200 years.
  
  wn.com/Paris_meridian
• 
  Sèvres
  Coordinates: 48°49′26″N 2°12′42″E / 48.8239°N 2.2117°E / 48.8239; 2.2117
  Sèvres is a commune in the southwestern suburbs of Paris, France. It is located 9.9 km (6.2 mi) from the centre of Paris.
  The town is known for its famous porcelain production at the Manufacture nationale de Sèvres and for being the location of the International Bureau of Weights and Measures.
  Sèvres is twinned with:
  Sèvres is served by Sèvres – Rive Gauche station on the Transilien Paris – Montparnasse suburban rail line.
  It is also served by Sèvres – Ville d'Avray station on the Transilien Paris – Saint-Lazare suburban rail line.
  It is also served by Musée de Sèvres station on the Tramway 2 that links Paris - Porte de Versailles and La Défense.
  Sèvres hosts the French Federation of Sport Blowgun (France Sport Blowgun Association), founded in 2004 by Stéphane Jouanneau (Blowgun Long-Distance Vice World Champion)
  
  wn.com/Sèvres
• 
  Watt
  The watt ( /ˈwɒt/ WOT; symbol: W) is a derived unit of power in the International System of Units (SI), named after the Scottish engineer James Watt (1736–1819). The unit, defined as one joule per second, measures the rate of energy conversion or transfer.
  
  
  
  
  ) is the SI derived unit of electrical resistance.
  The watt is named after the Scottish scientist James Watt for his contributions to the development of the steam engine. The unit was recognized by the Second Congress of the British Association for the Advancement of Science in 1882. The 11th General Conference on Weights and Measures in 1960 adopted it for the measurement of power into the International System of Units (SI).
  The femtowatt is equal to one quadrillionth (10⁻¹⁵) of a watt. Technologically important powers that are measured in femtowatts are typically found in reference(s) to radio and radar receivers. For example, meaningful FM tuner performance figures for sensitivity, quieting and signal-to-noise require that the RF energy applied to the antenna input be specified. These input levels are often stated in dBf (decibels referenced to 1 femtowatt). This is 0.2739 microvolt across a 75 ohm load or 0.5477 microvolt across a 300 ohm load; the specification takes into account the RF input impedance of the tuner.
  
  wn.com/Watt

• 
  Christiaan Huygens
  Christiaan Huygens, FRS (/ˈhaɪɡənz/; [ˈɦœyɣə(n)s] ( listen); 14 April 1629 – 8 July 1695) was a prominent Dutch mathematician, astronomer, physicist and horologist. His work included early telescopic studies elucidating the nature of the rings of Saturn and the discovery of its moon Titan, the invention of the pendulum clock and other investigations in timekeeping, and studies of both optics and the centrifugal force.
  Huygens achieved note for his argument that light consists of waves, now known as the Huygens–Fresnel principle, which two centuries later became instrumental in the understanding of wave-particle duality. He generally receives credit for his discovery of the centrifugal force, the laws for collision of bodies, for his role in the development of modern calculus and his original observations on sound perception (see repetition pitch).
  Christiaan Huygens was born in April 1629 at The Hague, the second son of Constantijn Huygens, (1596–1687), a friend of mathematician, philosopher and minor physicistRené Descartes, and of Suzanna van Baerle (deceased 1637), whom Constantijn had married on 6 April 1627. Christiaan studied law and mathematics at the University of Leiden and the College of Orange in Breda. After a stint as a diplomat, Huygens turned to science.
  
  wn.com/Christiaan_Huygens
• 
  Christopher Wren
  Sir Christopher Wren FRS (20 October 1632 – 25 February 1723) is one of the most highly acclaimed English architects in history. He was accorded responsibility for rebuilding 51 churches in the City of London after the Great Fire in 1666, including his masterpiece, St. Paul's Cathedral, on Ludgate Hill, completed in 1710. The principal creative responsibility for a number of the churches is now more commonly attributed to others in his office, especially Nicholas Hawksmoor. Other notable buildings by Wren include the Royal Naval College in Greenwich and the south front of Hampton Court Palace.
  Educated in Latin and Aristotelian physics at the University of Oxford, Wren was a notable astronomer, geometer, and mathematician-physicist, as well as an architect. He was a founder of the Royal Society (president 1680–82), and his scientific work was highly regarded by Sir Isaac Newton and Blaise Pascal.
  Wren was born at East Knoyle in Wiltshire, the only surviving son of Christopher Wren DD (1589–1658), at that time the rector of East Knoyle and later Dean of Windsor. A previous son of Dr Wren, also named Christopher, was born on 22 November 1631 and died the same day. John Aubrey’s confusion of the two persisted occasionally into late twentieth-century literature.
  
  wn.com/Christopher_Wren
• 
  John Wilkins
  John Wilkins FRS (1 January 1614 – 19 November 1672) was an English clergyman, natural philosopher and author, as well as a founder of the Invisible College and one of the founders of the Royal Society, and Bishop of Chester from 1668 until his death.
  Wilkins is one of the few persons to have headed a college at both the University of Oxford and the University of Cambridge. He was a polymath, although not one of the most important scientific innovators of the period. His personal qualities were brought out, and obvious to his contemporaries, in reducing political tension in Interregnum Oxford, in founding the Royal Society on non-partisan lines, and in efforts to reach out to religious nonconformists. He was one of the founders of the new natural theology compatible with the science of the time.
  He is particularly known for An Essay towards a Real Character and a Philosophical Language in which, amongst other things, he proposed a universal language and a decimal system of measure not unlike the modern metric system.
  
  wn.com/John_Wilkins
• 
  Pierre Méchain
  Pierre François André Méchain (16 August 1744 – 20 September 1804) was a French astronomer and surveyor who, with Charles Messier, was a major contributor to the early study of deep sky objects and comets.
  Pierre Méchain was born in Laon, the son of the ceiling designer and plasterer Pierre François Méchain. He displayed mental gifts in mathematics and physics but had to give up his studies for lack of money. However, his talents in astronomy were noticed by Joseph Jérôme Lalande, for whom he became a friend and proof-reader. Lalande then secured a position for him with the Naval Depot of Maps at Versailles, where he worked through the 1770s engaged in hydrographic work and coastline surveying. It was during this time—approximately 1774—that he met Charles Messier, with whom he also became friends. In this year he also produced his first astronomical work, a paper on an occultation of Aldebaran by the Moon.
  In 1777 he married Barbe-Thérèse Marjou, who bore him two sons and a daughter. He was admitted to the French Académie des sciences in 1782, and was the editor of Connaissance des Temps from 1785 to 1792; this was the journal which, among other things, first published the list of Messier objects.
  
  wn.com/Pierre_Méchain
• 
  Tito Livio Burattini
  Tito Livio Burattini (8 March 1617 – 17 November 1681) was an inventor, architect, Egyptologist, scientist, instrument-maker, traveller, engineer, and nobleman. He was born in Agordo, Italy, and studied in Padua and Venice. In 1639, he explored the Great Pyramid of Giza with English mathematician John Greaves; both Burattini and Sir Isaac Newton used measurements made by Greaves in an attempt to accurately determine the circumference of the earth.
  A year after leaving Egypt for Germany in 1641, the court of King Władysław IV invited him to Poland. In Warsaw, Burattini built a model aircraft with four fixed glider wings in 1647. Described as "four pairs of wings attached to an elaborate 'dragon'", it was said to have successfully lifted a cat in 1648 but not Burattini himself. According to Clive Hart's The Prehistory of Flight, he promised that "only the most minor injuries" would result from landing the craft.
  He later developed an early system of measurement based on time, similar to today's International System of Units; he published it in his book Misura universale (lit. "universal measure") in 1675 at Vilnius. His system includes the metro cattolico (lit. "catholic [i.e. universal] metre"), a unit of length equivalent to the length of a free seconds pendulum; it differs from the modern metre by half a centimetre. He is considered the first to recommend the name metre for a unit of length.
  
  wn.com/Tito_Livio_Burattini

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