History.

The precise details of Verona's early history remain a mystery. One theory is it was a city of the Euganei, who were obliged to give it up to the Cenomani (550 BC). With the conquest of the Valley of the Po, the Veronese territory became Roman (about 300 BC). Verona became a Roman "colonia" in 89 BC. It was classified as a "municipium" in 49 BC, when its citizens were ascribed to the Roman tribe "Poblilia" or "Publicia".  The city became important because it was at the intersection of several roads. Stilicho defeated Alaric and his Visigoths here in 403. But, after Verona was conquered by the Ostrogoths in 489, the Gothic domination of Italy began. Theoderic the Great was said to have built a palace there. It remained under the power of the Goths throughout the Gothic War (535–552), except for a single day in 541, when the Byzantine officer Artabazes made an entrance. The defections that took place among the Byzantine generals with regard to the booty made it possible for the Goths to regain possession of the city. In 552 Valerian vainly endeavored to enter the city, but it was only when the Goths were fully overthrown that they surrendered it.  In 569, it was taken by Alboin, King of the Lombards, in whose kingdom it was, in a sense, the second most important city. There, Alboin was killed by his wife in 572. The dukes of Treviso often resided there. Adalgisus, son of Desiderius, in 774 made his last desperate resistance in Verona to Charlemagne, who had destroyed the Lombard kingdom. Verona became the ordinary residence of the kings of Italy, the government of the city becoming hereditary in the family of Count Milo, progenitor of the counts of San Bonifacio. From 880 to 951 the two Berengarii resided there. Otto I ceded to Verona the marquisate dependent on the Duchy of Bavaria.  When Ezzelino III da Romano was elected "podestà" in 1226, he converted the office into a permanent lordship. In 1257 he caused the slaughter of 11,000 Paduans on the plain of Verona (Campi di Verona). Upon his death, the Great Council elected Mastino I della Scala as podestà, and he converted the "signoria" into a family possession, though leaving the burghers a share in the government. Failing to be re-elected podestà in 1262, he effected a coup d'état, and was acclaimed capitano del popolo, with the command of the communal troops. Long internal discord took place before he succeeded in establishing this new office, to which was attached the function of confirming the podestà. In 1277, Mastino della Scala was killed by the faction of the nobles. The reign of his son Alberto as capitano (1277–1302) was a time of incessant war against the counts of San Bonifacio, who were aided by the House of Este. Of his sons, Bartolomeo, Alboino and Cangrande I, only the last shared the government (1308); he was great as warrior, prince, and patron of the arts; he protected Dante, Petrarch, and Giotto. By war or treaty, he brought under his control the cities of Padua (1328), Treviso (1308) and Vicenza. At this time before the Black death the city was home to more than 40,000 people. Cangrande was succeeded by Mastino II (1329–1351) and Alberto, sons of Alboino. Mastino continued his uncle's policy, conquering Brescia in 1332 and carrying his power beyond the Po. He purchased Parma (1335) and Lucca (1339). After the King of France, he was the richest prince of his time. But a powerful league was formed against him in 1337 – Florence, Venice, the Visconti, the Este, and the Gonzaga. After a three years war, the Scaliger dominions were reduced to Verona and Vicenza (Mastino's daughter Regina-Beatrice della Scala married to Barnabò Visconti). Mastino's son Cangrande II (1351–1359) was a cruel, dissolute, and suspicious tyrant; not trusting his own subjects, he surrounded himself with Brandenburg mercenaries. He was killed by his brother Cansignorio (1359–1375), who beautified the city with palaces, provided it with aqueducts and bridges, and founded the state treasury. He also killed his other brother, Paolo Alboino. Fratricide seems to have become a family custom, for Antonio (1375–87), Cansignorio's natural brother, slew his brother Bartolomeo, thereby arousing the indignation of the people, who deserted him when Gian Galeazzo Visconti of Milan made war on him. Having exhausted all his resources, he fled from Verona at midnight (19 October 1387), thus putting an end to the Scaliger domination, which, however, survived in its monuments.  The year 1387 is also the year of the Battle of Castagnaro, between Giovanni Ordelaffi, for Verona, and John Hawkwood, for Padua, who was the winner.  Antonio's son Canfrancesco attempted in vain to recover Verona (1390). Guglielmo (1404), natural son of Cangrande II, was more fortunate; with the support of the people, he drove out the Milanese, but he died ten days after, and Verona then submitted to Venice (1405). The last representatives of the Scaligeri lived at the imperial court and repeatedly attempted to recover Verona by the aid of popular risings.  From 1508 to 1517, the city was in the power of the Emperor Maximilian I. There were numerous outbreaks of the plague, and in 1629–33 Italy was struck by its worst outbreak in modern times. Around 33,000 people died in Verona (over 60 per cent of the population at the time) in 1630–1631.  In 1776 was developed a method of bellringing called Veronese bellringing art. Verona was occupied by Napoleon in 1797, but on Easter Monday the populace rose and drove out the French. It was then that Napoleon made an end of the Venetian Republic. Verona became Austrian territory when Napoleon signed the Treaty of Campo Formio in October 1797. The Austrians took control of the city on 18 January 1798. It was taken from Austria by the Treaty of Pressburg in 1805 and became part of Napoleon's Kingdom of Italy, but was returned to Austria following Napoleon's defeat in 1814, when it became part of the Austrian-held Kingdom of Lombardy-Venetia.  The Congress of Verona, which met on 20 October 1822, was part of the, opening with the Congress of Vienna in 1814–15, that marked the effective breakdown of the "Concert of Europe".  In 1866, following the Third Italian War of Independence, Verona, along with the rest of Venetia, became part of United Italy.  The advent of fascism added another dark chapter to the annals of Verona. As throughout Italy, the Jewish population was hit by the Manifesto of Race, a series of anti-Semitic laws passed in 1938, and after the invasion by Nazi Germany in 1943, deportations to Nazi concentration camps. An Austrian Fort (now a church, the Santuario della Madonna di Lourdes), was used to incarcerate and torture Allied troops, Jews and anti-fascists, especially after 1943, when Verona became part of the Italian Social Republic.  As in Austrian times, Verona became of great strategic importance to the regime. Galeazzo Ciano, Benito Mussolini's son-in-law, was accused of plotting against the republic; in a show trial staged in January 1944 by the Nazi and fascist hierarchy at Castelvecchio (the Verona trial), Ciano was executed on the banks of the Adige with many other officers on what is today Via Colombo. This marked another turning point in the escalation of violence that would only end with the final liberation by allied troops and partisans in 1945. After World War II, as Italy entered into NATO, Verona once again acquired its strategic importance, due to its closeness to the Iron Curtain.  The city became the seat of SETAF (South European Allied Terrestrial Forces) and had during the whole duration of the Cold War period a strong military presence, especially American, which has since decreased.

Geography.

Climate.

Verona has a humid subtropical climate characteristic of Northern Italy's inland plains, with hot summers and cold, humid winters, even though Lake Garda has a partial influence on the city. The relative humidity is high throughout the year, especially in winter when it causes fog, mainly from dusk until late morning, although the phenomenon has become less and less frequent in recent years.

Demographics.

In 2009, there were 265,368 people residing in Verona, located in the province of Verona, Veneto, of whom 47.6% were male and 52.4% were female. Minors (children aged 0–17) totalled 16.05% of the population compared to pensioners who number 22.36%. This compares with the Italian average of 18.06% (minors) and 19.94% (pensioners). The average age of Verona residents is 43 compared to the Italian average of 42. In the five years between 2002 and 2007, the population of Verona grew by 3.05%, while Italy as a whole grew by 3.85%. The current birth rate of Verona is 9.24 births per 1,000 inhabitants compared to the Italian average of 9.45 births. , 87% of the population was Italian. The largest immigrant group comes from other European nations (the largest coming from Romania): 3.60%, South Asia: 2.03%, and sub-saharan Africa 1.50%. The city is predominantly Roman Catholic, but due to immigration now has some Orthodox Christian, and Muslim followers.

Government.

Since local government political reorganization in 1993, Verona has been governed by the City Council of Verona, which is based in "Palazzo Barbieri". Voters elect directly 33 councilors and the Mayor of Verona every five years. Verona is also the capital of its own province. The Provincial Council is seated in "Palazzo del Governo". The current Mayor of Verona is Federico Sboarina (FI), elected on 26 June 2017.  This is a list of the mayors of Verona since 1946:

Main sights.

Because of the value and importance of its many historical buildings, Verona has been named a UNESCO World Heritage Site. Verona preserved many ancient Roman monuments (including the magnificent Arena) in the early Middle Ages, but many of its early medieval edifices were destroyed or heavily damaged by the earthquake of 3 January 1117, which led to a massive Romanesque rebuilding. The Carolingian period "Versus de Verona" contains an important description of Verona in the early medieval era.

Roman edifices.

The Roman military settlement in what is now the centre of the city was to expand through the cardines and decumani that intersect at right angles. This structure has been kept to the present day and is clearly visible from the air. Further development has not reshaped the original map. Though the Roman city with its basalt-paved roads is mostly hidden from view it stands virtually intact about 6 m below the surface. Most palazzi and houses have cellars built on Roman structures that are rarely accessible to visitors. Piazza delle Erbe, near the Roman forum was rebuilt by Cangrande I and Cansignorio della Scala I, lords of Verona, using material (such as marble blocks and statues) from Roman spas and villas.  Verona is famous for its Roman amphitheatre, the Arena, found in the city's largest piazza, the Piazza Bra. Completed around 30 AD, it is the third largest in Italy after Rome's Colosseum and the arena at Capua. It measures 139 metres long and 110 metres wide, and could seat some 25,000 spectators in its 44 tiers of marble seats. The "ludi" (shows and gladiator games) performed within its walls were so famous that they attracted spectators from far beyond the city. The current two-story façade is actually the internal support for the tiers; only a fragment of the original outer perimeter wall in white and pink limestone from Valpolicella, with three stories remains.The interior is very impressive and is virtually intact, and has remained in use even today for public events, fairs, theatre and open-aired opera during warm summer nights. There is also a variety of other Roman monuments to be found in the town, such as the Roman theatre of Verona. This theatre was built in the 1st century BC, but through the ages had fallen in disuse and had been built upon to provide housing. In the 18th century Andrea Monga, a wealthy Veronese, bought all the houses that in time had been built over the theatre, demolished them, and saved the monument. Not far from it is the Ponte di Pietra ("Stone Wall Bridge"), another Roman landmark that has survived to this day.  The "Arco dei Gavi" (Gavi Arch) was built in the 1st century AD, and is famous for having the name of the builder (architect Lucius Vitruvius Cordone) engraved on it, a rare case in the architecture of the epoque. It originally straddled the main Roman road into the city, now the Corso Cavour. It was demolished by French troops in 1805 and rebuilt in 1932.  Nearby is the "Porta Borsari", an archway at the end of Corso Porta Borsari. This is the façade of a 3rd-century gate in the original Roman city walls. The inscription is dated 245 AD and gives the city name as "Colonia Verona Augusta". Corso Porta Borsari, the road passing through the gate is the original Via Sacra of the Roman city. Today, it is lined with several Renaissance palazzi and the ancient Church of Santi Apostoli, a few metres from Piazza delle Erbe.  "Porta Leoni" is the 1st century BC ruin of what was once part of the Roman city gate. A substantial portion is still standing as part of the wall of a medieval building. The street itself is an open archaeological site, and the remains of the original Roman street and gateway foundations can be seen a few feet below the present street level. As can be seen from there, the gate contains a small court guarded by towers. Here, carriages and travelers were inspected before entering or leaving the city.

Medieval architecture.

With a span length of, the segmental arch bridge Ponte Scaligero featured, at the time of its completion in 1356, the world's largest bridge arch.  Verona was the birthplace of Catullus, and the town that Julius Caesar chose for relaxing stays. It has had an association with many important people and events that have been significant in the history of Europe, such as Theoderic the Great, king of Ostrogoths, Alboin and Rosamund, the Lombard Dukes, Charlemagne and Pippin of Italy, Berengar I, and Dante. Conclaves were held here, as were important congresses. Verona featured in the travel diaries of Goethe, Stendhal, Paul Valéry and Michel de Montaigne.

Sport.

The city has three professional football teams. Historically, the city's major team has been Hellas Verona. Hellas Verona won the Italian Serie A championship in 1984–85, and played in the European Cup the following year. Chievo Verona represents Chievo, a suburb of Verona. As of the 2019–20 season, Hellas play in the first division of Italian football, Serie A, and Chievo play in the second division, Serie B. The teams contest the Derby della Scala and share the 38,402-seater Stadio Marcantonio Bentegodi, which was used as a venue at the 1990 FIFA World Cup. Virtus Vecomp Verona is another Verona-based football club.  Verona is home to the volleyball team Marmi Lanza Verona (now in Serie A1), the rugby team Franklin and Marshall Cus Verona Rugby (now in Serie A1), and the basketball team Scaligera Basket (now in Legadue).  The city has twice hosted the UCI Road World Championships, in 1999 (with Treviso as co-host) and in 2004. The city also regularly hosts stages of the Giro d'Italia annual cycling race. Verona also hosted the baseball world cup in 2009, and the Volleyball World Cup in September–October 2010. Verona is hosting the Volleyball Women's World Championship in September–October 2014.

Infrastructure and transport.

Buses.

Buses are operated by the provincial public transport company, "Azienda Trasporti Verona" (ATV).

Railways.

Verona lies at a major route crossing where the north-south rail line from the Brenner Pass to Rome intersects with the east-west line between Milan and Venice, giving the city rail access to most of Europe. In addition to regional and local services the city is served by direct international trains to Zurich, Innsbruck and Munich and by overnight sleeper services to Paris and Dijon (Thello), Munich and Vienna (ÖBB).  Verona's main station is Verona Porta Nuova railway station, to the south of the city centre. It is considered to be the ninth busiest railway station in Italy, handling approximately 68,000 passengers per day, or 25 million passengers per year.  There is a lesser station to the east of the city at Porta Vescovo, which used to be the main station in Verona, but now only receives trains between Venice and Porta Nuova.

Airport.

Verona Airport is located southwest of Verona. It handles around 3 million passengers per year. It is linked to Porta Nuova railway station by a frequent bus service.  There are direct flights between Verona and Rome Fiumicino, Munich, Berlin, Moscow, Naples, Frankfurt, Catania, Paris Charles De Gaulle, London Gatwick, Dublin, Palermo,Cork, Manchester, Vienna Schwechat, Liverpool and Cagliari among others.

International relations.

Twin towns - sister cities.

Verona is twinned with:

Friendship pacts.

Verona has friendy relations with:

In popular culture.

Two of William Shakespeare's plays, the famous "Romeo and Juliet", as well as the lesser-known "The Two Gentlemen of Verona", are set in the city of Verona. Although no surviving evidence suggests that Shakespeare had ever been to the city, or even the nation of Italy, for that matter, the city's presence in his work has inspired increased tourism to Verona and the surrounding areas ever since.

Verona (, ; or "Veròna") is a city on the Adige River in Veneto, Italy, with 258,108 inhabitants. It is one of the seven provincial capitals of the region. It is the second largest city municipality in the region and the third largest in northeast Italy. The metropolitan area of Verona covers an area of and has a population of 714,274 inhabitants. It is one of the main tourist destinations in northern Italy because of its artistic heritage and several annual fairs, shows, and operas, such as the lyrical season in the Arena, an ancient Roman amphitheater.

维罗纳(意大利语:)是位于意大利北部威尼托阿迪杰河畔的一座历史悠久的城市,2000年入选联合国教科文组织的世界遗产。


Etymology.

The state's name is derived from the Mississippi River, which

Geography.

Mississippi is bordered to the north by Tennessee, to the east by Alabama, to the south by Louisiana and a narrow coast on the Gulf of Mexico; and to the west, across the Mississippi River, by Louisiana and Arkansas.  In addition to its namesake, major rivers in Mississippi include the Big Black River, the Pearl River, the Yazoo River, the Pascagoula River, and the Tombigbee River. Major lakes include Ross Barnett Reservoir, Arkabutla Lake, Sardis Lake, and Grenada Lake with the largest lake being Sardis Lake.  Mississippi is entirely composed of lowlands, the highest point being Woodall Mountain, in the foothills of the Cumberland Mountains, above sea level. The lowest point is sea level at the Gulf Coast. The state's mean elevation is above sea level.  Most of Mississippi is part of the East Gulf Coastal Plain. The coastal plain is generally composed of low hills, such as the Pine Hills in the south and the North Central Hills. The Pontotoc Ridge and the Fall Line Hills in the northeast have somewhat higher elevations. Yellow-brown loess soil is found in the western parts of the state. The northeast is a region of fertile black earth that extends into the Alabama Black Belt.  The coastline includes large bays at Bay St. Louis, Biloxi, and Pascagoula. It is separated from the Gulf of Mexico proper by the shallow Mississippi Sound, which is partially sheltered by Petit Bois Island, Horn Island, East and West Ship Islands, Deer Island, Round Island, and Cat Island.  The northwest remainder of the state consists of the Mississippi Delta, a section of the Mississippi Alluvial Plain. The plain is narrow in the south and widens north of Vicksburg. The region has rich soil, partly made up of silt which had been regularly deposited by the flood waters of the Mississippi River.  Areas under the management of the National Park Service include:

Major cities and towns.

Mississippi City Population Rankings of at least 50,000 (United States Census Bureau as of 2017):  Mississippi City Population Rankings of at least 20,000 but fewer than 50,000 (United

Climate.

Mississippi has a humid subtropical climate with long, hot and humid summers, and short, mild winters. Temperatures average about 81°F (about 27°C) in July and about 42 °F (about 9 °C) in January. The temperature varies little statewide in the summer; however, in winter, the region near Mississippi Sound is significantly warmer than the inland portion of the state. The recorded temperature in Mississippi has ranged from, in 1966, at Corinth in the northeast, to, in 1930, at Holly Springs in the north. Heavy snowfall rarely occurs, but isn't unheard of, such as during the New Year's Eve 1963 snowstorm. Yearly precipitation generally increases from north to south, with the regions closer to the Gulf being the most humid. Thus, Clarksdale, in the northwest, gets about 50 inches (about 1,270 mm) of

Ecology, flora, and fauna.

Mississippi is heavily forested, with over half of the state's area covered by wild or cultivated trees. The southeastern part of the state is dominated by longleaf pine, in both uplands and lowland flatwoods and Sarracenia bogs. The Mississippi Alluvial Plain, or Delta, is primarily farmland and aquaculture ponds but also has sizeable tracts of cottonwood, willows, baldcypress, and oaks. A belt of loess extends north to south in the western part of the state, where the Mississippi Alluvial Plain reaches the first hills; this region is characterized by rich, mesic mixed hardwood forests, with some species disjunct from Appalachian forests. Two bands of historical prairie, the Jackson Prairie and the Black Belt, run northwest to southeast in the middle and northeastern part of the state. Although these areas have been highly degraded by conversion to agriculture, a

Ecological problems.

Flooding.

Due to seasonal flooding, possible from December to June, the Mississippi and Yazoo rivers and their tributaries created a fertile floodplain in the Mississippi Delta. The river's flooding created natural levees, which planters had built higher to try to prevent flooding of land cultivated for cotton crops. Temporary workers built levees along the Mississippi River on top of the natural levees that formed from dirt deposited after the river flooded.  From 1858 to 1861, the state took over levee building, accomplishing it through contractors and hired labor. In those years, planters considered their slaves too valuable to hire out for such dangerous work. Contractors hired gangs of Irish immigrant laborers to build levees and sometimes clear land. Many of the Irish were relatively recent immigrants from the famine years who were struggling to get established. Before the American Civil War, the earthwork levees averaged six feet in height, although in some areas they reached twenty feet.  Flooding has been an integral part of Mississippi history, but clearing of the land for cultivation and to supply wood fuel for steamboats took away the absorption of trees and undergrowth. The banks of the river were denuded, becoming unstable and changing the character of the river. After the Civil War, major floods swept down the valley in 1865, 1867, 1874 and 1882. Such floods regularly overwhelmed levees damaged by Confederate and Union fighting during the war, as well as those constructed after the

History.

Near 10,000 BC Native Americans or Paleo-Indians arrived in what today is referred to as the American South. Paleo-Indians in the South were hunter-gatherers who pursued the megafauna that became extinct following the end of the Pleistocene age. In the Mississippi Delta, Native American settlements and agricultural fields were developed on the natural levees, higher ground in the proximity of rivers. The Native Americans developed extensive fields near their permanent villages. Together with other practices, they created some localized deforestation but did not alter the ecology of the Mississippi Delta as a whole.  After thousands of years, succeeding cultures of the Woodland and Mississippian culture eras developed rich and complex agricultural societies, in which surplus supported the development of specialized trades. Both were mound builder cultures. Those of the Mississippian culture were the largest and most complex, constructed beginning about 950 AD. The peoples had a trading network spanning the continent from the Great Lakes to the Gulf Coast. Their large earthworks, which expressed their cosmology of political and religious concepts, still stand throughout the Mississippi and Ohio River valleys. Descendant Native American tribes of the Mississippian culture in the Southeast include the Chickasaw and Choctaw. Other tribes who inhabited the territory of Mississippi (and whose names were honored by colonists in local towns) include the Natchez, the Yazoo, and the Biloxi.  The first major European expedition into the territory that became Mississippi was that of the Spanish explorer, Hernando de Soto, who passed through the northeast part of the state in 1540, in his second expedition to the New World.

Colonial era.

In April 1699, French colonists established the first European settlement at "Fort Maurepas" (also known as Old Biloxi), built in the vicinity of present-day Ocean Springs on the Gulf Coast. It was settled by Pierre Le Moyne d'Iberville. In 1716, the French founded Natchez on the Mississippi River (as "Fort Rosalie"); it became the dominant town and trading post of the area. The French called the greater territory "New France"; the Spanish continued to claim part of the Gulf coast area (east of Mobile Bay) of present-day southern Alabama, in addition to the entire area of present-day Florida. Through the 18th century, the area was ruled variously by Spanish, French, and British colonial governments. The colonists imported African slaves as laborers. Under French and Spanish rule, there developed a class of free people of color ("gens de couleur libres"), mostly multiracial descendants of European men and enslaved or free black women, and their mixed-race children.

United States territory.

After the American Revolution (1765–83), Britain ceded this area to the new United States of America. The Mississippi Territory was organized on April 7, 1798, from territory ceded by Georgia and South Carolina to the United States. Their original colonial charters theoretically extended west to the Pacific Ocean. The Mississippi Territory was later twice expanded to include disputed territory claimed by both the United States and Spain.  From 1800 to about 1830, the United States purchased some lands (Treaty of Doak's Stand) from Native American tribes for new settlements of European Americans; they were mostly migrants from other Southern states, particularly Virginia and North Carolina, where soils were exhausted. On September 27, 1830, the Treaty of Dancing Rabbit Creek was signed between the U.S. Government and the Choctaw. The Choctaw agreed to sell their traditional homelands in Mississippi and

Statehood, 1817–1861.

Mississippi became the 20th state on December 10, 1817. David Holmes was the first governor. The state was still occupied as ancestral land by several Native American tribes, including Choctaw, Natchez, Houma, Creek, and Chickasaw.  Plantations were developed primarily along the major rivers, where the waterfront provided access to the major transportation routes. This is also where early towns developed, linked by the steamboats that carried commercial products and crops to markets. The remainder of Native American ancestral land remained largely undeveloped but was sold through treaties until 1826, when the Choctaws and Chickasaws refused to sell more land. The combination of the Mississippi state legislature's abolition of Choctaw Tribal Government in 1829, President Andrew Jackson's Indian Removal Act and the Treaty of Dancing Rabbit Creek of 1830, the Choctaw were effectively forced to sell their land and were transported to Oklahoma Territory. The forced migration of the Choctaw, together with

Civil War to 20th century.

On January 9, 1861, Mississippi became the second state to declare its secession from the Union, and it was one of the founding members of the Confederate States. The first six states to secede were those with the highest number of slaves. During the war, Union and Confederate forces struggled for dominance on the Mississippi River, critical to supply routes and commerce. More than 80,000 Mississippians fought in the Civil War, and casualties were extremely heavy. Union General Ulysses S. Grant's long siege of Vicksburg finally gained the Union control of the river in 1863.  In the postwar period, freedmen withdrew from white-run churches to set up independent congregations. The majority of blacks left the Southern Baptist Church, sharply reducing its membership. They created independent black Baptist congregations. By 1895 they had established numerous black Baptist state associations and the National Baptist Convention of black churches.  In addition, independent black

20th century to present.

In 1900, blacks made up more than half of the state's population. By 1910, a majority of black farmers in the Delta had lost their land and become sharecroppers. By 1920, the third generation after freedom, most African Americans in Mississippi were landless laborers again facing poverty. Starting about 1913, tens of thousands of black Americans left Mississippi for the North in the Great Migration to industrial cities such as St. Louis, Chicago, Detroit, Cleveland, Philadelphia and New York. They sought jobs, better education for their children, the right to vote, relative freedom from discrimination, and better living. In the migration of 1910–1940, they left a society that had been steadily closing off opportunity. Most migrants from Mississippi took trains directly north to Chicago and often settled near former neighbors.  Blacks also faced violence in the form of lynching, shooting, and the burning of churches. In 1923, the National Association for the Advancement of Colored People stated "the Negro feels that life is not safe in Mississippi and his life may be taken with impunity at any time upon the slightest pretext or provocation by a white man".  In the early 20th century, some industries were established in Mississippi, but jobs were generally restricted to whites, including child workers. The lack of jobs also drove some

Demographics.

The center of population of Mississippi is located in Leake County, in the town of Lena. The United States Census Bureau estimates that the population of Mississippi was 2,976,149 on July 1, 2019, a 0.30% increase since the 2010 census. The state's economist characterized the state as losing population as job markets elsewhere have caused 3.2 per 1000 to migrate recently.  From 2000 to 2010, the United States Census Bureau reported that Mississippi had the highest rate of increase in people identifying as mixed-race, up 70 percent in the decade; it amounts to a total of 1.1 percent of the population. In addition, Mississippi led the nation for most of the last decade in the growth of mixed marriages among its population. The total population has not increased significantly, but is young. Some of the above change in identification as mixed race is due to new births. But, it appears mostly to reflect those residents who have chosen to identify as more than one race, who in earlier years may have identified by just one ethnicity. A binary racial system had been in place since slavery times and the days of racial segregation. In the civil rights era, people of African descent banded together in an inclusive community to achieve political power and gain restoration of their civil rights.  As the demographer William H. Frey noted, "In Mississippi, I think it's [identifying as mixed race] changed from within." Historically in Mississippi, after Indian removal in the 1830s, the major groups were designated as black (African American), who were then mostly enslaved, and white (primarily European American). Matthew Snipp, also a demographer, commented on the increase in the 21st century in the number of people identifying as being of more than one race: "In a sense, they're rendering a more accurate portrait of their racial heritage that in the past would have been suppressed."  After having accounted for a majority of the state's population since well before the Civil War and through the 1930s, today African Americans constitute approximately 37 percent of the state's population. Most have ancestors who were enslaved, with many forcibly transported from the Upper South in the 19th century to work on the area's new plantations. Some of these slaves were mixed race, with European ancestors, as there were many children born into slavery with white fathers. Some also have Native American ancestry. During the first half of the 20th century, a total of nearly 400,000 African Americans left the state during the Great Migration, for opportunities in the North, Midwest and West. They became a minority in the state for the first time since early in its development.  The state has had conservative laws related to sexuality. The state's sodomy law criminalized consensual sex between adults of the same gender until 2003 (but was seldom enforced), when such laws were voided by the Supreme Court case "Lawrence v. Texas". In 2004, voters in Mississippi approved Amendment 1, amending the state's constitution to prohibit same-sex marriage; the measure passed with 86% of the vote, the highest margin of victory in the nation. This law was overturned by "Obergefell v. Hodges" (2015), the decision of the U.S. Supreme Court making same-sex marriage a constitutional right.  Despite conservative laws, same-sex couples were forming families in the state. According to the 2010 census, approximately 33% of households led by same-sex couples in Mississippi included at least one child, the highest such percentage in the nation.

Health.

The state is ranked 50th or last place among all the states for health care, according to the Commonwealth Fund, a nonprofit foundation working to advance performance of the health care system.  Mississippi has the highest rate of infant and neonatal deaths of any U.S. state. Age-adjusted data also shows Mississippi has the highest overall death rate, and the highest death rate from heart disease, hypertension and hypertensive renal disease, influenza and pneumonia.  In 2011, Mississippi (and Arkansas) had the fewest dentists in the United States.  For three years in a row, more than 30 percent of Mississippi's residents have been classified as obese. In a 2006 study, 22.8 percent of the state's children were classified as such. Mississippi had the highest rate of obesity of any U.S. state from 2005 to 2008, and also ranks first in the nation for

Economy.

The Bureau of Economic Analysis estimates that Mississippi's total state product in 2010 was $98 billion. GDP growth was.5 percent in 2015 and is estimated to be 2.4 in 2016 according to Dr. Darrin Webb, the state's chief economist, who noted it would make two consecutive years of positive growth since the recession. Per capita personal income in 2006 was $26,908, the lowest per capita personal income of any state, but the state also has the nation's lowest living costs. 2015 data records the adjusted per capita personal income at $40,105. Mississippians consistently rank as one of the highest per capita in charitable contributions.  At 56 percent, the state has one of the lowest workforce participation rates in the country. Approximately 70,000 adults are disabled, which is 10 percent of the workforce.  Mississippi's rank as one of the poorest states is related to its dependence on cotton agriculture before and after the Civil War, late development of its frontier bottomlands in the Mississippi Delta, repeated natural disasters of flooding in the late 19th and early 20th century that required massive capital investment in levees, and ditching and draining the bottomlands, and slow development of railroads to link bottomland towns and river cities. In addition, when Democrats regained control of the state legislature, they passed the 1890 constitution that discouraged corporate industrial development in favor of rural agriculture, a legacy that would slow the state's progress for years.  Before the Civil War, Mississippi was the fifth-wealthiest state in the nation, its wealth generated by the labor of slaves in cotton plantations along the rivers. Slaves were counted as property and the rise in the cotton markets since the 1840s had increased their value. By 1860, a majority—55 percent—of the population of Mississippi was enslaved. Ninety percent of the Delta bottomlands were undeveloped and the state had low overall density of population. Largely due to the domination of the plantation economy, focused on the production of agricultural cotton, the state's elite was reluctant to invest in infrastructure such as roads and railroads. They educated their children privately. Industrialization did not reach many areas until the late 20th century. The planter aristocracy, the elite of antebellum Mississippi, kept the tax structure low for their own benefit, making only private improvements. Before the war the most successful planters, such as Confederate President Jefferson Davis, owned riverside properties along the Mississippi and Yazoo rivers in the Mississippi Delta. Away from the riverfronts, most of the Delta was undeveloped frontier.  During the Civil War, 30,000 Mississippi soldiers, mostly white, died from wounds and disease, and many more were left crippled and wounded. Changes to the labor structure and an agricultural depression throughout the South caused severe losses in wealth. In 1860 assessed valuation of property in Mississippi had been more than $500 million, of which $218 million (43 percent) was estimated as the value of slaves. By 1870, total assets had decreased in value to roughly $177 million.  Poor whites and landless former slaves suffered the most from the postwar economic depression. The constitutional convention of early 1868 appointed a committee to recommend what was needed for relief of the state and its citizens. The committee found severe destitution among the laboring classes. It took years for the state to rebuild levees damaged in battles. The upset of the commodity system impoverished the state after the war. By 1868 an increased cotton crop began to show possibilities for free labor in the state, but the crop of 565,000 bales produced in 1870 was still less than half of prewar figures.  Blacks cleared land, selling timber and developing bottomland to achieve ownership. In 1900, two-thirds of farm owners in Mississippi were blacks, a major achievement for them and their families. Due to the poor economy, low cotton prices and difficulty of getting credit, many of these farmers could not make it through the extended financial difficulties. Two decades later, the majority of African Americans were sharecroppers. The low prices of cotton into the 1890s meant that more than a generation of African Americans lost the result of their labor when they had to sell their farms to pay off accumulated debts.  After the Civil War, the state refused for years to build human capital by fully educating all its citizens. In addition, the reliance on agriculture grew increasingly costly as the state suffered loss of cotton crops due to the devastation of the boll weevil in the early 20th century, devastating floods in 1912–1913 and 1927, collapse of cotton prices after 1920, and drought in 1930.  It was not until 1884, after the flood of 1882, that the state created the Mississippi-Yazoo Delta District Levee Board and started successfully achieving longer-term plans for levees in the upper Delta. Despite the state's building and reinforcing levees for years, the Great Mississippi Flood of 1927 broke through and caused massive flooding of throughout the Delta, homelessness for hundreds of thousands, and millions of dollars in property damages. With the Depression coming so soon after the flood, the state suffered badly during those years. In the Great Migration, hundreds of thousands of African Americans migrated North and West for jobs and chances to live as full citizens.

Politics and government.

As with all other U.S. states and the federal government, Mississippi's government is based on the separation of legislative, executive and judicial power. Executive authority in the state rests with the Governor, currently Tate Reeves (R). The lieutenant governor, currently Delbert Hosemann (R), is elected on a separate ballot. Both the governor and lieutenant governor are elected to four-year terms of office. Unlike the federal government, but like many other U.S. States, most of the heads of major executive departments are elected by the citizens of Mississippi rather than appointed by the governor.  Mississippi is one of five states that elects its state officials in odd-numbered years (the others are Kentucky, Louisiana, New Jersey and Virginia). Mississippi holds elections for these offices every four years, always in the year preceding presidential elections.

Laws.

In 2004, Mississippi voters approved a state constitutional amendment banning same-sex marriage and prohibiting Mississippi from recognizing same-sex marriages performed elsewhere. The amendment passed 86% to 14%, the largest margin in any state. Same-sex marriage became legal in Mississippi on June 26, 2015, when the United States Supreme Court invalidated all state-level bans on

Political alignment.

Mississippi led the South in developing a disenfranchising constitution, passing it in 1890. By raising barriers to voter registration, the state legislature disenfranchised most blacks and many poor whites, excluding them from politics until the late 1960s. It established a one-party state dominated by white Democrats.  In the 1980s whites divided evenly between the parties.

Transportation.

Air.

Mississippi has six airports with commercial passenger service, the

Roads.

Mississippi is the only American state where people in cars may legally consume beer. Some localities have laws restricting the practice. In 2018, the

Rail.

Passenger.

Amtrak provides scheduled passenger service along two routes, the "Crescent" and "City of New Orleans". Prior to severe

Freight.

All but two of the United States Class I railroads serve Mississippi (the exceptions are the Union Pacific and Canadian Pacific):  http://www.mvk.usace.army.mil/Missions/Recreation/Enid-Lake/

Education.

Until the Civil War era, Mississippi had a small number of schools and no educational institutions for African Americans. The first school for black students was not established until 1862.  During Reconstruction in 1871, black and white Republicans drafted a constitution that was the first to provide for a system of free public education in the state. The state's dependence on agriculture and resistance to taxation limited the funds it had available to spend on any schools. In the early 20th century, there were still few schools in rural areas, particularly for black children. With seed money from the Julius Rosenwald Fund, many rural black communities across Mississippi raised matching funds and contributed public funds to build new schools for their children. Essentially, many black adults taxed themselves twice and made significant sacrifices to raise money for the education of children in their communities, in many cases donating land and/or labor to build such schools.  Blacks and whites attended segregated and separate public schools in Mississippi until the late 1960s, although such segregation had been declared unconstitutional by the United States Supreme Court in its 1954 ruling in "Brown v. Board of Education". In the majority-black Mississippi Delta counties, white parents worked through White Citizens' Councils to set up private segregation academies, where they enrolled their children. Often funding declined for the public schools.  But in the state as a whole, only a small minority of white children were withdrawn from public schools. State officials believed they needed to maintain public education to attract new businesses. After several years of integration, whites often dominated local systems anyway, maintaining white supremacy. Many black parents complained that they had little representation in school administration, and that many of their former administrators and teachers had been pushed out. They have had to work to have their interests and children represented.  In the late 1980s Mississippi's 954 public schools

Culture.

While Mississippi has been especially known for its music and literature, it has embraced other forms of art. Its strong religious traditions have inspired striking works by outsider artists who have been shown nationally.  Jackson established the USA International Ballet Competition, which is held every four years. This ballet competition attracts the most talented young dancers from around the world.  The Magnolia Independent Film Festival, still held annually in Starkville, is the first and oldest in the state.  George Ohr, known as the "Mad Potter of Biloxi" and the father of abstract expressionism in pottery, lived and worked in Biloxi, MS.

Music.

Musicians of the state's Delta region were historically significant to the development of the blues. Although by the end of the 19th century, two-thirds of the farm owners were black, continued low prices for cotton and national financial pressures resulted in most of them losing their land. More problems built up with the boll weevil infestation, when thousands of agricultural jobs were lost.  Jimmie Rodgers, a native of Meridian and guitarist/singer/songwriter known as the "Father of Country Music", played a significant role in the development of the blues. He and Chester Arthur Burnett were friends and admirers of each other's music. Their friendship and respect is an important example of Mississippi's musical legacy. While the state has had a reputation for being the

Mississippi () is a state located in the Deep South region of the United States. Mississippi is the 32nd largest and 34th-most populous of the 50 United States. Mississippi is bordered to the north by Tennessee, to the east by Alabama, to the south by the Gulf of Mexico, to the southwest by Louisiana, and to the northwest by Arkansas. Mississippi's western boundary is largely defined by the Mississippi River. Jackson is both the state's capital and largest city. Greater Jackson, with an estimated population of 580,166 in 2018, is the most populous metropolitan area in Mississippi and the 95th-most populous in the United States.

密西西比州(英语:State of Mississippi)是美国南部的一个州。西边以密西西比河为州界,东南邻墨西哥湾。


History.

The idea of having an Athletics World Championships was around well before the competition's first event in 1983. In 1913, the IAAF decided that the Olympic Games would serve as the World Championships for athletics. This was considered suitable for over 50 years until in the late 1960s the desire of many IAAF members to have their own World Championships began to grow. In 1976 at the IAAF Council Meeting in Puerto Rico an Athletics World Championships separate from the Olympic Games was approved.  Following bids from both Stuttgart, West Germany and Helsinki, Finland, the IAAF Council awarded the inaugural competition to Helsinki, to take place in 1983 and be held in the Helsinki Olympic Stadium (where the 1952 Summer Olympics had been held).  Two IAAF world championship events preceded the inaugural edition of the World Championships in Athletics in 1983. The 1976 World Championships had just one event – the men's 50 kilometres walk which was dropped from the Olympic programme for the 1976 Summer Olympics and the IAAF responded by setting up their own contest. Four years later, the 1980 World Championships contained only two newly approved women's events, (400 metres hurdles and 3000 metres), neither of which featured on the programme for the 1980 Summer Olympics.  Over the years the competition has grown in size. In 1983 an estimated 1,300 athletes from 154 countries participated. By the 2003 competition, in Paris, it had grown to 1,907 athletes from 203 countries with coverage being transmitted to 179 different countries.  There has also been a change in composition over the years, with several new events, all for women, being added. By 2005, the only differences were men's competition in the 50 km walk, and equivalent events in women's 100 m hurdles and heptathlon to men's 110 m hurdles and decathlon.  The following list shows when new events were added for the first time.

All-time medal table.

Updated after the 2019 World Athletics Championships.  is the name, under which Russian athletes competed in the 2017 and 2019 Championships. Their medals were not included in the official medal table.

All-time placing table.

In the "IAAF placing table" the total score is obtained from assigning eight points to the first place and so on to one point for the eight placed finalists. Points are shared in situations where a tie occurs. However, the IAAF site shows all points rounded to the nearest integer.  "Updated after the 2017 Championships"  Sixteen male athletes have won at least six medals. Twenty two female athletes have won at least six medals.

Multiple winners.

Boldface denotes active athletes and highest medal count among all athletes (including these who not included in these tables) per type.

Men.

All events.

<nowiki>*</nowiki> including one medal in the relay event in which he participated in the heats only

Women.

All events.

<nowiki>*</nowiki> including one medal in the relay event in which she participated in the heats only
 <nowiki>***</nowiki> including three medals in the relay events in which she participated in the heats only
 <nowiki>****</nowiki> including four medals in the relay events in which she participated in the heats only

Athletes with most appearances.

There are 61 athletes that have competed in at least eight editions.  <nowiki>*</nowiki> At the 1993 World Championships in Athletics in Stuttgart, Germany, Dragutin Topić completed as Individual World Championship Participant (IWP) as Athletic Federation of Yugoslavia was suspended by IAAF due to United Nations sanctions stemming from the Yugoslav wars.

World records.

A total of 32 world records have been set or equalled at the competition, 17 by men, 13 by women and 2 – in the mixed relay.  The first world record to be set at the World Championships was by Jarmila Kratochvílová of Czechoslovakia, who ran 47.99 seconds to win the women's 400 m final.  A peak of five world records came at the 1993 World Championships in Athletics. The most recent world record was in the Women's 400 metres hurdles, which Dalilah Muhammad of the United States finished in 52.16 second in 2019. World records have become less common as the history of the event has expanded, with no world records set in the 1997, 2001, 2007 and 2013 editions.  American athletes have been the most successful with thirteen world records set by that nation in total, followed by Jamaica and Great Britain on four each. Jamaican sprinter Usain Bolt has broken the most world records at the competition, at four, one more than American Carl Lewis. Jonathan Edwards holds the distinction of breaking the world record twice in one championships – improving upon his own newly-set world record in the 1995 men's triple jump final. The men's 4 × 100 metres relay has yielded the most world records, with five set between 1983 and 2011.  Ben Johnson's time of 9.83 seconds at the 1987 World Championships men's 100 m final was initially considered a world record, but this was later rescinded after Johnson admitted to steroid use between 1981 and 1988.  Also, a doping disqualification has led to a performance being retrospectively recognised as a world record: the 2009 Jamaican men's 4 × 100 metres relay team time of 37.31 seconds was taken as the world record after the team's time of 37.10 at the 2008 Beijing Olympics was rescinded due to the disqualification of Nesta Carter (not present in the World Championships team).

The World Athletics Championships are a biennial athletics competition organized by World Athletics (formerly IAAF). The World Championships were started in 1976 in response to the International Olympic Committee dropping the men's 50 km walk from the Olympic programme for the 1976 Montreal Olympics, despite its constant presence at the games since 1932. The IAAF chose to host its own world championship event instead, a month and a half after the Olympics. It was the first World Championships that the IAAF had hosted separate from the Olympic Games (traditionally the main championship for the sport). A second limited event was held in 1980, and the inaugural championships in 1983, with all the events, is considered the official start of the competition. Until 1980, the Olympic champions were considered as reigning World Champions. At their debut, these championships were then held every four years, until 1991, when they switched to a two-year cycle since.

世界田径锦标赛(英语:IAAF World Championships in Athletics)是创始于1983年的国际田径赛事,由世界田径总会主办,最初是每四年一届,1991年起改为每两年一届。


Life.

Although little is known of Regiomontanus' early life, it is believed that at eleven years of age, he became a student at the University of Leipzig, Saxony. In 1451 he continued his studies at Alma Mater Rudolfina, the university in Vienna, Austria. There he became a pupil and friend of Georg von Peuerbach. In 1452 he was awarded the bachelor degree ("baccalaureus"), and he was awarded his "magister artium" (Master of Arts) at the age of 21 in 1457. It is known that he held lectures in optics and ancient literature.  In 1460 the papal legate Basilios Bessarion came to Vienna on a diplomatic mission. Being a humanist scholar and great fan of the mathematical sciences, Bessarion sought out Peuerbach's company. George of Trebizond who was Bessarion's philosophical rival had recently produced a new Latin translation of Ptolemy's "Almagest" from the Greek, which Bessarion, correctly, regarded as inaccurate and badly translated, so he asked Peuerbach to produce a new one. Peuerbach's Greek was not good enough to do a translation but he knew the "Almagest" intimately so instead he started work on a modernised, improved abridgement of the work. Bessarion also invited Peuerbach to become part of his household and to accompany him back to Italy when his work in Vienna was finished. Peuerbach accepted the invitation on the condition that Regiomontanus could also accompany them. However Peuerbach fell ill in 1461 and died only having completed the first six books of his abridgement of the "Almagest". On his death bed Peuerbach made Regiomontanus promise to finish the book and publish it.  In 1461 Regiomontanus left Vienna with Bessarion and spent the next four years travelling around Northern Italy as a member of Bessarion's household, looking for and copying mathematical and astronomical manuscripts for Bessarion, who possessed the largest private library in Europe at the time. Regiomontanus also made the acquaintance of the leading Italian mathematicians of the age such as Giovanni Bianchini and Paolo dal Pozzo Toscanelli who had also been friends of Peuerbach during his prolonged stay in Italy more than twenty years earlier.  In 1467, he went to work for János Vitéz, archbishop of Esztergom. There he calculated extensive astronomical tables and built astronomical instruments. Next he went to Buda, and the court of Matthias Corvinus of Hungary, for whom he built an astrolabe, and where he collated Greek manuscripts for a handsome salary. The tables that he created while living in Hungary, his "Tabulae directionum", were designed for astrology, including finding astrological houses.  In 1471 Regiomontanus moved to the Free City of Nuremberg, in Franconia, then one of the Empire's important seats of learning, publication, commerce and art, where he worked with the humanist and merchant Bernhard Walther. Here he founded the world's first scientific printing press, and in 1472 he published the first printed astronomical textbook, the "Theoricae novae Planetarum" of his teacher Georg von Peurbach.  Regiomontanus and Bernhard Walther observed the comet of 1472. Regiomontanus tried to estimate its distance from Earth, using the angle of parallax. According to David A. Seargeant:  The 1472 comet was visible from Christmas Day 1471 to 1 March 1472 (Julian Calendar), a total of 59 days.  In 1475, Regiomontanus was called to Rome by Pope Sixtus IV on to work on the planned calendar reform. Sixtus promised substantial rewards, including the title of bishop of Regensburg, it is unlikely that he was actually appointed to the role.  On his way to Rome, stopping in Venice, he commissioned the publication of his "Calendarium" with Erhard Ratdolt (printed in 1476). Regiomontanus reached Rome, but he died there after only a few months, in his 41st year, on 6 July 1476. According to a rumor repeated by Gassendi in his Regiomontanus biography, he was poisoned by relatives of George of Trebizond whom he had criticized in his writing; it is however considered more likely that he died from the plague.

Works.

During his time in Italy he completed Peuerbach's "Almagest" abridgement, "Epytoma in almagesti Ptolemei". In 1464, he completed "De Triangulis omnimodis". "De Triangulis" (On Triangles) was one of the first textbooks presenting the current state of trigonometry and included lists of questions for review of individual chapters. In it he wrote:  His work on arithmetic and algebra, "Algorithmus Demonstratus", was among the first containing symbolic algebra. In 1465, he built a portable sundial for Pope Paul II.  In "Epytoma in almagesti Ptolemei", he critiqued the translation of "Almagest" by George of Trebizond, pointing out inaccuracies. Later Nicolaus Copernicus would refer to this book as an influence on his own work.  A prolific author, Regiomontanus was internationally famous in his lifetime. Despite having completed only a quarter of what he had intended to write, he left a substantial body of work. Nicolaus Copernicus' teacher, Domenico Maria Novara da Ferrara, referred to Regiomontanus as having been his own teacher. There is speculation that Regiomontanus had arrived at a theory of heliocentrism before he died; a manuscript shows particular attention to the heliocentric theory of the Pythagorean Aristarchus, mention was also given to the motion of the earth in a letter to a friend.  Much of the material on spherical trigonometry in Regiomontanus' "On Triangles" was taken directly from the twelfth-century work of Jabir ibn Aflah otherwise known as Geber, as noted in the sixteenth century by Gerolamo Cardano.

Legacy.

Simon Stevin, in his book describing decimal representation of fractions (De Thiende), cites the trigonometric tables of Regiomontanus as suggestive of positional notation.  Regiomontanus designed his own astrological house system, which became one of the most popular systems in Europe.  In 1561, Daniel Santbech compiled a collected edition of the works of Regiomontanus, "De triangulis planis et sphaericis libri quinque" (first published in 1533) and "Compositio tabularum sinum recto", as well as Santbech's own "Problematum astronomicorum et geometricorum sectiones septem". It was published in Basel by Henrich Petri and Petrus Perna.  There is an image of him in Hartmann Schedel's 1493 "Nuremberg Chronicle". He is holding an astrolabe. Yet, although there are thirteen illustrations of comets in the "'Chronicle" (from 471 to 1472), they are stylized, rather than representing the actual objects.  The crater Regiomontanus on the Moon is named after him.

Johannes Müller von Königsberg (6 June 1436 – 6 July 1476), better known as Regiomontanus (), was a mathematician, astrologer and astronomer of the German Renaissance, active in Vienna, Buda and Nuremberg. His contributions were instrumental in the development of Copernican heliocentrism in the decades following his death.

约翰尼斯·缪勒(,1436年-6月6日-1476年-7月6日),拉丁文名称为雷吉奥蒙塔努斯(Regiomontanus),德国天文学家。


Timeline of analog computers.

Precursors.

This is a list of examples of early computation devices considered precursors of the modern computers. Some of them may even have been dubbed as 'computers' by the press, though they may fail to fit modern definitions. The Antikythera mechanism was an orrery and considered an early mechanical analog computer, according to Derek J. de Solla Price. It was designed to calculate astronomical positions. It was discovered in 1901 in the Antikythera wreck off the Greek island of Antikythera, between Kythera and Crete, and has been dated to "circa" 100 BC during the Hellenistic period of Greece. Devices of a level of complexity comparable to that of the Antikythera mechanism would not reappear until a thousand years later.  Many mechanical aids to calculation and measurement were constructed for astronomical and navigation use. The planisphere was first described by Ptolemy in the 2nd century AD. The astrolabe was invented in the Hellenistic world in either the 1st or 2nd centuries BC and is often attributed to Hipparchus. A combination of the planisphere and dioptra, the astrolabe was effectively an analog computer capable of working out several different kinds of problems in spherical astronomy. An astrolabe incorporating a mechanical calendar computer and gear-wheels was invented by Abi Bakr of Isfahan, Persia in 1235. Abū Rayhān al-Bīrūnī invented the first mechanical geared lunisolar calendar astrolabe, an early fixed-wired knowledge processing machine with a gear train and gear-wheels, "circa" 1000 AD. The castle clock, a hydropowered mechanical astronomical clock invented by Al-Jazari in 1206, was the first programmable analog computer.  The sector, a calculating instrument used for solving problems in proportion, trigonometry, multiplication and division, and for various functions, such as squares and cube roots, was developed in the late 16th century and found application in gunnery, surveying and navigation.  The planimeter was a manual instrument to calculate the area of a closed figure by tracing over it with a mechanical linkage. The slide rule was invented around 1620–1630, shortly after the publication of the concept of the logarithm. It is a hand-operated analog computer for doing multiplication and division. As slide rule development progressed, added scales provided reciprocals, squares and square roots, cubes and cube roots, as well as transcendental functions such as logarithms and exponentials, circular and hyperbolic trigonometry and other functions. Aviation is one of the few fields where slide rules are still in widespread use, particularly for solving time–distance problems in light aircraft.  Mathematician and engineer Giovanni Plana devised a Perpetual Calendar machine, which, though a system of pulleys and cylinders and over, could predict the perpetual calendar for every year from 0 AD to 4000 AD, keeping track of leap years and varying day length.  The tide-predicting machine invented by Sir William Thomson in 1872 was of great utility to navigation in shallow waters. It used a system of pulleys and wires to automatically calculate predicted tide levels for a set period at a particular location.  The differential analyser, a mechanical analog computer designed to solve differential equations by integration, used wheel-and-disc mechanisms to perform the integration. In 1876 James Thomson had already discussed the possible construction of such calculators, but he had been stymied by the limited output torque of the ball-and-disk integrators. In a differential analyzer, the output of one integrator drove the input of the next integrator, or a graphing output. The torque amplifier was the advance that allowed these machines to work. Starting in the 1920s, Vannevar Bush and others developed mechanical differential analyzers.

Modern era.

The Dumaresq was a mechanical calculating device invented around 1902 by Lieutenant John Dumaresq of the Royal Navy. It was an analog computer that related vital variables of the fire control problem to the movement of one's own ship and that of a target ship. It was often used with other devices, such as a Vickers range clock to generate range and deflection data so the gun sights of the ship could be continuously set. A number of versions of the Dumaresq were produced of increasing complexity as development proceeded.  By 1912 Arthur Pollen had developed an electrically driven mechanical analog computer for fire-control systems, based on the differential analyser. It was used by the Imperial Russian Navy in World War I.  Starting in 1929, AC network analyzers were constructed to solve calculation problems related to electrical power systems that were too large to solve with numerical methods at the time. These were essentially scale models of the electrical properties of the full-size system. Since network analyzers could handle problems too large for analytic methods or hand computation, they were also used to solve problems in nuclear physics and in the design of structures. More than 50 large network analyzers were built by the end of the 1950s.  World War II era gun directors, gun data computers, and bomb sights used mechanical analog computers. In 1942 Helmut Hölzer built a fully electronic analog computer at Peenemünde Army Research Center as an embedded control system ("mixing device") to calculate V-2 rocket trajectories from the accelerations and orientations (measured by gyroscopes) and to stabilize and guide the missile. Mechanical analog computers were very important in gun fire control in World War II, The Korean War and well past the Vietnam War; they were made in significant numbers.  In the period 1930–1945 in the Netherlands Johan van Veen developed an analogue computer to calculate and predict tidal currents when the geometry of the channels are changed. Around 1950 this idea was developed into the Deltar, an analogue computer supporting the closure of estuaries in the southwest of the Netherlands (the Delta Works).  The FERMIAC was an analog computer invented by physicist Enrico Fermi in 1947 to aid in his studies of neutron transport. Project Cyclone was an analog computer developed by Reeves in 1950 for the analysis and design of dynamic systems. Project Typhoon was an analog computer developed by RCA in 1952. It consisted of over 4000 electron tubes and used 100 dials and 6000 plug-in connectors to program. The MONIAC Computer was a hydraulic model of a national economy first unveiled in 1949.  Computer Engineering Associates was spun out of Caltech in 1950 to provide commercial services using the "Direct Analogy Electric Analog Computer" ("the largest and most impressive general-purpose analyzer facility for the solution of field problems") developed there by Gilbert D. McCann, Charles H. Wilts, and Bart Locanthi.  Educational analog computers illustrated the principles of analog calculation. The Heathkit EC-1, a $199 educational analog computer, was made by the Heath Company, US. It was programmed using patch cords that connected nine operational amplifiers and other components. General Electric also marketed an "educational" analog computer kit of a simple design in the early 1960s consisting of a two transistor tone generators and three potentiometers wired such that the frequency of the oscillator was nulled when the potentiometer dials were positioned by hand to satisfy an equation. The relative resistance of the potentiometer was then equivalent to the formula of the equation being solved. Multiplication or division could be performed, depending on which dials were inputs and which was the output. Accuracy and resolution was limited and a simple slide rule was more accurate—however, the unit did demonstrate the basic principle.  Analog computer designs were published in electronics magazines. One example is the PE Analogue Computer, published in Practical Electronics in the September 1978 edition. Another more modern hybrid computer design was published in Everyday Practical Electronics in 2002. An example described in the EPE Hybrid Computer was the flight of a VTOL aircraft like the Harrier jump jet. The altitude and speed of the aircraft were calculated by the analog part of the computer and sent to a PC via a digital microprocessor and displayed on the PC screen.  In industrial process control, analog loop controllers were used to automatically regulate temperature, flow, pressure, or other process conditions. The technology of these controllers ranged from purely mechanical integrators, through vacuum-tube and solid-state devices, to emulation of analog controllers by microprocessors.

Electronic analog computers.

The similarity between linear mechanical components, such as springs and dashpots (viscous-fluid dampers), and electrical components, such as capacitors, inductors, and resistors is striking in terms of mathematics. They can be modeled using equations of the same form.  However, the difference between these systems is what makes analog computing useful. If one considers a simple mass–spring system, constructing the physical system would require making or modifying the springs and masses. This would be followed by attaching them to each other and an appropriate anchor, collecting test equipment with the appropriate input range, and finally, taking measurements. In more complicated cases, such as suspensions for racing cars, experimental construction, modification, and testing is both complicated and expensive.  The electrical equivalent can be constructed with a few operational amplifiers (op amps) and some passive linear components; all measurements can be taken directly with an oscilloscope. In the circuit, the (simulated)'stiffness of the spring', for instance, can be changed by adjusting the parameters of a capacitor. The electrical system is an analogy to the physical system, hence the name, but it is less expensive to construct, generally safer, and typically much easier to modify.  As well, an electronic circuit can typically operate at higher frequencies than the system being simulated. This allows the simulation to run faster than real time (which could, in some instances, be hours, weeks, or longer). Experienced users of electronic analog computers said that they offered a comparatively intimate control and understanding of the problem, relative to digital simulations.  The drawback of the mechanical-electrical analogy is that electronics are limited by the range over which the variables may vary due to the fixed supply voltage. Therefore, each problem must be scaled to its parameters and dimensions—e.g., the expected magnitudes of the velocity and the position of a spring pendulum. Improperly scaled problems might suffer from higher noise levels. Floating-point digital calculations have a huge dynamic range but might also suffer from imprecision if tiny differences of huge values lead to numerical instability.  These electric circuits can also easily perform a wide variety of simulations. For example, voltage can simulate water pressure and electric current can simulate rate of flow in terms of cubic metres per second. An integrator can provide the total accumulated volume of liquid, using an input current proportional to the (possibly varying) flow rate.  Analog computers are especially well-suited to representing situations described by differential equations. Occasionally, they were used when a system of differential equations proved very difficult to solve by traditional means. As a simple example, the dynamics of a spring-mass system can be described by the equation formula_1, with formula_2 as the vertical position of a mass formula_3, formula_4 the damping coefficient, formula_5 the spring constant and formula_6 the gravity of Earth. For analog computing, the equation is programmed as formula_7. The equivalent analog circuit consists of two integrators for the state variables formula_8 (speed) and formula_2 (position), one inverter, and three potentiometers. The circuit has to consider that both integration and addition units invert the signal polarity.  The accuracy of an analog computer is limited by its computing elements as well as quality of the internal power and electrical interconnections. The precision of the analog computer readout was limited chiefly by the precision of the readout equipment used, generally three or four significant figures. The precision of a digital computer is limited by the word size; arbitrary-precision arithmetic, while relatively slow, provides any practical degree of precision that might be needed. However, in most cases the precision of an analog computer is absolutely sufficient given the uncertainty of the model characteristics and its technical parameters.  Many small computers dedicated to specific computations are still part of industrial regulation equipment, but from the 1950s to the 1970s, general-purpose analog computers were the only systems fast enough for real time simulation of dynamic systems, especially in the aircraft, military and aerospace field.  In the 1960s, the major manufacturer was Electronic Associates of Princeton, New Jersey, with its 231R Analog Computer (vacuum tubes, 20 integrators) and subsequently its EAI 8800 Analog Computer (solid state operational amplifiers, 64 integrators). Its challenger was Applied Dynamics of Ann Arbor, Michigan.  Although the basic technology for analog computers is usually operational amplifiers (also called "continuous current amplifiers" because they have no low frequency limitation), in the 1960s an attempt was made in the French ANALAC computer to use an alternative technology: medium frequency carrier and non dissipative reversible circuits.  In the 1970s every big company and administration concerned with problems in dynamics had a big analog computing center, for example:

Analog–digital hybrids.

Analog computing devices are fast, digital computing devices are more versatile and accurate, so the idea is to combine the two processes for the best efficiency. An example of such hybrid elementary device is the hybrid multiplier where one input is an analog signal, the other input is a digital signal and the output is analog. It acts as an analog potentiometer upgradable digitally. This kind of hybrid technique is mainly used for fast dedicated real time computation when computing time is very critical as signal processing for radars and generally for controllers in embedded systems.  In the early 1970s analog computer manufacturers tried to tie together their analog computer with a digital computer to get the advantages of the two techniques. In such systems, the digital computer controlled the analog computer, providing initial set-up, initiating multiple analog runs, and automatically feeding and collecting data. The digital computer may also participate to the calculation itself using analog-to-digital and digital-to-analog converters.  The largest manufacturer of hybrid computers was Electronics Associates. Their hybrid computer model 8900 was made of a digital computer and one or more analog consoles. These systems were mainly dedicated to large projects such as the Apollo program and Space Shuttle at NASA, or Ariane in Europe, especially during the integration step where at the beginning everything is simulated, and progressively real components replace their simulated part.  Only one company was known as offering general commercial computing services on its hybrid computers, CISI of France, in the 1970s.  The best reference in this field is the 100,000 simulations runs for each certification of the automatic landing systems of Airbus and Concorde aircraft.  After 1980, purely digital computers progressed more and more rapidly and were fast enough to compete with analog computers. One key to the speed of analog computers was their fully parallel computation, but this was also a limitation. The more equations required for a problem, the more analog components were needed, even when the problem wasn't time critical. "Programming" a problem meant interconnecting the analog operators; even with a removable wiring panel this was not very versatile. Today there are no more big hybrid computers, but only hybrid components.

Implementations.

Mechanical analog computers.

While a wide variety of mechanisms have been developed throughout history, some stand out because of their theoretical importance, or because they were manufactured in significant quantities.  Most practical mechanical analog computers of any significant complexity used rotating shafts to carry variables from one mechanism to another. Cables and pulleys were used in a Fourier synthesizer, a tide-predicting machine, which summed the individual harmonic components. Another category, not nearly as well known, used rotating shafts only for input and output, with precision racks and pinions. The racks were connected to linkages that performed the computation. At least one US Naval sonar fire control computer of the later 1950s, made by Librascope, was of this type, as was the principal computer in the Mk. 56 Gun Fire Control System.  Online, there is a remarkably clear illustrated reference (OP 1140) that describes the fire control computer mechanisms. For adding and subtracting, precision miter-gear differentials were in common use in some computers; the Ford Instrument Mark I Fire Control Computer contained about 160 of them.  Integration with respect to another variable was done by a rotating disc driven by one variable. Output came from a pickoff device (such as a wheel) positioned at a radius on the disc proportional to the second variable. (A carrier with a pair of steel balls supported by small rollers worked especially well. A roller, its axis parallel to the disc's surface, provided the output. It was held against the pair of balls by a spring.)  Arbitrary functions of one variable were provided by cams, with gearing to convert follower movement to shaft rotation.  Functions of two variables were provided by three-dimensional cams. In one good design, one of the variables rotated the cam. A hemispherical follower moved its carrier on a pivot axis parallel to that of the cam's rotating axis. Pivoting motion was the output. The second variable moved the follower along the axis of the cam. One practical application was ballistics in gunnery.  Coordinate conversion from polar to rectangular was done by a mechanical resolver (called a "component solver" in US Navy fire control computers). Two discs on a common axis positioned a sliding block with pin (stubby shaft) on it. One disc was a face cam, and a follower on the block in the face cam's groove set the radius. The other disc, closer to the pin, contained a straight slot in which the block moved. The input angle rotated the latter disc (the face cam disc, for an unchanging radius, rotated with the other (angle) disc; a differential and a few gears did this correction).  Referring to the mechanism's frame, the location of the pin corresponded to the tip of the vector represented by the angle and magnitude inputs. Mounted on that pin was a square block.  Rectilinear-coordinate outputs (both sine and cosine, typically) came from two slotted plates, each slot fitting on the block just mentioned. The plates moved in straight lines, the movement of one plate at right angles to that of the other. The slots were at right angles to the direction of movement. Each plate, by itself, was like a Scotch yoke, known to steam engine enthusiasts.  During World War II, a similar mechanism converted rectilinear to polar coordinates, but it was not particularly successful and was eliminated in a significant redesign (USN, Mk. 1 to Mk. 1A).  Multiplication was done by mechanisms based on the geometry of similar right triangles. Using the trigonometric terms for a right triangle, specifically opposite, adjacent, and hypotenuse, the adjacent side was fixed by construction. One variable changed the magnitude of the opposite side. In many cases, this variable changed sign; the hypotenuse could coincide with the adjacent side (a zero input), or move beyond the adjacent side, representing a sign change.  Typically, a pinion-operated rack moving parallel to the (trig.-defined) opposite side would position a slide with a slot coincident with the hypotenuse. A pivot on the rack let the slide's angle change freely. At the other end of the slide (the angle, in trig, terms), a block on a pin fixed to the frame defined the vertex between the hypotenuse and the adjacent side.  At any distance along the adjacent side, a line perpendicular to it intersects the hypotenuse at a particular point. The distance between that point and the adjacent side is some fraction that is the product of "1" the distance from the vertex, and "2" the magnitude of the opposite side.  The second input variable in this type of multiplier positions a slotted plate perpendicular to the adjacent side. That slot contains a block, and that block's position in its slot is determined by another block right next to it. The latter slides along the hypotenuse, so the two blocks are positioned at a distance from the (trig.) adjacent side by an amount proportional to the product.  To provide the product as an output, a third element, another slotted plate, also moves parallel to the (trig.) opposite side of the theoretical triangle. As usual, the slot is perpendicular to the direction of movement. A block in its slot, pivoted to the hypotenuse block positions it.  A special type of integrator, used at a point where only moderate accuracy was needed, was based on a steel ball, instead of a disc. It had two inputs, one to rotate the ball, and the other to define the angle of the ball's rotating axis. That axis was always in a plane that contained the axes of two movement-pickoff rollers, quite similar to the mechanism of a rolling-ball computer mouse (in this mechanism, the pickoff rollers were roughly the same diameter as the ball). The pickoff roller axes were at right angles.  A pair of rollers "above" and "below" the pickoff plane were mounted in rotating holders that were geared together. That gearing was driven by the angle input, and established the rotating axis of the ball. The other input rotated the "bottom" roller to make the ball rotate.  Essentially, the whole mechanism, called a component integrator, was a variable-speed drive with one motion input and two outputs, as well as an angle input. The angle input varied the ratio (and direction) of coupling between the "motion" input and the outputs according to the sine and cosine of the input angle.  Although they did not accomplish any computation, electromechanical position servos were essential in mechanical analog computers of the "rotating-shaft" type for providing operating torque to the inputs of subsequent computing mechanisms, as well as driving output data-transmission devices such as large torque-transmitter synchros in naval computers.  Other non-computational mechanisms included internal odometer-style counters with interpolating drum dials for indicating internal variables, and mechanical multi-turn limit stops.  Considering that accurately controlled rotational speed in analog fire-control computers was a basic element of their accuracy, there was a motor with its average speed controlled by a balance wheel, hairspring, jeweled-bearing differential, a twin-lobe cam, and spring-loaded contacts (ship's AC power frequency was not necessarily accurate, nor dependable enough, when these computers were designed).

Electronic analog computers.

Electronic analog computers typically have front panels with numerous jacks (single-contact sockets) that permit patch cords (flexible wires with plugs at both ends) to create the interconnections that define the problem setup. In addition, there are precision high-resolution potentiometers (variable resistors) for setting up (and, when needed, varying) scale factors. In addition, there is usually a zero-center analog pointer-type meter for modest-accuracy voltage measurement. Stable, accurate voltage sources provide known magnitudes.  Typical electronic analog computers contain anywhere from a few to a hundred or more operational amplifiers ("op amps"), named because they perform mathematical operations. Op amps are a particular type of feedback amplifier with very high gain and stable input (low and stable offset). They are always used with precision feedback components that, in operation, all but cancel out the currents arriving from input components. The majority of op amps in a representative setup are summing amplifiers, which add and subtract analog voltages, providing the result at their output jacks. As well, op amps with capacitor feedback are usually included in a setup; they integrate the sum of their inputs with respect to time.  Integrating with respect to another variable is the nearly exclusive province of mechanical analog integrators; it is almost never done in electronic analog computers. However, given that a problem solution does not change with time, time can serve as one of the variables.  Other computing elements include analog multipliers, nonlinear function generators, and analog comparators.  Electrical elements such as inductors and capacitors used in electrical analog computers had to be carefully manufactured to reduce non-ideal effects. For example, in the construction of AC power network analyzers, one motive for using higher frequencies for the calculator (instead of the actual power frequency) was that higher-quality inductors could be more easily made. Many general-purpose analog computers avoided the use of inductors entirely, re-casting the problem in a form that could be solved using only resistive and capacitive elements, since high-quality capacitors are relatively easy to make.  The use of electrical properties in analog computers means that calculations are normally performed in real time (or faster), at a speed determined mostly by the frequency response of the operational amplifiers and other computing elements. In the history of electronic analog computers, there were some special high-speed types.  Nonlinear functions and calculations can be constructed to a limited precision (three or four digits) by designing function generators—special circuits of various combinations of resistors and diodes to provide the nonlinearity. Typically, as the input voltage increases, progressively more diodes conduct.  When compensated for temperature, the forward voltage drop of a transistor's base-emitter junction can provide a usably accurate logarithmic or exponential function. Op amps scale the output voltage so that it is usable with the rest of the computer.  Any physical process that models some computation can be interpreted as an analog computer. Some examples, invented for the purpose of illustrating the concept of analog computation, include using a bundle of spaghetti as a model of sorting numbers; a board, a set of nails, and a rubber band as a model of finding the convex hull of a set of points; and strings tied together as a model of finding the shortest path in a network. These are all described in Dewdney (1984).

Components.

Analog computers often have a complicated framework, but they have, at their core, a set of key components that perform the calculations. The operator manipulates these through the computer's framework.  Key hydraulic components might include pipes, valves and containers.  Key mechanical components might include rotating shafts for carrying data within the computer, miter gear differentials, disc/ball/roller integrators, cams (2-D and 3-D), mechanical resolvers and multipliers, and torque servos.  Key electrical/electronic components might include:  The core mathematical operations used in an electric analog computer are:  In some analog computer designs, multiplication is much preferred to division. Division is carried out with a multiplier in the feedback path of an Operational Amplifier.  Differentiation with respect to time is not frequently used, and in practice is avoided by redefining the problem when possible. It corresponds in the frequency domain to a high-pass filter, which means that high-frequency noise is amplified; differentiation also risks instability.

Limitations.

In general, analog computers are limited by non-ideal effects. An analog signal is composed of four basic components: DC and AC magnitudes, frequency, and phase. The real limits of range on these characteristics limit analog computers. Some of these limits include the operational amplifier offset, finite gain, and frequency response, noise floor, non-linearities, temperature coefficient, and parasitic effects within semiconductor devices. For commercially available electronic components, ranges of these aspects of input and output signals are always figures of merit.

Decline.

In the 1950s to 1970s, digital computers based on first vacuum tubes, transistors, integrated circuits and then micro-processors became more economical and precise. This led digital computers to largely replace analog computers. Even so, some research in analog computation is still being done. A few universities still use analog computers to teach control system theory. The American company Comdyna manufactured small analog computers. At Indiana University Bloomington, Jonathan Mills has developed the Extended Analog Computer based on sampling voltages in a foam sheet. At the Harvard Robotics Laboratory, analog computation is a research topic. Lyric Semiconductor's error correction circuits use analog probabilistic signals. Slide rules are still popular among aircraft personnel.

Resurgence.

With the development of very-large-scale integration (VLSI) technology, Yannis Tsividis' group at Columbia University has been revisiting analog/hybrid computers design in standard CMOS process. Two VLSI chips have been developed, an 80th-order analog computer (250 nm) by Glenn Cowan in 2005 and a 4th-order hybrid computer (65 nm) developed by Ning Guo in 2015, both targeting at energy-efficient ODE/PDE applications. Glenn's chip contains 16 macros, in which there are 25 analog computing blocks, namely integrators, multipliers, fanouts, few nonlinear blocks. Ning's chip contains one macro block, in which there are 26 computing blocks including integrators, multipliers, fanouts, ADCs, SRAMs and DACs. Arbitrary nonlinear function generation is made possible by the ADC+SRAM+DAC chain, where the SRAM block stores the nonlinear function data. The experiments from the related publications revealed that VLSI analog/hybrid computers demonstrated about 1–2 orders magnitude of advantage in both solution time and energy while achieving accuracy within 5%, which points to the promise of using analog/hybrid computing techniques in the area of energy-efficient approximate computing. In 2016, a team of researchers developed a compiler to solve differential equations using analog circuits.

Practical examples.

These are examples of analog computers that have been constructed or practically used:  Analog (audio) synthesizers can also be viewed as a form of analog computer, and their technology was originally based in part on electronic analog computer technology. The ARP 2600's Ring Modulator was actually a moderate-accuracy analog multiplier.  The Simulation Council (or Simulations Council) was an association of analog computer users in US. It is now known as The Society for Modeling and Simulation International. The Simulation Council newsletters from 1952 to 1963 are available online and show the concerns and technologies at the time, and the common use of analog computers for missilry.

An analog computer or analogue computer is a type of computer that uses the continuously changeable aspects of physical phenomena such as electrical, mechanical, or hydraulic quantities to model the problem being solved. In contrast, digital computers represent varying quantities symbolically and by discrete values of both time and amplitude.

模拟计算机(Analog computer),是计算机的一种形式,它使用电子的,机械的或液压的量等物理现象的不断变化的方面来模拟所要解决的问题。 相反,数字计算机象征性地表示不同数量,因为它们的数值发生了变化。 由于模拟计算机不使用离散值,而是使用连续值,所以过程不能像精确等同那样可靠地重复进行,就像它们可以使用图灵机一样。 与数字信号处理不同,模拟计算机不受量化噪声的影响,但受模拟噪声的限制。