Branches of Mathematics

Pure mathematics

• Algebra
• Calculus
• Geometry
• Topology
• Trignometry
• Combinatorics
• Logic
• Number theory

Applied mathematics

• Dynamical systems and differential equations
• Mathematical physics
• Computing
• Information theory and signal processing
• Probability and statistics
• Game theory
• Operations research

Related Topics

• Electromagnetic Spectrum
• Linear Equations
• Applied Physics
• Nano Technology
• Engineering Sciences
• Mathematical Medicine
• Fluid dynamics
• Computational Mathematics
• Gamma Ray Optics
• Onfrared Optics
• Relative Velocity
• Iciam
• Intelligent Imaging Neuroscience
• Biomedical Engineering
• Neuroscience Research
• Quantum Cosmology
• Brain Research

• Active fault
• Aerial tramway
• Akashi Kaikyō Bridge
• Akashi-Kaikyo Bridge
• Ambassador Bridge
• Annonay
• Anthony Wayne Bridge
• Arch bridge
• Beam bridge
• Bear Mountain Bridge
• Bedrock
• Ben Franklin Bridge
• Bosphorus Bridge
• Bridge
• Brooklyn Bridge
• Budapest
• Burr Truss
• Cable stayed bridge
• Cable-stayed bridge
• Cantilever
• Cantilever bridge
• Canyon
• Catenary
• Charles Ellet, Jr.
• Column
• Dome
• Dry Bridge
• Duksum
• Edinburgh
• Eyebar
• Falsework
• Fausto Veranzio
• Force (physics)
• Fribourg
• Galloping Gertie
• Geneva
• Golden Gate Bridge
• Great Belt Bridge
• Humber Bridge
• Inca rope bridges
• John A. Roebling
• Joseph Chaley
• Kingston-upon-Hull
• Light rail
• Lions' Gate Bridge
• List of bridge types
• List of bridges
• Little Belt
• Mackinac Bridge
• Manhattan Bridge
• Marc Seguin
• Mechanical cable
• Minneapolis
• Moveable bridge
• New Jersey
• Ohio River
• Otto Beit Bridge
• Parabola
• Punalur
• Rio-Antirio bridge
• Runyang Bridge
• Scaffolding
• Severn Bridge
• Si Du River Bridge
• Silver Bridge
• Steel rope
• Suspension bridge
• Tacoma Narrows
• Tension (mechanics)
• Thangtong Gyalpo
• Through arch bridge
• Tibetan people
• Timber bridge
• Toledo, Ohio
• Tower
• Trashi Yangtse
• Truss bridge
• Tsing Ma Bridge
• Tubular bridge
• Union Bridge (Tweed)
• Wrought iron
• Xihoumen Bridge
• Yangpu Bridge
• Yangtze River
• Yi Sun-sin bridge
• Yichang Bridge
• Zrenjanin
• 
  

• 
  Beam bridge
  Beam bridges are the most simple of structural forms being supported by an abutment at each end of the bridge deck. No moments are transferred throughout the support hence their structural type is known as simply supported.
  The simplest beam bridge could be a slab of stone, or a plank of wood laid across a stream. Bridges designed for modern infrastructure will usually be constructed of steel or reinforced concrete, or a combination of both. The concrete used can either be reinforced, prestressed or post-tensioned.
  Types of construction could include having many beams side by side with a deck across the top of them, to a main beam either side supporting a deck between them. The main beams could be I-beams, trusses, or box girders. They could be half-through, or braced across the top to create a through bridge.
  Because no moments are transferred, thrust, as from an arch bridge, cannot be accommodated, so leading to innovative designs, such as lenticular trusses & bow string arches, which contain the horizontal forces within the superstructure.
  
  wn.com/Beam_bridge
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  Budapest
  Budapest ( /ˈbuːdəpɛst/, /ˈbuːdəpɛʃt/ or /ˈbʊdəpɛst/; Hungarian pronunciation: [ˈbudɒpɛʃt] ( listen); names in other languages) is the capital and the largest city of Hungary, the largest in East-Central Europe and the seventh largest in the European Union. It is the country's principal political, cultural, commercial, industrial, and transportation centre, sometimes described as the primate city of Hungary. According to 2011 Census, Budapest had 1.74 million inhabitants, down from its 1989 peak of 2.1 million due to suburbanization. The Budapest Commuter Area is home to 3.3 million people. The city covers an area of 525 square kilometres (202.7 sq mi) within the city limits. Budapest became a single city occupying both banks of the river Danube with a unification on 17 November 1873 of west-bank Buda and Óbuda with east-bank Pest.
  The history of Budapest began with Aquincum, originally a Celtic settlement that became the Roman capital of Lower Pannonia.Hungarians arrived in the territory in the 9th century. Their first settlement was pillaged by the Mongols in 1241-42. The re-established town became one of the centres of Renaissance humanist culture in the 15th century. Following the Battle of Mohács and nearly 150 years of Ottoman rule, development of the region entered a new age of prosperity in the 18th and 19th centuries, and Budapest became a global city after the 1873 unification. It also became the second capital of Austria-Hungary, a great power that dissolved in 1918. After the Treaty of Trianon in 1920, when Hungary lost 72% of its former territory, culturally and economically the country became wholly Budapest-dominated. The capital dominates the country both by the size of its population—which dwarfs those of Hungary's other cities Budapest was the focal point of the Hungarian Revolution of 1848, the Hungarian Soviet Republic of 1919, Operation Panzerfaust in 1944, the Battle of Budapest of 1945, and the Revolution of 1956.
  
  wn.com/Budapest
• 
  Dry Bridge
  Dry Bridge (Serbian: Мост на сувом, Суви мост) is a bridge in Zrenjanin, Serbia. It is a unique bridge because it currently does not span any physical obstacle, since the flow of the river under it was diverted.
  The bridge was built in 1962 by the project of engineer Rada Janjatov, as a suspension bridge. Its purpose was to connect Zrenjanin city center with Mala Amerika quarter. Two holding towers, one on the north side and the other on the south side, are made of steel and concrete. The northern tower is an 23-meter-high pylon, while the southern tower is A-shaped and 16 meters high. The suspension cable is made of 102 steel wires.
  In 1985, city authorities decided to fill in the secondary bed of the Begej river. A dike between two lakes of the former Begej bed was built at the bridge site, and 23 years after being built, Dry Bridge lost its purpose.
  As of 2008^[update], 23 years since the filling of the river, the bridge still stands, although rusty and in bad condition. City authorities plan to demolish Dry Bridge since it does not have any purpose and for safety reasons. Some residents claim that Dry Bridge has become an ironic symbol of Zrenjanin, and should not be demolished, on the basis that it is one of only two bridges in the world that does not span any kind of physical obstacle; Trinity Bridge is another example, but its by far smaller and older.
  
  wn.com/Dry_Bridge
• 
  Duksum
  Duksum is a village in north-eastern Bhutan. It is located in Trashigang District.
  Population 283 (2005 census).
  
  
  
  wn.com/Duksum
• 
  Edinburgh
  Edinburgh (ⁱ/ˈɛdɪnbʌrə/ ED-in-burr-ə; Scottish Gaelic: Dùn Èideann) is the capital city of Scotland and the seat of the Scottish Parliament. It is the second largest city in Scotland and the seventh most populous in the United Kingdom. The City of Edinburgh Council governs one of Scotland's 32 local government council areas. The council area includes urban Edinburgh and a 30 square miles (78 km²) rural area. Located in the south-east of Scotland, Edinburgh lies on the east coast of the Central Belt, along the Firth of Forth, near the North Sea.
  The city was one of the historical major centres of the Enlightenment, led by the University of Edinburgh, helping to earn it the nickname Athens of the North. The Old Town and New Town districts of Edinburgh were listed as a UNESCO World Heritage Site in 1995 in recognition of the unique character of the Medieval Old Town and the planned Georgian New Town. It covers both the Old and New Towns together with the Dean Village and the Calton Hill areas. There are over 4,500 listed buildings within the city. In May 2010, it had a total of 40 conservation areas covering 23% of the building stock and 23% of the population, the highest such ratios of any major city in the UK. In the 2011 mid-year population estimates, Edinburgh had a total resident population of 495,360.
  
  wn.com/Edinburgh
• 
  Great Belt Bridge
  The Great Belt Fixed Link (Danish: Storebæltsforbindelsen) is the fixed link between the Danish islands of Zealand and Funen across the Great Belt. It consists of a road suspension bridge and railway tunnel between Zealand and the island Sprogø, as well as a box girder bridge between Sprogø and Funen. The "Great Belt Bridge" (Danish: Storebæltsbroen) commonly refers to the suspension bridge, although it may also be used to mean the beam bridge or the link in its entirety. The suspension bridge, known as the East Bridge, has the world's third longest main span (1.6 km), and the longest outside of Asia. It was designed by the Danish architectural practice Dissing+Weitling.
  The link replaces the ferry service which had been the primary means of crossing the Great Belt. After more than five decades of speculation and debate, the decision to construct the link was made in 1986; while the original intent was to complete the railway link three years before opening the road connection, the link was opened to rail traffic in 1997 and road traffic in 1998. At an estimated cost of DKK 21.4 billion (1988 prices), the link is the largest construction project in Danish history.
  
  wn.com/Great_Belt_Bridge
• 
  Kingston-upon-Hull
  Kingston upon Hull (ⁱ/ˌkɪŋstən əpɒn ˈhʌl/ KING-stən ə-pon HUL), usually referred to as Hull, is a city and unitary authority area in the ceremonial county of the East Riding of Yorkshire, England. It stands on the River Hull at its junction with the Humber estuary, 25 miles (40 km) inland from the North Sea. Hull has a resident population of 263,900 (2010 est.). The Larger Urban Zone (LUZ) population stands at 573,300.
  Renamed Kings town upon Hull by King Edward I in 1299, the town and city of Hull has served as market town, military supply port, a trading hub, fishing and whaling centre, and industrial metropolis.
  Hull was an early theatre of battle in the English Civil Wars. Its 18th-century Member of Parliament, William Wilberforce, played a key role in the abolition of the slave trade in Britain.
  The city is unique in the UK in having had a municipally-owned telephone system from 1902, sporting cream, not red, telephone boxes.
  After suffering heavy damage during the Second World War, Hull weathered a period of post-industrial decline, during which the city gained unfavourable results on measures of social deprivation, education and policing. In recent years the city has embarked on an extensive programme of economic regeneration, reconstruction and urban renewal. The economic crisis since 2008 has caused some setbacks to these developments.
  
  wn.com/Kingston-upon-Hull
• 
  Little Belt
  The Little Belt (Danish: Lillebælt) is a strait between the Danish island of Funen and the Jutland Peninsula.
  The belt is about 50 km long and 800m to 28 km wide, the maximum depth is approximately 75 m, and contains numerous small Danish islands.
  Two bridges cross the belt, the Old Lille Belt bridge and the New Little Belt bridge; also the two Little Belt overhead powerline crossings.
  The Belt is mentioned in the German national anthem (written 1841), the Deutschlandlied, to define the northern limit of territories advocated in the song as a unified Germany. Its inclusion reflects the bilingual nature of the former Duchy of Schleswig, which as populated by both Danes, Germans and bilinguals. It was also mentioned for the same reason in the 1813 song, Was ist des Deutschen Vaterland?, written by Ernst Moritz Arndt.
  Coordinates: 55°11′N 9°50′E / 55.183°N 9.833°E / 55.183; 9.833
  
  
  
  wn.com/Little_Belt
• 
  Minneapolis
  Minneapolis (pronunciation: ⁱ/ˌmɪniːˈæpəlɪs/), nicknamed "City of Lakes" and the "Mill City", is the county seat of Hennepin County, the largest city in the state of Minnesota, and the 48th largest in the United States. Its name is attributed to the city's first schoolteacher, who combined mni, the Dakota word for water, and polis, the Greek word for city.
  As of the 2010 Census, the population of the city of Minneapolis is 382,578. Minneapolis lies on both banks of the Mississippi River, just north of the river's confluence with the Minnesota River, and adjoins Saint Paul, the state's capital. Known as the Twin Cities, Minneapolis-Saint Paul is the 16th-largest metropolitan area in the U.S., with approximately 3.3 million residents. The city is abundantly rich in water, with over twenty lakes and wetlands, the Mississippi river, creeks and waterfalls, many connected by parkways in the Chain of Lakes and the Grand Rounds National Scenic Byway. Among cities of similar densities, Minneapolis has the most dedicated parkland. It was once the world's flour milling capital and a hub for timber, and today is the primary business center between Chicago and Seattle, with Minneapolis proper containing the fifth highest concentration of Fortune 500 companies. It has cultural organizations that draw creative people and audiences to the city for theater, visual art, writing, and music. The community's diverse population has a long tradition of charitable support through progressive public social programs and VOLAGs, as well as private and corporate philanthropy.
  
  wn.com/Minneapolis
• 
  New Jersey
  New Jersey (ⁱ/nuː ˈdʒɜrzi/) is a state in the Northeastern and Middle Atlantic regions of the United States. It is bordered on the north and east by the U.S. state of New York, on the southeast and south by the Atlantic Ocean, on the west by Pennsylvania, and on the southwest by Delaware. New Jersey is the 4th least extensive, but the 11th most populous and the most densely populated of the 50 United States. New Jersey lies mostly within the sprawling metropolitan areas of New York City and Philadelphia. It is also the third wealthiest by 2009–2010 median household income.
  The area was inhabited by Native Americans for more than 2,800 years, with historical tribes such as the Lenape along the coast. In the early 17th century, the Dutch and the Swedes made the first European settlements. The British later seized control of the region, naming it the Province of New Jersey. It was granted as a colony to Sir George Carteret and John Berkeley, 1st Baron Berkeley of Stratton. At this time, it was named after the largest of the British Channel Islands, Jersey, Carteret's birthplace. New Jersey was the site of several decisive battles during the American Revolutionary War.
  
  wn.com/New_Jersey
• 
  Rio-Antirio bridge
  The Rio-Antirio bridge (Greek: Γέφυρα Ρίου-Αντιρρίου), officially the Charilaos Trikoupis bridge after the statesman who first envisaged it, is the world's longest multi-span cable-stayed bridge. It crosses the Gulf of Corinth near Patras, linking the town of Rio on the Peloponnese to Antirio on mainland Greece.
  Its official name is the Charilaos Trikoupis Bridge. Charilaos Trikoupis was a 19th century Greek prime minister, and suggested the idea of building a bridge between Rio and Antirrio; however, the endeavour was too expensive at the time, when Greece was trying to get a late foot into the Industrial Revolution.
  The 2,880 m (9,449 ft) long bridge dramatically improves access to and from the Peloponnese, which could previously be reached only by ferry or via the isthmus of Corinth at its extreme east end. Its width is 28 m (92 ft) — it has two vehicle lanes per direction, an emergency lane and a pedestrian walkway. Its five-span four-pylon cable-stayed portion of length 2,252 m (7,388 ft) is the world's second longest cable-stayed deck; only the deck of the Millau Viaduct is longer at 2,460 m (8,071 ft). However, as the latter is also supported by bearings at the pylons apart from cable stays, the Rio-Antirrio bridge deck might be considered the longest cable-stayed "suspended" deck.
  
  wn.com/Rio-Antirio_bridge
• 
  Silver Bridge
  Coordinates: 38°50′42″N 82°08′28″W / 38.845°N 82.14111°W / 38.845; -82.14111
  The Silver Bridge was an eyebar-chain suspension bridge built in 1928 and named for the color of its aluminum paint. The bridge connected Point Pleasant, West Virginia and Gallipolis, Ohio, over the Ohio River.
  On December 15, 1967, the Silver Bridge collapsed while it was full of rush-hour traffic, resulting in the deaths of 46 people. Two of the victims were never found. Investigation of the wreckage pointed to the cause of the collapse being the failure of a single eyebar in a suspension chain, due to a small defect 0.1 inch (2.5 mm) deep. Analysis showed that the bridge was carrying much heavier loads than it had originally been designed for and was poorly maintained.
  The collapsed bridge was replaced by the Silver Memorial Bridge, which was completed in 1969.
  At the time of the Silver Bridge construction, eyebar bridges had been built for about 100 years. Such bridges had usually been constructed from redundant bar links, using rows of four to six bars, sometimes using several such chains in parallel. An example can be seen in the Clifton Suspension Bridge, designed by Isambard Kingdom Brunel. The chain eyebars are redundant in two dimensions. This is an early suspension bridge still in service. Other bridges of similar design include the earlier road bridge over the Menai Strait built by Thomas Telford in 1826; the Széchenyi Chain Bridge in Budapest, built in 1839-1849, destroyed in the closing days of World War II by retreating Germans in 1945, and rebuilt identically by 1949, with redundant chains and hangers; and the Three Sisters, suspension bridges of similar design in Pittsburgh.
  
  wn.com/Silver_Bridge
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  Tacoma Narrows
  The Tacoma Narrows (or The Narrows), a strait, is part of Puget Sound in the U.S. state of Washington. A navigable maritime waterway between glacial landforms, the Narrows separates the Kitsap Peninsula from the city of Tacoma.
  The Narrows is spanned by the twin Tacoma Narrows Bridges (State Route 16). An earlier bridge collapsed shortly after it opened. Some of the largest octopuses in the world, the Giant Pacific Octopus, live among the ruins of the original Tacoma Narrows Bridge.
  In 1841 Charles Wilkes, during the United States Exploring Expedition, named the strait simply Narrows. Its name was formally set as The Narrows by Henry Kellett during the British Admiralty chart reorganization of 1847.
  Coordinates: 47°17′N 122°32′W / 47.28°N 122.54°W / 47.28; -122.54
  
  
  
  wn.com/Tacoma_Narrows
• 
  Toledo, Ohio
  Toledo is the fourth most populous city in the U.S. state of Ohio and is the county seat of Lucas County. Toledo is in northwest Ohio, on the western end of Lake Erie, and borders the State of Michigan. The city was founded in 1833 on the west bank of the Maumee River, originally incorporated as part of Monroe County, Michigan Territory, then re-founded in 1837, after conclusion of the Toledo War, when it was incorporated in Ohio. Toledo grew quickly as a result of the Miami and Erie Canal and its position on the railway line between New York and Chicago. It has since become a city well known for its industry, particularly in glass and auto assembly, as well as for its art community, education, and local sports teams. The population of Toledo as of the 2010 Census was 287,208, while the Toledo metropolitan area had a population of 651,409.
  French trading posts operated in the area as far back as 1680. The area was first settled by Americans in 1845, after the Battle of Fallen Timbers, with the founding of Fort Industry. However, many settlers fled the area during the War of 1812. Resettlement began around 1868 when a Cincinnati syndicate purchased a 974-acre (3.9 km²) tract at the mouth of Cedar Creek and named it Port Lawrence, creating the modern downtown area. Immediately to the north of that, another syndicate founded the town of Vistula, the historic north end. These two towns physically bordered each other with Cherry Street dividing them. This is why present day streets on the northeast side of Cherry Street run at a slightly different angle from those to the southwest of it.
  
  wn.com/Toledo,_Ohio
• 
  Tsing Ma Bridge
  The Tsing Ma Bridge is a bridge in Hong Kong. It is the world's seventh-longest span suspension bridge, and was the second longest at time of completion. The bridge was named after two of the islands at its ends, namely Tsing Yi and Ma Wan . It has two decks and carries both road and rail traffic, which also makes it the largest suspension bridge of this type. The bridge has a main span of 1,377 metres (4,518 ft) and a height of 206 metres (676 ft). The span is the largest of all bridges in the world carrying rail traffic.
  The 41-metre (135 ft) wide bridge deck carries six lanes of automobile traffic, with three lanes in each direction. The lower level contains two rail tracks and two sheltered carriageways, used for maintenance access and traffic lanes when particularly severe typhoons strike Hong Kong and the bridge deck is closed to traffic.
  Construction of the bridge was carried out by a Costain / Mitsui / Trafalgar House joint venture. Construction work of the bridge began in May 1992 and ended in May 1997. It cost HK$7.2 billion. The Lantau Link, of which the bridge is an integral part, was opened on April 27, 1997. The ceremony was inaugurated by the former British Prime Minister Margaret Thatcher.
  
  wn.com/Tsing_Ma_Bridge
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  Zrenjanin
  Zrenjanin (Serbian Cyrillic: Зрењанин, pronounced [zrɛ̌ɲanin]) is a city and municipality located in the eastern part of Serbian province of Vojvodina. It is the administrative centre of the Central Banat District of Serbia. In 2011, the city's population was 75,743, while the Zrenjanin municipality had 122,714 inhabitants.
  Zrenjanin is the largest city in the Serbian Banat, the third largest city in Vojvodina (after Novi Sad and Subotica) and the sixth largest city of Serbia.
  The city was named after Žarko Zrenjanin Uča (1902–1942) in honour and remembrance of his name in 1946. He was one of the leaders of the Vojvodinian Communists and Partisans. During World War II, he was imprisoned and released^{[citation needed]} after being tortured by the Nazis for months.^{[citation needed]} Later he was killed while trying to escape from being recaptured. The former Serbian name of the city was Bečkerek (Бечкерек) or Veliki Bečkerek (Велики Бечкерек). In 1935 the city was renamed to Petrovgrad (Петровград) in honor of king Peter I of Serbia.
  
  wn.com/Zrenjanin

• 
  Charles Ellet, Jr.
  Charles Ellet, Jr. (1 January 1810 – 21 June 1862) was a civil engineer and a colonel during the American Civil War, mortally wounded at the Battle of Memphis.
  Ellet was born in Bucks County, Pennsylvania, brother of Alfred W. Ellet, also a civil engineer and a brigadier general in the Union Army during the war.
  Charles studied civil engineering at École nationale des Ponts et Chaussées in Paris, France, and in 1832 submitted proposals for a suspension bridge across the Potomac River. In 1842, he designed and built the first major wire-cable suspension bridge in the United States, spanning 358 feet over the Schuylkill River at Fairmount, Philadelphia, Pennsylvania. He designed the record-breaking Wheeling suspension bridge over the Ohio River at Wheeling, West Virginia in 1848, and a 770-foot suspension footbridge at Niagara Falls at the same time.
  His other civil engineering accomplishments include supervising both the James River & Kanawha Canal in Virginia and the Schuylkill Navigation improvements in Pennsylvania, and also constructing railroads in those states. Ellet developed theories for improving flood control and navigation of mid-western rivers. In 1849 he had advocated the use of reservoirs, built in the upper reaches of drainage basins, to retain water from the wet season that could be released during periods of low water to improve navigation; to some degree this also would tend to lessen the level of flooding during high flow. In 1850, the Secretary of War, conforming to an Act of Congress, directed Ellet to make surveys and reports on the Mississippi and Ohio Rivers with a view to the preparation of adequate plans for flood prevention and navigation improvement. His report was very complete, and it exercised considerable influence on later engineering thought and navigation improvements.
  
  wn.com/Charles_Ellet,_Jr.
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  Fausto Veranzio
  Fausto Veranzio or Faust Vrančić (Latin: Faustus Verantius; Hungarian and Vernacular Latin: Verancsics Faustus) (circa 1551 – January 17, 1617) was a polymath and bishop from the Venetian Republic.
  Fausto was born in Sebenico in the Croatian noble family of counts Veranzio (a branch of which later merged with Draganić family, creating the Counts Draganić-Veranzio), a notable family of writers.
  He was the son of Michele Veranzio, a Latin poet, and the nephew of Antonio (Croatian: Antun Vrančić),archbishop of Esztergom (1504–1573), a diplomat and a civil servant, who was in touch with Erasmus (1465–1536), Philipp Melanchthon (1497–1560), and Nikola Šubić Zrinski (1508–1566), who took Fausto with him during some of his travels through Hungary and in the Republic of Venice. Fausto's mother was from the Berislavić family. His brother, Giovanni, died still young in battle.
  
  While the family's main residence was in city of Šibenik, they owned a big summer house on island Prvić, in place Šepurine, a neighboring place to Prvić-Luka (where he is buried in local church). The baroque castle that was used by Vrančić family as summer residence is now in possession of the Draganić family.
  
  wn.com/Fausto_Veranzio
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  John A. Roebling
  John Augustus Roebling (born Johann August Röbling, June 12, 1806 – July 22, 1869) was a German-born American civil engineer. He is famous for his wire rope suspension bridge designs, in particular, the design of the Brooklyn Bridge.
  Roebling was the youngest of four children. He was baptized in the Lutheran church Divi Blasii at Mühlhausen. As a young boy he played the bass clarinet and the french horn. He also exhibited great artistic talent for sketches and paintings. His father owned a small tobacco shop, but the business was insufficient to provide livelihood for all three sons. Roebling's sister Friederike Amalie married Carl August Meissner, a poor merchant in the town, and his oldest brother Herman Christian Roebling prepared to take over the tobacco shop.
  At first John attended the gymnasium in Mühlhausen. Recognizing his intelligence at a young age, Roebling's mother, Friederike Dorothea Roebling arranged for him to be tutored in mathematics and science at Erfurt by Ephraim Salomon Unger. He went to Erfurt when he was 15. In 1824 he passed his Surveyor's examination and returned home for a year. In 1824 he enrolled for two semesters at the Bauakademie in Berlin where he studied architecture and engineering under Martin Friedrich Rabe (1765–1856), bridge construction and foundation construction under Johann Friedrich Dietlein (1782–1837), hydraulics under Johann Albert Eytelwein (1764–1848), and languages. Roebling also attended lectures of the philosopher Hegel. Roebling developed an interest in natural philosophy and many years later he worked on a 1000 page treatise about his own concepts of the universe.
  
  wn.com/John_A._Roebling
• Joseph Chaley
  Joseph Chaley (1795 – April 15, 1861) was a French civil engineer and a pioneer designer of suspension bridges in the 19th century. He was a medical officer in the army before becoming a bridge designer.
  Chaley pioneered the construction of suspension bridge cables by bringing together individual wire strands in mid-air, a technique later known as aerial spinning. Previously, the entire cable had been bound together before lifting into place, but Chaley's system, inspired by the ideas of Louis Vicat, allowed considerably longer cables to be erected at less cost.
  He built the Grand Pont Suspendu at Fribourg in 1834, a world record-breaking span of 273m, only overtaken 16 years later by Charles Ellet Jr.'s 308m span Wheeling Suspension Bridge. Chaley had previously worked with Marc Seguin's brother Jules on the Tarascon-Beaucaire Bridge (1828) and also the Chazey-sur-Ain Bridge (1829).
  Chaley first presented a proposal for the Grand Pont Suspendu in February 1830, and was awarded the contract in June of that year. His estimated cost of less than 300,000 florins was well below other competitors, including Guillaume Henri Dufour. Chaley's bridge was supported on four main cables (two per side), each consisting of 1056 wires each 3.08mm in diameter. It carried 2000 people on its opening day. It was replaced in 1923 by a reinforced concrete arch bridge.
  
  wn.com/Joseph_Chaley
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  Marc Seguin
  Marc Seguin (April 20, 1786 - February 24, 1875) was a French engineer, inventor of the wire-cable suspension bridge and the multi-tubular steam-engine boiler.
  Born in Annonay, Ardèche to Marc François Seguin (founder of Seguin & Co.) and Thérèse-Augustine de Montgolfier (niece of Joseph Montgolfier), he was an inventor and entrepreneur. He developed the first suspension bridge in continental Europe, building and administering toll-bridges for a total of 186 bridges throughout France.
  Shortly after the Stockton and Darlington Railway in England opened (1825) he visited it and observed George Stephenson's Locomotion in operation. In 1829, he delivered two steam locomotives of his own design to the Saint-Étienne–Lyon railway. These used an innovative multi-tube boiler and also prominent mechanically driven fans to provide draught on the fire, rather than the blastpipe that was coming into common service at this period. This boiler resembled the later Scotch marine boiler in some aspects, in that the boiler had a large single flue from the furnace, then many small-diameter firetubes returning to a chimney above the firebox door. Uniquely, Seguin's design also arranged the furnace in a large square water-jacketed firebox beneath the boiler to provide a large grate area and greater heating capacity. Robert Stephenson had also made the same decision with his Rocket, but placed his firebox separately and behind the main boiler shell. Seguin's boiler enabled steam-engine trains to increase power and velocity from 4 miles per hour to 25 miles per hour making railroad a more viable mode of transportation. Inventor but also entrepreneur, teaming with his brothers, Camille, Jules, Paul and Charles, as well as his brother in law Vincent Mignot he continued his father's successful business in textiles, paper, gas-lighting, coal mines, construction and added to it a railroad company and a bridge construction business.
  
  wn.com/Marc_Seguin
• 
  Tibetan people
  The Tibetan people (Tibetan: བོད་པ།་, Wylie: Bodpa; Chinese: 藏族; pinyin: Zàng Zú) are an ethnic group that is native to Tibet, which is mostly in the People's Republic of China. They number 5.4 million and are the 10th largest ethnic group in the country. Significant Tibetan minorities also live in India, Nepal, and Bhutan. The Khampas of Tibet are originally from Mongolia.
  Tibetans speak the Tibetan language, which belongs to the Sino-Tibetan languages and has many mutually unintelligible dialects. The traditional, or mythological, explanation of the Tibetan people's origin is that they are the descendants of the monkey Pha Trelgen Changchup Sempa and rock ogress Ma Drag Sinmo. Most Tibetans practice Tibetan Buddhism, though some observe the indigenous Bön and others are Muslims. Tibetan Buddhism influences Tibetan art, drama, and architecture, while the harsh geography of Tibet has produced an adaptive culture of Tibetan medicine and cuisine.
  As of 2008, there are 5.4 million Tibetans in China. The SIL Ethnologue in 2009 documents an additional 189,000 Tibetan language speakers living in India, 5,280 in Nepal, and 4,800 in Bhutan. The Central Tibetan Administration's (CTA) own refugee register counts 145,150 Tibetans outside Tibet: a little over 100,000 in India; in Nepal there are over 16,000; over 1,800 in Bhutan and more than 25,000 in other parts of the world. There are Tibetan communities in the Australia, Canada, Costa Rica, France, Mexico, Norway, Taiwan, Switzerland, United Kingdom, and USA.^{[citation needed]}
  
  wn.com/Tibetan_people

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