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20125
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Maastricht
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Maastricht
municipalities (some in Belgium) and from members of the Dutch and Belgian parliament. The plan has been the subject of various legal challenges and has not been carried out up to this date (2014).
On 16 December 2010, the Court of Justice of the European Union upheld a local Maastricht ban on the sale of cannabis to foreign tourists, restricting entrance to coffeeshops to residents of Maastricht. The ban did not affect scientific or medical usage. In 2011, the Dutch government introduced a similar national system, the "wietpas" ("cannabis pass"), restricting access to Dutch coffeeshops to residents of the Netherlands. After protests from local mayors about the difficulty of implementing the
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Maastricht
issuing of wietpasses, Dutch parliament in 2012 agreed to replace the pass by any proof of residency. The new system has led to a slight reduction in drug tourism to cannabis shops in Maastricht but at the same time to an increase of drug dealing on the street.
# Transport.
## By car.
Maastricht is served by the A2 and A79 motorways. The city can be reached from Brussels and Cologne in approximately one hour and from Amsterdam in about two and a half hours.
The A2 motorway runs through Maastricht in a double-decked tunnel. Before 2016, the A2 motorway ran through the city; heavily congested, it caused air pollution in the urban area. Construction of a two-level tunnel designed to solve these
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problems started in 2011 and was opened (in stages) by December 2016.
In spite of several large underground car parks, parking in the city centre forms a major problem during weekends and bank holidays because of the large numbers of visitors. Parking fees are deliberately high to make visitors to use public transport or park and ride facilities away from the centre.
## By train.
Maastricht is served by three rail operators, all of which call at the main Maastricht railway station near the centre and two of which call at the smaller Maastricht Randwyck, near the business and university district. Only Arriva also calls at Maastricht Noord, which opened in 2013. Intercity trains northwards
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to Amsterdam, Eindhoven, Den Bosch and Utrecht are operated by Dutch Railways. The National Railway Company of Belgium runs south to Liège in Belgium. The line to Heerlen, Valkenburg and Kerkrade is operated by Arriva. The former railway to Aachen was closed down in the 1980s. A small section of the old westbound railway to Hasselt (Belgium) was restored in recent years and will be used as a modern tramline, scheduled to open in 2023.
## By tram.
The Dutch and Flanders governments reached an agreement in 2014 to build a new tram route, the Hasselt – Maastricht tramway, as part of the larger Spartacus scheme. It was scheduled to take three years, from 2015 to 2018, and to cost €283 million.
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Maastricht
However, the planning process has been heavily delayed, and as of 2018, construction has not yet started. The tram is now scheduled to be operating in 2024. When completed, the tram will carry passengers from Maastricht city centre to Hasselt city centre in 30 minutes. It will be operated by the Belgian transport company De Lijn, with 2 scheduled stops in Maastricht and another 10 in Flanders.
## By bus.
Regular bus lines connect the city centre, outer areas, business districts and railway stations. The regional Arriva bus network extends to most parts of South Limburg and Aachen in Germany. Regional buses by De Lijn connect Maastricht with Hasselt, Tongeren and Maasmechelen, and one bus connects
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Maastricht with Liège, operated by TEC.
## By air.
Maastricht is served by the nearby Maastricht Aachen Airport , in nearby Beek, and it is informally referred to by that name. The airport is served by Corendon Dutch Airlines and Ryanair. The airport has regular scheduled flights to destinations around the Mediterranean as well as charter flights to Lourdes and operated by Enter Air. The airport is located about north of the city centre.
## By boat.
Maastricht has a river port ("Beatrixhaven") and is connected by water with Belgium and the rest of the Netherlands through the river Meuse, the Juliana Canal, the Albert Canal and the Zuid-Willemsvaart. Although there are no regular boat connections
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to other cities, various organized boat trips for tourists connect Maastricht with Belgium cities such as Liège.
## Distances to other cities.
These distances are as the crow flies and so do not represent actual overland distances.
- Liège: south
- Aachen: east
- Eindhoven: north-west
- Düsseldorf: north-east
- Cologne: east
- Brussels: west
- Antwerp: north-west
- Bonn: south-east
- Charleroi: south-west
- Luxembourg City: south
- Ghent: west
- Utrecht: north-west
- Rotterdam: north-west
- Amsterdam: north-west
- Lille: west
- Frankfurt am Main: south-east
- Groningen: north
- Strasbourg: south-east
- Paris: south-west
- Hannover: north-east
- Stuttgart: south-east
-
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Basel: south-east
- London: north-west
- Zürich: south-east
# Education.
## Secondary education.
- "Bernard Lievegoedschool" (Anthroposophical education)
- "Bonnefantencollege"
- "Porta Mosana College"
- Sint-Maartenscollege
- United World College Maastricht
## Tertiary education.
- Maastricht University (Dutch: "Universiteit Maastricht" or UM) including:
- University College Maastricht
- Maastricht School of Management
- Teikyo University (Maastricht campus closed in 2007)
- Zuyd University of Applied Sciences (Dutch: "Hogeschool Zuyd", also has departments in Sittard and Heerlen) including:
- Academy for Dramatic Arts Maastricht (Dutch: "Toneelacademie Maastricht")
- School
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of Fine Arts Maastricht (Dutch: "Academie Beeldende Kunsten Maastricht")
- Maastricht Academy of Music (Dutch: "Conservatorium Maastricht")
- "Academy of architecture"
- "Teachers training college"
- "Faculty of International Business and Communication"
- "Maastricht Hotel Management School"
## Other.
- Jan Van Eyck Academie - post-academic art institute
- Berlitz Language School Maastricht
- "Talenacademie Nederland"
# International relations.
## Twin towns.
Maastricht is twinned with:
- Liège, Belgium
- Koblenz, Germany
- Rama, Nicaragua
- Chengdu, China (since 2012)
## Other relations.
- Most Ancient European Towns Network
# Notable people.
## Born in Maastricht.
- Bryan
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Smeets (born 1992) - Football player
- Jean-Eugène-Charles Alberti (1777 – after 1843) – painter
- Henri Arends (1921–1993) – conductor
- Doris Baaten (born 1956) – voice actress
- Mieke de Boer (born 1980) – female darts player
- Alphons Boosten (1893–1951) – architect
- Theo Bovens (born 1959) – politician
- Joseph Bruyère (born 1948) – Belgian cyclist
- Jean-Baptiste Coclers (1696–1772) – painter
- Louis Bernard Coclers (1740–1817) – painter
- Peter Debye (1884–1966) – Nobel prize winning chemist
- Tom Dumoulin (born 1990) – cyclist, Giro d'Italia winner
- Hendrick Fromantiou (1633/4 – after 1693) – still life painter
- Joop Haex (1911–2002) – politician
- André Henri Constant
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van Hasselt (1806–1874) – French-writing poet
- Hubert Hermans (born 1937) – psychologist and creator of Dialogical Self Theory
- Pieter van den Hoogenband (born 1978) – swimmer and a triple Olympic champion
- Pierre Kemp (1886–1967) – poet
- Sjeng Kerbusch (1947–1991) – behavior geneticist
- Mathieu Kessels (1784–1836) – sculptor
- Lambert of Maastricht (c. 636 – c. 705) – bishop, saint
- Eric van der Luer (born 1965) – footballer, football manager
- Pierre Lyonnet (1708–1789) – naturalist, cryptographer, engraver
- Félix de Mérode (1791–1857) – politician, writer
- Jan Pieter Minckeleers (1748–1824) – scientist and inventor of coal gas lighting
- Bram Moszkowicz (born 1960) – ex-barrister
-
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Benny Neyman (1951–2008) – singer of popular songs
- Tom Nijssen (born 1964) – tennis player
- Jacques Ogg (born 1948) – harpsichordist
- Henrietta d'Oultremont (1792–1864) – second wife of William I of the Netherlands
- Jan Peumans (born 1951) – Belgian politician
- Guido Pieters (born 1948) – film director
- Dick Raaymakers (1930–2013) – composer, theater maker
- Prince Rajcomar (born 1985) – football player
- Louis Regout (1861–1915) – politician
- André Rieu (born 1949) – violinist, conductor and composer
- Fred Rompelberg (born 1945) – cyclist, former holder of the world record for paced bicycle land speed
- Louis Rutten (1884-1946) – Dutch geologist
- Henri Sarolea (1844–1900)
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– railway entrepreneur and contractor
- Hubert Soudant (born 1946) – conductor
- Victor de Stuers (1843–1916) – politician, monument conservationist
- Jac. P. Thijsse (1865–1945) – botanist, conservationist
- Frans Timmermans (born 1961) – politician
- Johann Friedrich August Tischbein (1750–1812) – portrait painter
- Maxime Verhagen (born 1956) – politician
- Hubert Vos (1855–1935) – painter
- Ad Wijnands (born 1959) – cyclist, Tour de France stage winner
- Jeroen Willems (1962–2012) – actor, singer
- Henri Winkelman (1876–1952) – general
- Danny Wintjens (born 1983) – football goalkeeper
- Boudewijn Zenden (born 1976) – football player
- Kim Zwarts (born 1955) – photographer
##
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Residing in Maastricht.
- Jo Bonfrere (born 1946) – football player
- Willy Brokamp (born 1946) – football player
- Jeroen Brouwers (born 1940) – writer, journalist
- Gondulph of Maastricht (c. 524 – c. 607) – bishop, saint
- Theo Hiddema (born 1944) – lawyer
- Willem Hofhuizen (1915–1986) – painter
- Monulph of Maastricht (6th century) – bishop, saint
- Max Moszkowicz (born 1926) – lawyer
- Servatius of Maastricht (4th century – 384?) – bishop, saint
- Jan van Steffeswert (15th/16th century) – sculptor, wood carver
- Aert van Tricht (15th/16th century) – metal caster
- Henric van Veldeke (12th century) – poet, hagiographer
# Local anthem.
In 2002 the municipal government officially
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agiographer
# Local anthem.
In 2002 the municipal government officially adopted a local anthem (Limburgish (Maastrichtian variant): "Mestreechs Volksleed", ) composed of lyrics in Maastrichtian. The theme was originally written by Ciprian Porumbescu (1853–1883).
# See also.
- Jewish inhabitants of Maastricht
- Maastricht Treaty
- Treaty of Maastricht (1843)
- The Maastrichtian Age marks the end of the Cretaceous Period of geological time
# References.
- Notes
- Literature
# External links.
- Maastricht city portal
- Maastricht municipality website
- Maastricht in Roman times
- Webpage about Maastricht fortifications
- Webpage about the 1673 siege
- Maastricht tourism website
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20145
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Maroboduus
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https://en.wikipedia.org/w/index.php?title=Maroboduus
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Maroboduus
Maroboduus
Maroboduus (born "circa" 30 BC, died in AD 37), was a Romanized king of the Germanic Suebi, who under pressure from the wars of the Cherusci and Romans, and losing the Suevic Semnones and Langobardi from his kingdom, moved with the Marcomanni into the forests of Bohemia, near to the Quadi.
The name "Maroboduus" can be broken down into two Celtic elements, "māro-" meaning "great" (cf. Welsh "mawr", Irish "mór"), and "bodwos" meaning "raven" (cf. Irish "badhbh").
# Biography.
Maroboduus was born into a noble family of the Marcomanni. As a young man, he lived in Italy and enjoyed the favour of the Emperor Augustus. The Marcomanni had been beaten utterly by the Romans in 10 BC. About
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Maroboduus
9 BC, Maroboduus returned to Germania and became ruler of his people. To deal with the threat of Roman expansion into the Rhine-Danube basin, he led the Marcomanni to the area later known as Bohemia to be outside the range of the Roman influence. There, he took the title of king and organized a confederation of several neighboring Germanic tribes. He was the first documented ruler of Bohemia.
Augustus planned in 6 AD to destroy the kingdom of Maroboduus, which he considered to be too dangerous for the Romans. The future emperor Tiberius commanded 12 legions to attack the Marcomanni, but the outbreak of a revolt in Illyria, and the need for troops there, forced Tiberius to conclude a treaty
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with Maroboduus and to recognize him as king.
# War with Arminius and death.
His rivalry with Arminius, the Cheruscan leader who inflicted the devastating defeat at the Battle of the Teutoburg Forest on the Romans under Publius Quinctilius Varus in 9 AD, prevented a concerted attack on Roman territory across the Rhine in the north (by Arminius) and in the Danube basin in the south (by Maroboduus).
However, according to the first-century AD historian Marcus Velleius Paterculus, Arminius sent Varus's head to Maroboduus, but the king of the Marcomanni sent it to Augustus. In the revenge war of Tiberius and Germanicus against the Cherusci, Maroboduus stayed neutral.
In 17 AD, war broke out between
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Maroboduus
Arminius and Maroboduus, and after an indecisive battle, Maroboduus withdrew into the hilly forests of Bohemia, in 18 AD. In the next year, Catualda, a young Marcomannic nobleman living in exile among the Gutones, returned, perhaps by a subversive Roman intervention, and defeated Maroboduus. The deposed king had to flee to Italy, and Tiberius detained him 18 years in Ravenna. There, Maroboduus died in 37 AD. Catualda was, in turn, defeated by the Hermunduri Vibilius, after which the realm was ruled by the Quadian Vannius. Vannius was himself also deposed by Vibilius, in coordination with his nephews Vangio and Sido, who then ruled as Roman client kings.
# Further reading.
- Peter Kehne: "Marbod."
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comannic nobleman living in exile among the Gutones, returned, perhaps by a subversive Roman intervention, and defeated Maroboduus. The deposed king had to flee to Italy, and Tiberius detained him 18 years in Ravenna. There, Maroboduus died in 37 AD. Catualda was, in turn, defeated by the Hermunduri Vibilius, after which the realm was ruled by the Quadian Vannius. Vannius was himself also deposed by Vibilius, in coordination with his nephews Vangio and Sido, who then ruled as Roman client kings.
# Further reading.
- Peter Kehne: "Marbod." In: "Reallexikon der Germanischen Altertumskunde", vol. 19 (2001), p. 258-262.
- Tacitus, "Annals", & .
# External links.
- Gaulish English Dictionary
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20149
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Mike Muuss
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https://en.wikipedia.org/w/index.php?title=Mike%20Muuss
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Mike Muuss
Mike Muuss
Michael John Muuss (October 16, 1958 – November 20, 2000) was the American author of the freeware network tool ping.
# Career.
A graduate of Johns Hopkins University, Muuss was a senior scientist specializing in geometric solid modeling, ray-tracing, MIMD architectures and digital computer networks at the United States Army Research Laboratory at Aberdeen Proving Ground, Maryland when he died. He wrote a number of software packages (including BRL-CAD) and network tools (including ttcp and the concept of the default route or "default gateway") and contributed to many others (including BIND).
However, the thousand-line ping, which he wrote in December 1983 while working at the Ballistic
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Mike Muuss
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Mike Muuss
Research Laboratory, is the program for which he is most remembered. Due to its usefulness, ping has been implemented on a large number of operating systems, initially BSD and Unix, but later others including Windows and Mac OS X.
In 1993, the USENIX Association gave a Lifetime Achievement Award ("Flame") to the Computer Systems Research Group at University of California, Berkeley, honoring 180 individuals, including Muuss, who contributed to the CSRG's 4.4BSD-Lite release.
Muuss is mentioned in two books, "The Cuckoo's Egg" () and "Cyberpunk: Outlaws and Hackers on the Computer Frontier" (), for his role in tracking down crackers. He also is mentioned in Peter Salus's "A Quarter Century of
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Mike Muuss
uckoo's Egg" () and "Cyberpunk: Outlaws and Hackers on the Computer Frontier" (), for his role in tracking down crackers. He also is mentioned in Peter Salus's "A Quarter Century of UNIX".
Muuss died in an automobile collision on Interstate 95 on November 20, 2000. The Michael J. Muuss Research Award, set up by friends and family of Muuss, memorializes him at Johns Hopkins University.
# See also.
- Heterogeneous Element Processor
- ttcp
- ping
- BRL-CAD
# External links.
- Mike Muuss's home page
- Mike Muuss, The Story of the PING Program
- An Early UseNet Post by Mike Muuss Discussing Ping's history ICMP As A Diagnostic Tool?
- Mike Muuss, The Story of the TTCP Program
- BRL-CAD
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20151
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Mousse
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https://en.wikipedia.org/w/index.php?title=Mousse
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Mousse
Mousse
A mousse (French 'foam' ) is a soft prepared food that incorporates air bubbles to give it a light and airy texture. It can range from light and fluffy to creamy and thick, depending on preparation techniques. A mousse may be sweet or savory.
Sweet mousses are typically made with whipped egg whites, whipped cream, or both, and flavored with one or more of chocolate, coffee, caramel, puréed fruits, or various herbs and spices, such as mint or vanilla. In the case of some chocolate mousses, egg yolks are often stirred into melted chocolate to give the final product a richer mouthfeel. Mousses are also typically chilled before being served, which gives them a denser texture. Sweetened mousse
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is served as a dessert, or used as an airy cake filling. It is sometimes stabilized with gelatin.
Savory mousses can be made from meat, fish, shellfish, foie gras, cheese, or vegetables. Hot mousses often get their light texture from the addition of beaten egg whites.
# History.
Various desserts consisting of whipped cream in pyramidal shapes with coffee, liqueurs, chocolate, fruits, and so on either in the mixture or poured on top were called "crème en mousse" 'cream in a foam', "crème mousseuse" 'foamy cream', "mousse" 'foam', and so on, as early as 1768. Modern mousses are a continuation of this tradition.
# See also.
- Foam (culinary)
- Bavarian cream
- Fruit whip
- Flourless chocolate
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illing. It is sometimes stabilized with gelatin.
Savory mousses can be made from meat, fish, shellfish, foie gras, cheese, or vegetables. Hot mousses often get their light texture from the addition of beaten egg whites.
# History.
Various desserts consisting of whipped cream in pyramidal shapes with coffee, liqueurs, chocolate, fruits, and so on either in the mixture or poured on top were called "crème en mousse" 'cream in a foam', "crème mousseuse" 'foamy cream', "mousse" 'foam', and so on, as early as 1768. Modern mousses are a continuation of this tradition.
# See also.
- Foam (culinary)
- Bavarian cream
- Fruit whip
- Flourless chocolate cake
- Mousseline sauce
- Parfait (food)
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M. C. Escher
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M. C. Escher
M. C. Escher
Maurits Cornelis Escher (; 17 June 1898 – 27 March 1972) was a Dutch graphic artist who made mathematically-inspired woodcuts, lithographs, and mezzotints.
Despite wide popular interest, Escher was for long somewhat neglected in the art world, even in his native Netherlands. He was 70 before a retrospective exhibition was held. In the twenty-first century, he became more widely appreciated, with exhibitions across the world.
His work features mathematical objects and operations including impossible objects, explorations of infinity, reflection, symmetry, perspective, truncated and stellated polyhedra, hyperbolic geometry, and tessellations. Although Escher believed he had no mathematical
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M. C. Escher
ability, he interacted with the mathematicians George Pólya, Roger Penrose, Harold Coxeter and crystallographer Friedrich Haag, and conducted his own research into tessellation.
Early in his career, he drew inspiration from nature, making studies of insects, landscapes, and plants such as lichens, all of which he used as details in his artworks. He traveled in Italy and Spain, sketching buildings, townscapes, architecture and the tilings of the Alhambra and the Mezquita of Cordoba, and became steadily more interested in their mathematical structure.
Escher's art became well known among scientists and mathematicians, and in popular culture, especially after it was featured by Martin Gardner
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in his April 1966 Mathematical Games column in "Scientific American". Apart from being used in a variety of technical papers, his work has appeared on the covers of many books and albums. He was one of the major inspirations of Douglas Hofstadter's Pulitzer Prize-winning 1979 book "Gödel, Escher, Bach".
# Early life.
Maurits Cornelis Escher was born on 17 June 1898 in Leeuwarden, Friesland, the Netherlands, in a house that forms part of the Princessehof Ceramics Museum today. He was the youngest son of the civil engineer George Arnold Escher and his second wife, Sara Gleichman. In 1903, the family moved to Arnhem, where he attended primary and secondary school until 1918. Known to his friends
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M. C. Escher
and family as "Mauk", he was a sickly child and was placed in a special school at the age of seven; he failed the second grade. Although he excelled at drawing, his grades were generally poor. He took carpentry and piano lessons until he was thirteen years old.
In 1918, he went to the Technical College of Delft. From 1919 to 1922, Escher attended the Haarlem School of Architecture and Decorative Arts, learning drawing and the art of making woodcuts. He briefly studied architecture, but he failed a number of subjects (due partly to a persistent skin infection) and switched to decorative arts, studying under the graphic artist Samuel Jessurun de Mesquita.
# Study journeys.
In 1922, an important
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year of his life, Escher traveled through Italy, visiting Florence, San Gimignano, Volterra, Siena, and Ravello. In the same year, he traveled through Spain, visiting Madrid, Toledo, and Granada. He was impressed by the Italian countryside and, in Granada, by the Moorish architecture of the fourteenth-century Alhambra. The intricate decorative designs of the Alhambra, based on geometrical symmetries featuring interlocking repetitive patterns in the coloured tiles or sculpted into the walls and ceilings, triggered his interest in the mathematics of tessellation and became a powerful influence on his work.
Escher returned to Italy and lived in Rome from 1923 to 1935. While in Italy, Escher met
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Jetta Umiker – a Swiss woman, like himself attracted to Italy – whom he married in 1924. The couple settled in Rome where their first son, Giorgio (George) Arnaldo Escher, named after his grandfather, was born. Escher and Jetta later had two more sons – Arthur and Jan.
He travelled frequently, visiting (among other places) Viterbo in 1926, the Abruzzi in 1927 and 1929, Corsica in 1928 and 1933, Calabria in 1930, the Amalfi coast in 1931 and 1934, and Gargano and Sicily in 1932 and 1935. The townscapes and landscapes of these places feature prominently in his artworks. In May and June 1936, Escher travelled back to Spain, revisiting the Alhambra and spending days at a time making detailed drawings
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M. C. Escher
of its mosaic patterns. It was here that he became fascinated, to the point of obsession, with tessellation, explaining:
The sketches he made in the Alhambra formed a major source for his work from that time on. He also studied the architecture of the Mezquita, the Moorish mosque of Cordoba. This turned out to be the last of his long study journeys; after 1937, his artworks were created in his studio rather than in the field. His art correspondingly changed sharply from being mainly observational, with a strong emphasis on the realistic details of things seen in nature and architecture, to being the product of his geometric analysis and his visual imagination. All the same, even his early work
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already shows his interest in the nature of space, the unusual, perspective, and multiple points of view.
# Later life.
In 1935, the political climate in Italy (under Mussolini) became unacceptable to Escher. He had no interest in politics, finding it impossible to involve himself with any ideals other than the expressions of his own concepts through his own particular medium, but he was averse to fanaticism and hypocrisy. When his eldest son, George, was forced at the age of nine to wear a Ballila uniform in school, the family left Italy and moved to Château-d'Œx, Switzerland, where they remained for two years.
The Netherlands post office had Escher design a semi-postal stamp for the "Air
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Fund" in 1935, and again in 1949 he designed Netherlands stamps. These were for the 75th anniversary of the Universal Postal Union; a different design was used by Surinam and the Netherlands Antilles for the same commemoration.
Escher, who had been very fond of and inspired by the landscapes in Italy, was decidedly unhappy in Switzerland. In 1937, the family moved again, to Uccle (Ukkel), a suburb of Brussels, Belgium. World War II forced them to move in January 1941, this time to Baarn, Netherlands, where Escher lived until 1970. Most of Escher's best-known works date from this period. The sometimes cloudy, cold, and wet weather of the Netherlands allowed him to focus intently on his work.
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After 1953, Escher lectured widely. A planned series of lectures in North America in 1962 was cancelled after an illness, and he stopped creating artworks for a time, but the illustrations and text for the lectures were later published as part of the book "Escher on Escher". He was awarded the Knighthood of the Order of Orange-Nassau in 1955; he was later made an Officer in 1967.
In July 1969 he finished his last work, a large woodcut with threefold rotational symmetry called "Snakes", in which snakes wind through a pattern of linked rings. These shrink to infinity toward both the center and the edge of a circle. It was exceptionally elaborate, being printed using three blocks, each rotated
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three times about the center of the image and precisely aligned to avoid gaps and overlaps, for a total of nine print operations for each finished print. The image encapsulates Escher's love of symmetry; of interlocking patterns; and, at the end of his life, of his approach to infinity. The care that Escher took in creating and printing this woodcut can be seen in a video recording.
Escher moved to the Rosa Spier Huis in Laren in 1970, an artists' retirement home in which he had his own studio. He died in a hospital in Hilversum on 27 March 1972, aged 73. He is buried at the New Cemetery in Baarn.
# Mathematically inspired work.
Escher's work is inescapably mathematical. This has caused a
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disconnect between his full-on popular fame and the lack of esteem with which he has been viewed in the art world. His originality and mastery of graphic techniques are respected, but his works have been thought too intellectual and insufficiently lyrical. Movements such as conceptual art have, to a degree, reversed the art world's attitude to intellectuality and lyricism, but this did not rehabilitate Escher, because traditional critics still disliked his narrative themes and his use of perspective. However, these same qualities made his work highly attractive to the public.
Escher is not the first artist to explore mathematical themes: Parmigianino (1503–1540) had explored spherical geometry
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and reflection in his 1524 "Self-portrait in a Convex Mirror", depicting his own image in a curved mirror, while William Hogarth's 1754 "Satire on False Perspective" foreshadows Escher's playful exploration of errors in perspective. Another early artistic forerunner is Giovanni Battista Piranesi (1720–1778), whose dark "fantastical" prints such as "The Drawbridge" in his "Carceri" ("Prisons") sequence depict perspectives of complex architecture with many stairs and ramps, peopled by walking figures. Only with 20th century movements such as Cubism, De Stijl, Dadaism, and Surrealism did mainstream art start to explore Escher-like ways of looking at the world with multiple simultaneous viewpoints.
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However, although Escher had much in common with, for example, Magritte's surrealism, he did not make contact with any of these movements.
## Tessellation.
In his early years, Escher sketched landscapes and nature. He also sketched insects such as ants, bees, grasshoppers, and mantises, which appeared frequently in his later work. His early love of Roman and Italian landscapes and of nature created an interest in tessellation, which he called "Regular Division of the Plane"; this became the title of his 1958 book, complete with reproductions of a series of woodcuts based on tessellations of the plane, in which he described the systematic buildup of mathematical designs in his artworks. He
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wrote, "Mathematicians have opened the gate leading to an extensive domain".
After his 1936 journey to the Alhambra and to La Mezquita, Cordoba, where he sketched the Moorish architecture and the tessellated mosaic decorations, Escher began to explore the properties and possibilities of tessellation using geometric grids as the basis for his sketches. He then extended these to form complex interlocking designs, for example with animals such as birds, fish, and reptiles. One of his first attempts at a tessellation was his pencil, India ink, and watercolour "Study of Regular Division of the Plane with Reptiles" (1939), constructed on a hexagonal grid. The heads of the red, green, and white reptiles
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meet at a vertex; the tails, legs, and sides of the animals interlock exactly. It was used as the basis for his 1943 lithograph "Reptiles".
His first study of mathematics began with papers by George Pólya and by the crystallographer Friedrich Haag on plane symmetry groups, sent to him by his brother Berend, a geologist. He carefully studied the 17 canonical wallpaper groups and created periodic tilings with 43 drawings of different types of symmetry. From this point on, he developed a mathematical approach to expressions of symmetry in his artworks using his own notation. Starting in 1937, he created woodcuts based on the 17 groups. His "Metamorphosis I" (1937) began a series of designs that
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told a story through the use of pictures. In "Metamorphosis I", he transformed convex polygons into regular patterns in a plane to form a human motif. He extended the approach in his piece "Metamorphosis III", which is four metres long.
In 1941 and 1942, Escher summarized his findings for his own artistic use in a sketchbook, which he labeled (following Haag) "Regelmatige vlakverdeling in asymmetrische congruente veelhoeken" ("Regular division of the plane with asymmetric congruent polygons"). The mathematician Doris Schattschneider unequivocally described this notebook as recording "a methodical investigation that can only be termed mathematical research." She defined the research questions
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he was following as
## Geometries.
Although Escher did not have mathematical training—his understanding of mathematics was largely visual and intuitive—his art had a strong mathematical component, and several of the worlds that he drew were built around impossible objects. After 1924, Escher turned to sketching landscapes in Italy and Corsica with irregular perspectives that are impossible in natural form. His first print of an impossible reality was "Still Life and Street" (1937); impossible stairs and multiple visual and gravitational perspectives feature in popular works such as "Relativity" (1953). "House of Stairs" (1951) attracted the interest of the mathematician Roger Penrose and his
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father, the biologist Lionel Penrose. In 1956, they published a paper, "Impossible Objects: A Special Type of Visual Illusion" and later sent Escher a copy. Escher replied, admiring the Penroses' continuously rising flights of steps, and enclosed a print of "Ascending and Descending" (1960). The paper also contained the tribar or Penrose triangle, which Escher used repeatedly in his lithograph of a building that appears to function as a perpetual motion machine, "Waterfall" (1961).
Escher was interested enough in Hieronymus Bosch's 1500 triptych "The Garden of Earthly Delights" to re-create part of its right-hand panel, "Hell", as a lithograph in 1935. He reused the figure of a Mediaeval woman
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in a two-pointed headdress and a long gown in his lithograph "Belvedere" in 1958; the image is, like many of his other "extraordinary invented places", peopled with "jesters, knaves, and contemplators". Thus, Escher not only was interested in possible or impossible geometry but was, in his own words, a "reality enthusiast"; he combined "formal astonishment with a vivid and idiosyncratic vision".
Escher worked primarily in the media of lithographs and woodcuts, although the few mezzotints he made are considered to be masterpieces of the technique. In his graphic art, he portrayed mathematical relationships among shapes, figures, and space. Integrated into his prints were mirror images of cones,
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spheres, cubes, rings, and spirals.
Escher was also fascinated by mathematical objects such as the Möbius strip, which has only one surface. His wood engraving "Möbius Strip II" (1963) depicts a chain of ants marching forever over what, at any one place, are the two opposite faces of the object—which are seen on inspection to be parts of the strip's single surface. In Escher's own words:
The mathematical influence in his work became prominent after 1936, when, having boldly asked the Adria Shipping Company if he could sail with them as travelling artist in return for making drawings of their ships, they surprisingly agreed, and he sailed the Mediterranean, becoming interested in order and
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symmetry. Escher described this journey, including his repeat visit to the Alhambra, as "the richest source of inspiration I have ever tapped".
Escher's interest in curvilinear perspective was encouraged by his friend and "kindred spirit", the art historian and artist Albert Flocon, in another example of constructive mutual influence. Flocon identified Escher as a "thinking artist" alongside Piero della Francesca, Leonardo da Vinci, Albrecht Dürer, Wenzel Jamnitzer, Abraham Bosse, Girard Desargues, and Père Nicon. Flocon was delighted by Escher's "Grafiek en tekeningen" ("Graphics in Drawing"), which he read in 1959. This stimulated Flocon and André Barre to correspond with Escher and to write
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the book "La Perspective curviligne" ("Curvilinear perspective").
## Platonic and other solids.
Escher often incorporated three-dimensional objects such as the Platonic solids such as spheres, tetrahedrons, and cubes into his works, as well as mathematical objects such as cylinders and stellated polyhedra. In the print "Reptiles", he combined two- and three-dimensional images. In one of his papers, Escher emphasized the importance of dimensionality:
Escher's artwork is especially well-liked by mathematicians such as Doris Schattschneider and scientists such as Roger Penrose, who enjoy his use of polyhedra and geometric distortions. For example, in "Gravitation", animals climb around a stellated
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dodecahedron.
The two towers of "Waterfall" impossible building are topped with compound polyhedra, one a compound of three cubes, the other a stellated rhombic dodecahedron now known as Escher's solid. Escher had used this solid in his 1948 woodcut "Stars", which also contains all five of the Platonic solids and various stellated solids, representing stars; the central solid is animated by chameleons climbing through the frame as it whirls in space. Escher possessed a 6 cm refracting telescope and was a keen-enough amateur astronomer to have recorded observations of binary stars.
## Levels of reality.
Escher's artistic expression was created from images in his mind, rather than directly
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from observations and travels to other countries. His interest in the multiple levels of reality in art is seen in works such as "Drawing Hands" (1948), where two hands are shown, each drawing the other. The critic Steven Poole commented that
## Infinity and hyperbolic geometry.
In 1954, the International Congress of Mathematicians met in Amsterdam, and N. G. de Bruin organized a display of Escher's work at the Stedelijk Museum for the participants. Both Roger Penrose and H. S. M. Coxeter were deeply impressed with Escher's intuitive grasp of mathematics. Inspired by "Relativity", Penrose devised his tribar, and his father, Lionel Penrose, devised an endless staircase. Roger Penrose sent sketches
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of both objects to Escher, and the cycle of invention was closed when Escher then created the perpetual motion machine of "Waterfall" and the endless march of the monk-figures of "Ascending and Descending".
In 1957, Coxeter obtained Escher's permission to use two of his drawings in his paper "Crystal symmetry and its generalizations". He sent Escher a copy of the paper; Escher recorded that Coxeter's figure of a hyperbolic tessellation "gave me quite a shock": the infinite regular repetition of the tiles in the hyperbolic plane, growing rapidly smaller towards the edge of the circle, was precisely what he wanted to allow him to represent infinity on a two-dimensional plane.
Escher carefully
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studied Coxeter's figure, marking it up to analyse the successively smaller circles with which (he deduced) it had been constructed. He then constructed a diagram, which he sent to Coxeter, showing his analysis; Coxeter confirmed it was correct, but disappointed Escher with his highly technical reply. All the same, Escher persisted with hyperbolic tiling, which he called "Coxetering". Among the results were the series of wood engravings "Circle Limit I–IV". In 1959, Coxeter published his finding that these works were extraordinarily accurate: "Escher got it absolutely right to the millimeter".
# Legacy.
Escher's special way of thinking and rich graphics have had a continuous influence in mathematics
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and art, as well as in popular culture.
## In art collections.
The Escher intellectual property is controlled by the M.C. Escher Company, while exhibitions of his artworks are managed separately by the M.C. Escher Foundation.
The primary institutional collections of original works by M.C. Escher are the Escher Museum in The Hague; the National Gallery of Art (Washington, DC); the National Gallery of Canada (Ottawa); the Israel Museum (Jerusalem); and the Huis ten Bosch (Nagasaki, Japan).
## Exhibitions.
Despite wide popular interest, Escher was for a long time somewhat neglected in the art world; even in his native Netherlands, he was 70 before a retrospective exhibition was held. In the
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twenty-first century, major exhibitions have been held in cities across the world. An exhibition of his work in Rio de Janeiro attracted more than 573,000 visitors in 2011; its daily visitor count of 9,677 made it the most visited museum exhibition of the year, anywhere in the world. No major exhibition of Escher's work was held in Britain until 2015, when the Scottish National Gallery of Modern Art ran one in Edinburgh from June to September 2015, moving in October 2015 to the Dulwich Picture Gallery, London. The exhibition moved to Italy in 2015–2016, attracting over 500,000 visitors in Rome and Bologna, and then Milan.
## In mathematics and science.
Doris Schattschneider identifies 11 strands
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of mathematical and scientific research anticipated or directly inspired by Escher. These are the classification of regular tilings using the edge relationships of tiles: two-color and two-motif tilings (counterchange symmetry or antisymmetry); color symmetry (in crystallography); metamorphosis or topological change; covering surfaces with symmetric patterns; Escher's algorithm (for generating patterns using decorated squares); creating tile shapes; local versus global definitions of regularity; symmetry of a tiling induced by the symmetry of a tile; orderliness not induced by symmetry groups; the filling of the central void in Escher's lithograph "Print Gallery" by H. Lenstra and B. de Smit.
The
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Pulitzer Prize-winning 1979 book "Gödel, Escher, Bach" by Douglas Hofstadter discusses the ideas of self-reference and strange loops, drawing on a wide range of artistic and scientific sources including Escher's art and the music of J. S. Bach.
The asteroid 4444 Escher was named in Escher's honor in 1985.
## In popular culture.
Escher's fame in popular culture grew when his work was featured by Martin Gardner in his April 1966 "Mathematical Games" column in "Scientific American". Escher's works have appeared on many album covers including The Scaffold's 1969 "L the P" with "Ascending and Descending"; Mott the Hoople's eponymous 1969 record with "Reptiles", Beaver & Krause's 1970 "In A Wild
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Sanctuary" with "Three Worlds"; and Mandrake Memorial's 1970 "Puzzle" with "House of Stairs" and (inside) "Curl Up". His works have similarly been used on many book covers, including some editions of Edwin Abbott's "Flatland", which used "Three Spheres"; E. H. Gombrich's "Meditations on a Hobby Horse" with "Horseman"; Pamela Hall's "Heads You Lose" with "Plane Filling 1"; Patrick A. Horton's "Mastering the Power of Story" with "Drawing Hands"; Erich Gamma et al.'s "Design Patterns: Elements of Reusable Object-oriented software" with "Swans"; and Arthur Markman's "Knowledge Representation" with "Reptiles". The "World of Escher" markets posters, neckties, T-shirts, and jigsaw puzzles of Escher's
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artworks. Both Austria and the Netherlands have issued postage stamps commemorating the artist and his works.
# Selected works.
- "Trees", ink (1920)
- "St. Bavo's, Haarlem", ink (1920)
- "Flor de Pascua (The Easter Flower)", woodcut/book illustrations (1921)
- "Eight Heads", woodcut (1922)
- "Dolphins" also known as "Dolphins in Phosphorescent Sea", woodcut (1923)
- "Tower of Babel", woodcut (1928)
- "Street in Scanno, Abruzzi", lithograph (1930)
- "Castrovalva", lithograph (1930)
- "The Bridge", lithograph (1930)
- "Palizzi, Calabria", woodcut (1930)
- "Pentedattilo, Calabria", lithograph (1930)
- "Atrani, Coast of Amalfi", lithograph (1931)
- "Ravello and the Coast of Amalfi",
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lithograph (1931)
- "Covered Alley in Atrani, Coast of Amalfi", wood engraving (1931)
- "Phosphorescent Sea", lithograph (1933)
- "Still Life with Spherical Mirror", lithograph (1934)
- "Hand with Reflecting Sphere" also known as "Self-Portrait in Spherical Mirror", lithograph (1935)
- "Inside St. Peter's", wood engraving (1935)
- "Portrait of G.A. Escher", lithograph (1935)
- ""Hell"", lithograph, (copied from a painting by Hieronymus Bosch) (1935)
- "Regular Division of the Plane", series of drawings that continued until the 1960s (1936)
- "Still Life and Street" (his first impossible reality), woodcut (1937)
- "Metamorphosis I", woodcut (1937)
- "Day and Night", woodcut (1938)
-
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"Cycle", lithograph (1938)
- "Sky and Water I", woodcut (1938)
- "Sky and Water II", lithograph (1938)
- "Metamorphosis II", woodcut (1939–1940)
- "Verbum (Earth, Sky and Water)", lithograph (1942)
- "Reptiles", lithograph (1943)
- "Ant", lithograph (1943)
- "Encounter", lithograph (1944)
- "Doric Columns", wood engraving (1945)
- "Balcony", lithograph (1945)
- "Three Spheres I", wood engraving (1945)
- "Magic Mirror", lithograph (1946)
- "Three Spheres II", lithograph (1946)
- "Another World Mezzotint" also known as "Other World Gallery", mezzotint (1946)
- "Eye", mezzotint (1946)
- "Another World" also known as "Other World", wood engraving and woodcut (1947)
- "Crystal", mezzotint
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(1947)
- "Up and Down" also known as "High and Low", lithograph (1947)
- "Drawing Hands", lithograph (1948)
- "Dewdrop", mezzotint (1948)
- "Stars", wood engraving (1948)
- "Double Planetoid", wood engraving (1949)
- "Order and Chaos (Contrast)", lithograph (1950)
- "Rippled Surface", woodcut and linoleum cut (1950)
- "Curl-up", lithograph (1951)
- "House of Stairs", lithograph (1951)
- "House of Stairs II", lithograph (1951)
- "Puddle", woodcut (1952)
- "Gravitation", (1952)
- "Dragon", woodcut lithograph and watercolor (1952)
- "Cubic Space Division", lithograph (1952)
- "Relativity", lithograph (1953)
- "Tetrahedral Planetoid", woodcut (1954)
- "Compass Rose (Order and Chaos
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II)", lithograph (1955)
- "Convex and Concave", lithograph (1955)
- "Three Worlds", lithograph (1955)
- "Print Gallery", lithograph (1956)
- "Mosaic II", lithograph (1957)
- "Cube with Magic Ribbons", lithograph (1957)
- "Belvedere", lithograph (1958)
- "Sphere Spirals", woodcut (1958)
- "Circle Limit III", woodcut (1959)
- "Ascending and Descending", lithograph (1960)
- "Waterfall", lithograph (1961)
- "Möbius Strip II (Red Ants)", woodcut (1963)
- "Knot", pencil and crayon (1966)
- "Metamorphosis III", woodcut (1967–1968)
- "Snakes", woodcut (1969)
# See also.
- Victor Vasarely
- Escher sentences, named after works like "Ascending and Descending"
# Further reading.
## Media.
-
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", woodcut (1959)
- "Ascending and Descending", lithograph (1960)
- "Waterfall", lithograph (1961)
- "Möbius Strip II (Red Ants)", woodcut (1963)
- "Knot", pencil and crayon (1966)
- "Metamorphosis III", woodcut (1967–1968)
- "Snakes", woodcut (1969)
# See also.
- Victor Vasarely
- Escher sentences, named after works like "Ascending and Descending"
# Further reading.
## Media.
- Escher, M. C. "The Fantastic World of M. C. Escher", Video collection of examples of the development of his art, and interviews, Director, Michele Emmer.
# External links.
- — physical replicas of some of Escher's "impossible" designs
- Copyright issue regarding Escher from the Artquest Artlaw archive.
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Marcomanni
The Marcomanni were a Germanic tribal confederation who eventually came to live in a powerful kingdom north of the Danube, somewhere in the region near modern Bohemia, during the peak of power of the nearby Roman Empire. According to Tacitus and Strabo they were Suebian.
# History.
## Origin.
It is believed their name derives possibly from the Proto-Germanic forms of "march" ("frontier, border") and "men", "*Markōmanniz", which would have been rendered in Latin form as "Marcomanni".
The Marcomanni first appear in historical records as confederates of the Suebi of Ariovistus fighting against Julius Caesar in Gaul (modern France), having crossed the Rhine from present-day southern
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Germany. The exact position of their lands at this time is not known. The fact that their name existed before the Romans had territory near the Danube or Rhine raises the question of which border they lived near in order to explain their name. Their name may echo an earlier demarcation between the northern Germanic tribes of the Jastorf cultural circle, and those of the Celtic maximum expansion during the earlier and later Iron Age of La Tene dominance throughout Europe, that from findings in the archaeological record pressed North through with some influence as far as into Jutland, but mostly remained separated South and settled on Oppidas over today Thuringia and Saxony along the Hercynian
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forest, intrinsically connected to the major trade roads that went into the more evolved centers of Bohemia, Moravia and Silesia all still Celtic regions then. It has been suggested that they may have lived near the conjunction of Rhine and Main river, at the areas formerly inhabited but left deserted by the Helvetii and Taurisci. However the historian Florus reports that Drusus erected a mound of their spoils during his campaign of 12-9 BC, after defeating the Tencteri and Chatti, and before next turning to Cherusci, Suevi, and Sicambri, suggesting that they were not close to any obvious border at the time.
According to the accounts of Tacitus (Germ. 42), Paterculus (2.108), Pliny the Elder,
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and Strabo (vii. p. 290) they eventually moved into the large area previously occupied by the Boii, specifically in a region already called "Baiohaemum", where their allies and fellow Suevi the Quadi lived. This was described as being within the Hercynian forest and was possibly in the region of modern Bohemia, although this is not certain. By 6 BC, their king, Maroboduus, had established a powerful kingdom there that Augustus perceived as a threat to Rome. Before he could act, however, the revolt in Illyria intervened. Eventually Maroboduus was deposed and exiled by Catualda (AD 19). Catualda was in turn deposed by Vibilius of the Hermunduri the same year, and succeeded by the Quadian Vannius.
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Around 50 AD, Vannius was himself also deposed by Vibilius, in coordination with his nephews Vangio and Sido.
Tacitus, in the late 1st century mentions ("Germania" I.42) the Marcomanni as being under kings appointed by Rome.
## Marcomannic Wars.
In the 2nd century AD, the Marcomanni entered into a confederation with other peoples including the Quadi, Vandals, and Sarmatians, against the Roman Empire. This was probably driven by movements of larger tribes, like the Goths. According to the historian Eutropius, the forces of the emperor, Marcus Aurelius, battled against the Marcomannic confederation for three years at the fortress of Carnuntum in Pannonia. Eutropius compared the war, and Aurelius's
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success against the Marcomanni and their allies, to the Punic Wars. The comparison was apt in that this war marked a turning point and had significant Roman defeats; it caused the death of two Praetorian Guard commanders. The war began in 166, when the Marcomanni overwhelmed the defences between Vindobona and Carnuntum, penetrated along the border between the provinces of Pannonia and Noricum, laid waste to Flavia Solva, and could be stopped only shortly before reaching Aquileia on the Adriatic Sea. The war lasted until Aurelius's death in 180. It would prove to be only a limited success for Rome; the Danube river remained as the frontier of the empire until the final fall of the West.
## Later
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history.
The Christianisation of the Marcomanni, at least into a Roman orthodox form of Christianity, seems to have occurred under their queen, Fritigil (wife of an unnamed king) in the mid fourth century. She corresponded with Ambrose of Milan to bring about the conversion. This was the last clear evidence of the Marcomanni having a polity. It was possibly on the Roman side of the Danube by this time. Soon after, the Pannonian and Danubian area went into a long period of turmoil.
After crossing the Rhine in 406 and the Pyrenees in 409, a group of Suevi, who had migrated together with Vandals and Alans, established themselves in the Roman province of Gallaecia (modern Galicia and northern
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Portugal), where they were considered "foederati" and founded the Suebi Kingdom of Gallaecia. These Suevi were probably a mix of Suevian groups from the area north of Danube and Pannonian basin such as the Marcomanni, Quadi and Buri.
There, Hermeric swore fealty to the emperor in 410. Bracara Augusta, the modern city of Braga in Portugal, previously the capital of Roman Gallaecia, now became the capital of the Suebic Kingdom.
The Danubian area meanwhile became the core of Attila the Hun's empire, and within it there seem to have been many Suebians. One group of them managed to reform into an independent group after the Battle of Nedao in 454, like many other groups who emerged from Attila's
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confederation. These Suevi eventually came into conflict with the Ostrogoths, who had been on the losing side at Nadao.
Jordanes, the historian of the Goths, reported ("Getica" 280) that after the Battle of Bolia, the Ostrogoths attacked the Suevi (ruled by a man named Hunimund, who also seems to have led an attack on Passau) by crossing the Danube when frozen, and going into a high Alpine area held by the confederates of the Suevi at this time, the Alamanni. (He said that several streams start in this area which enter the Danube with a loudly.) The region held by these Suevi was described as having Bavarians to the west, Franks to the east, Burgundians to the south, and Thuringians to the
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north. The text seems to indicate that these Suevi had moved into the Alamannic area but that these specific Suevi were seen as distinct from both Alamanni and Bavarians. This was also the first mention of Bavarians and they are also often proposed to have had Marcomanni in their ancestry.
According to historians such as Herwig Wolfram:
The Marcomanni and the Quadi gave up their special names after crossing the Danube, in fact both the emigrants and the groups remaining in Pannonia became Suebi again. The Pannonian Suebi became subjects of the Huns. After the battle at the Nadao they set up their kingdom, and when it fell, they came, successively under Herulian and Longobard rule, south of
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Danube under Gothic rule, and eventually again under Longobard rule.
There is a runic alphabet called the Marcomannic runes, but they are not believed to be related to the Marcomannic people.
# Kings of the Marcomanni.
- Maroboduus, c. 9 BC – 18 AD
- Catualda, 18 – 20
- Vannius, 20 – c. 50
- Vangio and Sido, c. 50 – ?
- Ballomar, c. 166? – 172 or 178?
- Attalus, c. 160/8
# See also.
- History of Portugal
- History of Spain
- Irminones
- List of ancient Germanic peoples
- Migrations period
- Timeline of Germanic kingdoms
# Classical sources.
- Caesar "De Bello Gallico", at The Latin Library
- Tacitus "Germania", at The Latin Library
- Tacitus "Annales", at The Latin Library
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Microwave
Microwaves are a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter; with frequencies between and . Different sources define different frequency ranges as microwaves; the above broad definition includes both UHF and EHF (millimeter wave) bands. A more common definition in radio engineering is the range between 1 and 100 GHz (wavelengths between 0.3 m and 3 mm). In all cases, microwaves include the entire SHF band (3 to 30 GHz, or 10 to 1 cm) at minimum. Frequencies in the microwave range are often referred to by their IEEE radar band designations: S, C, X, K, K, or K band, or by similar NATO or EU designations.
The prefix "" in "microwave"
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is not meant to suggest a wavelength in the micrometer range. Rather, it indicates that microwaves are "small" (having shorter wavelengths), compared to the radio waves used prior to microwave technology. The boundaries between far infrared, terahertz radiation, microwaves, and ultra-high-frequency radio waves are fairly arbitrary and are used variously between different fields of study.
Microwaves travel by line-of-sight; unlike lower frequency radio waves they do not diffract around hills, follow the earth's surface as ground waves, or reflect from the ionosphere, so terrestrial microwave communication links are limited by the visual horizon to about 40 miles (64 km). At the high end of the
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band they are absorbed by gases in the atmosphere, limiting practical communication distances to around a kilometer. Microwaves are widely used in modern technology, for example in point-to-point communication links, wireless networks, microwave radio relay networks, radar, satellite and spacecraft communication, medical diathermy and cancer treatment, remote sensing, radio astronomy, particle accelerators, spectroscopy, industrial heating, collision avoidance systems, garage door openers and keyless entry systems, and for cooking food in microwave ovens.
# Electromagnetic spectrum.
Microwaves occupy a place in the electromagnetic spectrum with frequency above ordinary radio waves, and below
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infrared light:
In descriptions of the electromagnetic spectrum, some sources classify microwaves as radio waves, a subset of the radio wave band; while others classify microwaves and radio waves as distinct types of radiation. This is an arbitrary distinction.
# Propagation.
Microwaves travel solely by line-of-sight paths; unlike lower frequency radio waves, they do not travel as ground waves which follow the contour of the Earth, or reflect off the ionosphere (skywaves). Although at the low end of the band they can pass through building walls enough for useful reception, usually rights of way cleared to the first Fresnel zone are required. Therefore, on the surface of the Earth, microwave
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communication links are limited by the visual horizon to about . Microwaves are absorbed by moisture in the atmosphere, and the attenuation increases with frequency, becoming a significant factor (rain fade) at the high end of the band. Beginning at about 40 GHz, atmospheric gases also begin to absorb microwaves, so above this frequency microwave transmission is limited to a few kilometers. A spectral band structure causes absorption peaks at specific frequencies (see graph at right). Above 100 GHz, the absorption of electromagnetic radiation by Earth's atmosphere is so great that it is in effect opaque, until the atmosphere becomes transparent again in the so-called infrared and optical window
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frequency ranges.
## Troposcatter.
In a microwave beam directed at an angle into the sky, a small amount of the power will be randomly scattered as the beam passes through the troposphere. A sensitive receiver beyond the horizon with a high gain antenna focused on that area of the troposphere can pick up the signal. This technique has been used at frequencies between 0.45 and 5 GHz in tropospheric scatter (troposcatter) communication systems to communicate beyond the horizon, at distances up to 300 km.
# Antennas.
The short wavelengths of microwaves allow omnidirectional antennas for portable devices to be made very small, from 1 to 20 centimeters long, so microwave frequencies are widely
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used for wireless devices such as cell phones, cordless phones, and wireless LANs (Wi-Fi) access for laptops, and Bluetooth earphones. Antennas used include short whip antennas, rubber ducky antennas, sleeve dipoles, patch antennas, and increasingly the printed circuit inverted F antenna (PIFA) used in cell phones.
Their short wavelength also allows narrow beams of microwaves to be produced by conveniently small high gain antennas from a half meter to 5 meters in diameter. Therefore, beams of microwaves are used for point-to-point communication links, and for radar. An advantage of narrow beams is that they don't interfere with nearby equipment using the same frequency, allowing frequency reuse
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by nearby transmitters. Parabolic ("dish") antennas are the most widely used directive antennas at microwave frequencies, but horn antennas, slot antennas and dielectric lens antennas are also used. Flat microstrip antennas are being increasingly used in consumer devices. Another directive antenna practical at microwave frequencies is the phased array, a computer-controlled array of antennas which produces a beam which can be electronically steered in different directions.
At microwave frequencies, the transmission lines which are used to carry lower frequency radio waves to and from antennas, such as coaxial cable and parallel wire lines, have excessive power losses, so when low attenuation
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is required microwaves are carried by metal pipes called waveguides. Due to the high cost and maintenance requirements of waveguide runs, in many microwave antennas the output stage of the transmitter or the RF front end of the receiver is located at the antenna.
# Design and analysis.
The term "microwave" also has a more technical meaning in electromagnetics and circuit theory. Apparatus and techniques may be described qualitatively as "microwave" when the wavelengths of signals are roughly the same as the dimensions of the circuit, so that lumped-element circuit theory is inaccurate, and instead distributed circuit elements and transmission-line theory are more useful methods for design
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and analysis.
As a consequence, practical microwave circuits tend to move away from the discrete resistors, capacitors, and inductors used with lower-frequency radio waves. Open-wire and coaxial transmission lines used at lower frequencies are replaced by waveguides and stripline, and lumped-element tuned circuits are replaced by cavity resonators or resonant stubs. In turn, at even higher frequencies, where the wavelength of the electromagnetic waves becomes small in comparison to the size of the structures used to process them, microwave techniques become inadequate, and the methods of optics are used.
# Microwave sources.
High-power microwave sources use specialized vacuum tubes to generate
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microwaves. These devices operate on different principles from low-frequency vacuum tubes, using the ballistic motion of electrons in a vacuum under the influence of controlling electric or magnetic fields, and include the magnetron (used in microwave ovens), klystron, traveling-wave tube (TWT), and gyrotron. These devices work in the density modulated mode, rather than the current modulated mode. This means that they work on the basis of clumps of electrons flying ballistically through them, rather than using a continuous stream of electrons.
Low-power microwave sources use solid-state devices such as the field-effect transistor (at least at lower frequencies), tunnel diodes, Gunn diodes,
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and IMPATT diodes. Low-power sources are available as benchtop instruments, rackmount instruments, embeddable modules and in card-level formats. A maser is a solid state device which amplifies microwaves using similar principles to the laser, which amplifies higher frequency light waves.
All warm objects emit low level microwave black-body radiation, depending on their temperature, so in meteorology and remote sensing microwave radiometers are used to measure the temperature of objects or terrain. The sun and other astronomical radio sources such as Cassiopeia A emit low level microwave radiation which carries information about their makeup, which is studied by radio astronomers using receivers
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called radio telescopes. The cosmic microwave background radiation (CMBR), for example, is a weak microwave noise filling empty space which is a major source of information on cosmology's Big Bang theory of the origin of the Universe.
# Microwave uses.
Microwave technology is extensively used for point-to-point telecommunications (i.e. non-broadcast uses). Microwaves are especially suitable for this use since they are more easily focused into narrower beams than radio waves, allowing frequency reuse; their comparatively higher frequencies allow broad bandwidth and high data transmission rates, and antenna sizes are smaller than at lower frequencies because antenna size is inversely proportional
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to transmitted frequency. Microwaves are used in spacecraft communication, and much of the world's data, TV, and telephone communications are transmitted long distances by microwaves between ground stations and communications satellites. Microwaves are also employed in microwave ovens and in radar technology.
## Communication.
Before the advent of fiber-optic transmission, most long-distance telephone calls were carried via networks of microwave radio relay links run by carriers such as AT&T Long Lines. Starting in the early 1950s, frequency division multiplex was used to send up to 5,400 telephone channels on each microwave radio channel, with as many as ten radio channels combined into one
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antenna for the "hop" to the next site, up to 70 km away.
Wireless LAN protocols, such as Bluetooth and the IEEE 802.11 specifications used for Wi-Fi, also use microwaves in the 2.4 GHz ISM band, although 802.11a uses ISM band and U-NII frequencies in the 5 GHz range. Licensed long-range (up to about 25 km) Wireless Internet Access services have been used for almost a decade in many countries in the 3.5–4.0 GHz range. The FCC recently carved out spectrum for carriers that wish to offer services in this range in the U.S. — with emphasis on 3.65 GHz. Dozens of service providers across the country are securing or have already received licenses from the FCC to operate in this band. The WIMAX service
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offerings that can be carried on the 3.65 GHz band will give business customers another option for connectivity.
Metropolitan area network (MAN) protocols, such as WiMAX (Worldwide Interoperability for Microwave Access) are based on standards such as IEEE 802.16, designed to operate between 2 and 11 GHz. Commercial implementations are in the 2.3 GHz, 2.5 GHz, 3.5 GHz and 5.8 GHz ranges.
Mobile Broadband Wireless Access (MBWA) protocols based on standards specifications such as IEEE 802.20 or ATIS/ANSI HC-SDMA (such as iBurst) operate between 1.6 and 2.3 GHz to give mobility and in-building penetration characteristics similar to mobile phones but with vastly greater spectral efficiency.
Some
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mobile phone networks, like GSM, use the low-microwave/high-UHF frequencies around 1.8 and 1.9 GHz in the Americas and elsewhere, respectively. DVB-SH and S-DMB use 1.452 to 1.492 GHz, while proprietary/incompatible satellite radio in the U.S. uses around 2.3 GHz for DARS.
Microwave radio is used in broadcasting and telecommunication transmissions because, due to their short wavelength, highly directional antennas are smaller and therefore more practical than they would be at longer wavelengths (lower frequencies). There is also more bandwidth in the microwave spectrum than in the rest of the radio spectrum; the usable bandwidth below 300 MHz is less than 300 MHz while many GHz can be used
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above 300 MHz. Typically, microwaves are used in television news to transmit a signal from a remote location to a television station from a specially equipped van. See broadcast auxiliary service (BAS), remote pickup unit (RPU), and studio/transmitter link (STL).
Most satellite communications systems operate in the C, X, K, or K bands of the microwave spectrum. These frequencies allow large bandwidth while avoiding the crowded UHF frequencies and staying below the atmospheric absorption of EHF frequencies. Satellite TV either operates in the C band for the traditional large dish fixed satellite service or K band for direct-broadcast satellite. Military communications run primarily over X or
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K-band links, with K band being used for Milstar.
## Navigation.
Global Navigation Satellite Systems (GNSS) including the Chinese Beidou, the American Global Positioning System (introduced in 1978) and the Russian GLONASS broadcast navigational signals in various bands between about 1.2 GHz and 1.6 GHz.
## Radar.
Radar is a radiolocation technique in which a beam of radio waves emitted by a transmitter bounces off an object and returns to a receiver, allowing the location, range, speed, and other characteristics of the object to be determined. The short wavelength of microwaves causes large reflections from objects the size of motor vehicles, ships and aircraft. Also, at these wavelengths,
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the high gain antennas such as parabolic antennas which are required to produce the narrow beamwidths needed to accurately locate objects are conveniently small, allowing them to be rapidly turned to scan for objects. Therefore, microwave frequencies are the main frequencies used in radar. Microwave radar is widely used for applications such as air traffic control, weather forecasting, navigation of ships, and speed limit enforcement. Long distance radars use the lower microwave frequencies since at the upper end of the band atmospheric absorption limits the range, but millimeter waves are used for short range radar such as collision avoidance systems.
## Radio astronomy.
Microwaves emitted
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by astronomical radio sources; planets, stars, galaxies, and nebulas are studied in radio astronomy with large dish antennas called radio telescopes. In addition to receiving naturally occurring microwave radiation, radio telescopes have been used in active radar experiments to bounce microwaves off planets in the solar system, to determine the distance to the Moon or map the invisible surface of Venus through cloud cover.
A recently completed microwave radio telescope is the Atacama Large Millimeter Array, located at more than 5,000 meters (16,597 ft) altitude in Chile, observes the universe in the millimetre and submillimetre wavelength ranges. The world's largest ground-based astronomy project
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to date, it consists of more than 66 dishes and was built in an international collaboration by Europe, North America, East Asia and Chile.
A major recent focus of microwave radio astronomy has been mapping the cosmic microwave background radiation (CMBR) discovered in 1964 by radio astronomers Arno Penzias and Robert Wilson. This faint background radiation, which fills the universe and is almost the same in all directions, is "relic radiation" from the Big Bang, and is one of the few sources of information about conditions in the early universe. Due to the expansion and thus cooling of the Universe, the originally high-energy radiation has been shifted into the microwave region of the radio
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spectrum. Sufficiently sensitive radio telescopes can detected the CMBR as a faint signal that is not associated with any star, galaxy, or other object.
## Heating and power application.
A microwave oven passes microwave radiation at a frequency near through food, causing dielectric heating primarily by absorption of the energy in water. Microwave ovens became common kitchen appliances in Western countries in the late 1970s, following the development of less expensive cavity magnetrons. Water in the liquid state possesses many molecular interactions that broaden the absorption peak. In the vapor phase, isolated water molecules absorb at around 22 GHz, almost ten times the frequency of the
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microwave oven.
Microwave heating is used in industrial processes for drying and curing products.
Many semiconductor processing techniques use microwaves to generate plasma for such purposes as reactive ion etching and plasma-enhanced chemical vapor deposition (PECVD).
Microwaves are used in stellarators and tokamak experimental fusion reactors to help break down the gas into a plasma, and heat it to very high temperatures. The frequency is tuned to the cyclotron resonance of the electrons in the magnetic field, anywhere between 2-200 GHz, hence it is often referred to as Electron Cyclotron Resonance Heating (ECRH). The upcoming ITER thermonuclear reactor will use up to 20 MW of 170 GHz microwaves.
Microwaves
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can be used to transmit power over long distances, and post-World War II research was done to examine possibilities. NASA worked in the 1970s and early 1980s to research the possibilities of using solar power satellite (SPS) systems with large solar arrays that would beam power down to the Earth's surface via microwaves.
Less-than-lethal weaponry exists that uses millimeter waves to heat a thin layer of human skin to an intolerable temperature so as to make the targeted person move away. A two-second burst of the 95 GHz focused beam heats the skin to a temperature of at a depth of . The United States Air Force and Marines are currently using this type of active denial system in fixed installations.
##
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