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OpenMath is the name of a markup language for specifying the meaning of mathematical formulae . Among other things, it can be used to complement MathML , a standard which mainly focuses on the presentation of formulae, with information about their semantic meaning. OpenMath can be encoded in XML or in a binary format.

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126-467: OpenMath consists of the definition of "OpenMath Objects", which is an abstract datatype for describing the logical structure of a mathematical formula and the definition of "OpenMath Content Dictionaries", or collections of names for mathematical concepts. The names available from the latter type of collections are specifically intended for use in extending MathML, and conversely, a basic set of such "Content Dictionaries" has been designed to be compatible with

252-664: A 113-meter-tall hotel and a 24-story residential tower have been approved. 121- and 93-meter-tall office buildings are planned to be built in Ruoholahti . Well over 200 high-rise buildings will be built in Helsinki in the 2020s. Well-known statues and monuments strongly embedded in the cityscape of Helsinki include the Keisarinnankivi ("Stone of the Empress", 1835), the statue of Russian Emperor Alexander II (1894),

378-541: A 15-minute walk or bike ride but the concept was left out of the green capital program and other parts of the 12 million euro program amount to a collection of temporary and one-off projects without any structural and lasting changes. Tallinn is situated on the southern coast of the Gulf of Finland , in north-western Estonia. The largest lake in Tallinn is Lake Ülemiste (9.44 km (3.6 sq mi)), which serves as

504-554: A canonical encoding for content dictionaries, but only requires an infrastructure sufficient for unique referencing in OMS elements. OpenMath provides a very basic XML encoding that meets these requirements, and a set of specific content dictionaries for some areas of mathematics, in particular covering the K-14 fragment covered by content MathML. For more richly structured content dictionaries (and generally for arbitrary mathematical documents)

630-597: A first layer of argillite followed by first layer of sandstone and siltstone and then another layer of argillite also followed by sandstone and siltstone. In other places of the city, hard sedimentary rock is only to be found beneath Quaternary sediments at depths reaching as much as 120 m below sea level. Underlying the sedimentary rock are the rocks of the Fennoscandian Craton including gneisses and other metamorphic rocks with volcanic rock protoliths and rapakivi granites . These rocks are much older than

756-502: A landscape of small villages. Some of the old villages from the 1240s in the area of present-day Helsinki, such as Koskela and Töölö , are now Helsinki districts, as are the rest of the 27 medieval villages. The area gradually became part of the Kingdom of Sweden and Christianity. Kuninkaantie , or the "King's Road", ran through the area and two interesting medieval buildings were built here: Vartiokylä hillfort  [ fi ] in

882-597: A more solid naval defence in front of the city. Little came of these plans, however, as Helsinki remained a small town plagued by poverty, war and disease. The plague of 1710 killed most of Helsinki's population. After the Russians captured Helsinki in May 1713 during the Great Northern War , the retreating Swedish administration set fire to parts of the city. Despite this, the city's population grew to 3,000 by

1008-554: A period of alternating Scandinavian and Teutonic rulers. Due to the strategic location by the sea, its medieval port became a significant trade hub , especially in the 14–16th centuries, when Tallinn grew in importance as the northernmost member city of the Hanseatic League . Tallinn Old Town is one of the best-preserved medieval cities in Europe and is listed as a UNESCO World Heritage Site . In 2012, Tallinn had

1134-421: A toponym Kolyvan , which has been discovered from later East Slavic chronicles. However, a number of historians have considered connecting any of al-Idrisi's placenames with modern Tallinn erroneous, unfounded, or speculative. The first archaeological traces of a small hunter-fisherman community's presence in what is now Tallinn's city centre are about 5,000 years old. The comb ceramic pottery found on

1260-528: A total area of 95,480 acres (38,640 ha). Of the total area, 48,190 acres (19,500 ha) are water areas and 47,290 acres (19,140 ha) are land areas. The city also has seven nature reserves in Espoo , Sipoo , Hanko and Ingå . The largest nature reserve is the Vanhankaupunginselkä , with an area of 30,600 acres (12,400 ha). The city's first nature reserve, Tiiraluoto of Lauttasaari,

1386-580: A train") and frowned upon by locals. Helsset is the Northern Sami name for Helsinki. After the end of the Ice Age and the retreat of the ice sheet, the first settlers arrived in the Helsinki area around 5000 BC. Their presence has been documented by archaeologists in Vantaa , Pitäjänmäki and Kaarela . Permanent settlements did not appear until the beginning of the 1st millennium AD, during

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1512-1138: A year. Snowfall is common during the winters, which are cloudy and characterised by low amounts of sunshine, ranging from only 20.7 hours of sunshine per month in December to 58.8 hours in February. At the winter solstice , daylight lasts for less than 6 hours and 5 minutes. Spring starts out cool, with freezing temperatures common in March and April, but gradually becomes warmer and sunnier in May, when daytime temperatures average 15.4 °C (59.7 °F), although nighttime temperatures still remain cool, averaging −3.7 to 5.2 °C (25.3 to 41.4 °F) from March to May. In early spring, freezing temperatures are common in March and snowfall can occur in April. Summers are warm with daytime temperatures hovering around 19.2 to 22.2 °C (66.6 to 72.0 °F) and nighttime temperatures averaging between 9.8 to 13.1 °C (49.6 to 55.6 °F) from June to August. The warmest month

1638-410: Is appointed by the city government. The function of the "district governments", however, is not directly governing, but just limited to providing advice to the city government and the city council on issues related to the administration of respective districts. The districts are administratively further divided into 84 asum (subdistricts or "neighbourhoods" with officially defined borders). The city

1764-516: Is around 19 to 22 °C (66 to 72 °F). Due to the sea effect, especially on hot summer days, daytime temperatures are slightly cooler and nighttime temperatures higher than further inland. The highest temperature recorded in the city was 33.2 °C (91.8 °F) on 28 July 2019 at the Kaisaniemi weather station, breaking the previous record of 33.1 °C (91.6 °F) set in July 1945 at

1890-652: Is chosen in the nationally held municipal elections , which are held every four years. Helsinki's city council consists of eighty-five members. Following the most recent municipal elections in 2017, the three largest parties are the National Coalition Party (25), the Green League (21), and the Social Democratic Party (12). The Mayor of Helsinki is Juhana Vartiainen . The city of Helsinki has 683,669 inhabitants, making it

2016-532: Is classified as a major port city, and in 2017 it was rated the world's busiest passenger port. According to a theory put forward in the 1630s, at the time of Swedish colonisation of the Finnish coast, colonists from Hälsingland in central Sweden arrived at what is now the Vantaa River and called it Helsingå ('Helsinge River'), giving rise to the names of the village and church of Helsinge in

2142-420: Is comparatively high in certain parts of downtown Helsinki, reaching 16,494 inhabitants per square kilometre (42,720/sq mi) in the district of Kallio , overall Helsinki's population density is 3,147 per square kilometre. Outside the city centre, much of Helsinki consists of post-war suburbs separated by patches of forest. A narrow, 10 kilometres (6.2 mi) long Helsinki Central Park , which stretches from

2268-456: Is criticised for being inadequate for general mathematics, exposing not enough formal precision to capture the intricacies of numerics, lacking a proof-of-concept and as an inferior technology to already established approaches of encoding mathematical semantics, amongst other presumed shortcomings. Helsinki Helsinki is the capital and most populous city in Finland . It is on

2394-488: Is derived. Official Finnish government documents and Finnish language newspapers have used the name Helsinki since 1819, when the Senate of Finland moved to the city from Turku , the former capital of Finland. Decrees issued in Helsinki were dated with Helsinki as the place of issue. This is how the form Helsinki came to be used in written Finnish. When Finland became a Grand Duchy of Finland, an autonomous state under

2520-541: Is divided into three major areas: Helsinki Downtown ( Finnish : Helsingin kantakaupunki , Swedish : Helsingfors innerstad ), North Helsinki ( Finnish : Pohjois-Helsinki , Swedish : Norra Helsingfors ) and East Helsinki ( Finnish : Itä-Helsinki , Swedish : Östra Helsingfors ). Of these, Helsinki Downtown means the undefined core area of capital, as opposed to suburbs . The designations business center and city center usually refer to Kluuvi , Kamppi and Punavuori . Other subdivisional centers outside

2646-530: Is governed by the Tallinn City Council which consists of 79 members elected to four year terms via party list. The mayor is elected by the city council. The population of Tallinn on 1 January 2024 was 457,572. It is the primate and most populous city in Estonia, the 3rd most populous city in the three Baltic States (Estonia, Latvia, Lithuania), as well as the 59th most populous city in

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2772-421: Is mainly due to the location between a more maritime and a more continental climate and the variation in the duration of sunshine as a consequence of its high latitude. Riga and Helsinki took second and third places. . Tallinn is subdivided into eight administrative linnaosa (districts). Each district has a linnaosa valitsus (district government) which is managed by a linnaosavanem (district elder) who

2898-638: Is situated in Hiiu , Nõmme District, in the south-west of the city. A large limestone cliff runs through the city. It can be seen at Toompea, Lasnamäe , and Astangu . However, the hill at Toompea is not geologically part of the larger limestone cliff. The rocks and sediments underneath Tallinn are of different composition and age. Youngest are the Quaternary deposits. The materials of these deposits are till , varved clay , sand, gravel, and pebbles that are of glacial , marine and lacustrine origin. Some of

3024-779: Is the Sederholm House  [ fr ] (1757) at the intersection of Senate Square and the Katariinankatu street. Suomenlinna also has buildings completed in the 18th century, including the Kuninkaanportti on the Kustaanmiekka Island  [ fr ] (1753–1754). The oldest church in Helsinki is the Östersundom church, built in 1754. Helsinki is also home to numerous Art Nouveau -influenced ( Jugend in Finnish) buildings belonging to

3150-522: Is the capital and most populous city of Estonia . Situated on a bay in north Estonia, on the shore of the Gulf of Finland of the Baltic Sea , Tallinn has a population of about 457,000 (as of 2024) and administratively lies in the Harju maakond (county). Tallinn is the main governmental, financial, industrial, and cultural centre of Estonia. It is located 187 km (116 mi) northwest of

3276-604: Is the third-largest municipality in the Nordic countries, after Stockholm and Oslo . Its urban area is the third-largest in the Nordic countries, after Stockholm and Copenhagen. Helsinki Airport , in the neighbouring city of Vantaa, serves the city with frequent flights to numerous destinations in Europe, North America, and Asia. Helsinki is a bilingual municipality with Finnish and Swedish as its official languages. The population consists of 75% Finnish speakers, 5% Swedish speakers, and 20% speakers of other languages (which

3402-545: Is the largest such area in Finland, with a land area of 669.31 square kilometres (258.42 sq mi) and approximately 1.36  million inhabitants. Helsinki has a cold hemiboreal humid continental climate ( Köppen : Dfb , Trewartha Dcbo ). Due to the moderating influence of the Baltic Sea and the North Atlantic Current (see also Extratropical cyclone ), winter temperatures are higher than

3528-473: Is the most densely populated area of Finland . The Capital Region spreads over a land area of 770 square kilometres (300 sq mi) and has a population density of 1,619 per sg km. With over 20 percent of the country's population in just 0.2 percent of its surface area, the area's housing density is high by Finnish standards. The Helsinki metropolitan area or the Greater Helsinki consists of

3654-575: Is the only regulated exchange in Estonia. Port of Tallinn is one of the biggest ports in the Baltic sea region, whereas the largest cargo port of Estonia, the Port of Muuga , which is operated by the same business entity, is located in the neighboring town of Maardu . Old City Harbour has been known as a convenient harbour since the medieval times, but nowadays the cargo operations are shifted to Muuga Cargo Port and Paldiski South Harbour . As of 2010, there

3780-424: Is to this day, the most populous district of Tallinn. The official language of Tallinn is Estonian. As of 2011, 50.1% of the city's residents were native speakers of Estonian, whereas 46.7% had Russian as their first language . While English is the most frequently used foreign language by the residents of Tallinn, there are also a significant number of native speakers of Ukrainian and Finnish . The pie chart to

3906-622: Is usually July, with an average of 17.6 °C (63.7 °F). During summer, partly cloudy or clear days are common and it is the sunniest season, ranging from 255.6 hours of sunshine in August to 312.1 hours in July although precipitation is higher during these months. At the summer solstice , daylight lasts for more than 18 hours and 40 minutes. Autumn starts out mild, with a September average daily mean of 12.0 °C (53.6 °F) and increasingly becomes cooler and cloudier in November. In

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4032-517: Is well above the national average). Helsinki hosted the 1952 Summer Olympics , the first CSCE / OSCE Summit in 1975, the first World Athletics Championships in 1983, the 52nd Eurovision Song Contest in 2007 and it was the 2012 World Design Capital . Helsinki has one of the highest standards of urban living in the world. In 2011, the British magazine Monocle ranked Helsinki as the world's most liveable city in its livable cities index . In

4158-592: The Battle at Herdaler was a battle between the Norse Viking leader Olav Haraldsson (later King Olaf II of Norway , also known as Saint Olaf) and local Finns at Herdaler (now Ingå ), not far from Helsinga, around 1007–8. The Saga of Olaf Haraldson tells how Olav raided the coasts of Finland and was almost killed in battle. He ran away in fear and after that the Vikings did not raid the coasts of Finland. Later

4284-631: The Economist Intelligence Unit's 2016 livability survey, Helsinki ranked ninth out of 140 cities. In July 2021, the American magazine Time named Helsinki one of the world's greatest places, a city that "can grow into a burgeoning cultural nest in the future" and is already known as an environmental pioneer. In an international Cities of Choice survey conducted in 2021 by the Boston Consulting Group and

4410-824: The House of Nobility in Kruununhaka and the Catholic St. Henry's Cathedral . In addition to other cities in Northern Europe that were not under the Soviet Union , such as Stockholm , Sweden, Helsinki's neoclassical buildings gained also popularity as a backdrop for scenes intended to depict the Soviet Union in numerous Hollywood movies during the Cold War era, when filming within the actual USSR

4536-649: The Ilmala weather station. The lowest temperature recorded in the city was −34.3 °C (−29.7 °F) on 10 January 1987, although an unofficial low of −35 °C (−31 °F) was recorded in December 1876. Helsinki Airport (in Vantaa, 17 km north of Helsinki city centre) recorded a maximum temperature of 33.7 °C (92.7 °F) on 29 July 2010 and a minimum of −35.9 °C (−33 °F) on 9 January 1987. Precipitation comes from frontal passages and thunderstorms. Thunderstorms are most common in summer. Helsinki

4662-517: The Iron Age , when the area was inhabited by the Tavastians . They used the area for fishing and hunting, but due to the lack of archaeological finds it is difficult to say how extensive their settlements were. Pollen analysis has shown that there were agricultural settlements in the area in the 10th century, and surviving historical records from the 14th century describe Tavastian settlements in

4788-474: The OMDoc format extends OpenMath by a “statement level” (including structures like definitions, theorems, proofs and examples, as well as means for interrelating them) and a “theory level”, where a theory is a collection of several contextually related statements. OMDoc's theories are designed to be compatible to OpenMath content dictionaries, but they can also be set into inheritance and import relations. OpenMath

4914-723: The Scandinavian and German languages as Reval ( Latin : Revalia ). Reval was in official use in Estonia until 1918. In international use, the English and German-language ( Reval ; German: [ˈʁeːval] ) as well as the Russian analog Revel ( Ревель ) were all gradually replaced by the Estonian name after the country became independent in 1918. At first, both Estonian forms, Tallinna and Tallinn , were used. Tallinna in Estonian denotes also

5040-505: The Senate Square and Helsinki Cathedral are located. During the second half of the 17th century, Helsinki, as a wooden city, suffered from regular fires , and by the beginning of the 18th century the population had fallen below 1,700. For a long time Helsinki was mainly a small administrative town for the governors of Nyland and Tavastehus County , but its importance began to grow in the 18th century when plans were made to build

5166-678: The Soviet air force . During the most destructive Soviet bombing raid on 9–10 March 1944 , over a thousand incendiary bombs were dropped on the town, causing widespread fires, killing 757 people, and leaving over 20,000 residents of Tallinn without shelter. After the German retreat in September 1944, the city was occupied again by the Soviet Union . During the 1980 Summer Olympics , the sailing (then known as yachting) events were held at Pirita , north-east of central Tallinn. Many buildings, such as

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5292-663: The Tallinn TV Tower , "Olümpia" hotel, the new Main Post Office building, and the Regatta Centre, were built for the Olympics. In 1991, the independent democratic Estonian nation was restored and a period of quick development as a modern European capital ensued. Tallinn became the capital of a de facto independent country once again on 20 August 1991. The Old Town became a World Heritage Site in 1997, and

5418-535: The bourgeoisie of Porvoo , Raseborg , Rauma and Ulvila to move there. The shallowness of the bay made it impossible to build a harbour, and the king allowed the settlers to leave the unfortunate location. In 1640, Count Per Brahe the Younger , together with some descendants of the original settlers, moved the centre of the city to the Vironniemi peninsula by the sea, today's Kruununhaka district, where

5544-650: The genitive case of the name, as in Tallinna Sadam ('the Port of Tallinn '). Henry of Livonia , in his chronicle ( c.  1229 ), called the town with the name that is also known to have been used up to the 13th century by Scandinavians: Lindanisa (or Lyndanisse in Danish , Lindanäs in Swedish and Ledenets in Old East Slavic ). In 1154, a town called قلون ( Qlwn or Quwri )

5670-474: The 1219 battle of Lyndanisse. The Icelandic Njal's saga —composed after 1270, but describing events between 960 and 1020—mentions an event that occurred somewhere in the area of Tallinn and calls the place Rafala (probably a derivation of Rävala , Revala , or some other variant of the Estonian name of the adjacent medieval Estonian county ). Soon after the Danish conquest in 1219, the town became known in

5796-469: The 1300s. This theory is questionable, as dialect research suggests that the settlers came from Uppland and the surrounding areas. Others have suggested that the name derives from the Swedish word helsing , an archaic form of the word hals (' neck '), which refers to the narrowest part of a river, the rapids . Other Scandinavian towns in similar geographical locations were given similar names at

5922-645: The 1380s and the Church of St. Lawrence in 1455. In the Middle Ages, several thousand people lived in Helsinki's keep . There was a lot of trade across the Baltic Sea . The shipping route to the coast, and especially to Reval , meant that by the end of the Middle Ages the Helsinki region had become an important trading centre for wealthy peasants , priests and nobles in Finland, after Vyborg and Pohja . Furs , wood , tar , fish and animals were exported from Helsinki, and salt and grain were brought to

6048-430: The 13th century when Christianity was forcibly imposed on the local population. Danish rule of Tallinn and northern Estonia started in 1219. In 1285, Tallinn, then known more widely as Reval, became the northernmost member of the Hanseatic League  – a mercantile and military alliance of German-dominated cities in Northern Europe. The king of Denmark sold Reval along with other land possessions in northern Estonia to

6174-544: The 1810s, when it replaced Turku as the capital of the Grand Duchy of Finland , which later became the sovereign Republic of Finland . The city continued its growth from that time on, with an exception during the Finnish Civil War . From the end of World War II up until the 1970s there was a massive exodus of people from the countryside to the cities of Finland, in particular Helsinki. Between 1944 and 1969

6300-512: The 1930s included the 18-story "Kino" palace, a 17-story apartment building, and a 30-story Stockmann building were proposed but only the 70-meter-tall 14-story Hotel Torni was built. (Hotel Torni was the tallest high-rise in Finland until 1976, when the 83-meter-tall Neste headquarters were completed in Espoo; Helsinki had rejected the tower. ) Twin 30-story buildings were proposed in Pasila in

6426-604: The 1940 Helsinki Olympic Games; the games were initially cancelled due to the Second World War , but the venues fulfilled their purpose in the 1952 Olympic Games . Many of them are listed by DoCoMoMo as significant examples of modern architecture. The Olympic Stadium and Helsinki-Malmi Airport are also catalogued by the Finnish Heritage Agency as cultural-historical environments of national significance. When Finland became heavily urbanized in

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6552-487: The 1960s and 1970s, the district of Pihlajamäki , for example, was built in Helsinki for new residents, where for the first time in Finland, precast concrete was used on a large scale. Pikku Huopalahti , built in the 1980s and 1990s, has tried to get rid of a one-size-fits-all grid pattern, which means that its look is very organic and its streets are not repeated in the same way. Itäkeskus in Eastern Helsinki

6678-446: The 1967 British-American espionage thriller Billion Dollar Brain , starring Michael Caine . The city has large amounts of underground areas such as shelters and tunnels, many used daily as swimming pool, church, water management, entertainment etc. Helsinki also features several buildings by Finnish architect Alvar Aalto , recognized as one of the pioneers of architectural functionalism . However, some of his works, such as

6804-422: The 1970s but were rejected. In 1990 a planned 104-meter-tall tower for the Kone company was also cancelled. Highrise construction only started in the beginning of the 21st century, when the city decided to allow the construction of skyscrapers. Highrises were first built in Kalasatama , a primarily-residential district built on a former container port . As of 2024, four residential towers have been completed:

6930-492: The 1970s, which occurred late compared to the rest of Europe, tripled the population of the metropolitan area, and the Helsinki Metro subway system was built. Known as the "Daughter of the Baltic" or the "Pearl of the Baltic", Helsinki is located at the tip of a peninsula and on 315 islands. The city centre is located on a southern peninsula, Helsinginniemi ("Cape of Helsinki"), which is rarely referred to by its actual name, Vironniemi ("Cape of Estonia"). Population density

7056-452: The 35-story, 282-apartment, 134-metre-tall (440 ft) Majakka in 2019 (which is the tallest building in Finland ); the 32-story, 124-meter Loisto in 2021; the 31-story, 120-meter Lumo One in 2022; and the 24-story, 98-meter Visio in 2023. The 26-story, 111-meter-tall office building Horisontti is to be completed in 2025, and three further towers are to be built in the complex. Tall residential towers have also been built in

7182-443: The BCG Henderson Institute, Helsinki was ranked the third-best city in the world to live in, with London and New York City coming in first and second. In the Condé Nast Traveler magazine's 2023 Readers' Choice Awards, Helsinki was ranked the 4th-friendliest city in Europe. Helsinki, along with Rovaniemi in Lapland , is also one of Finland's most important tourist cities. Due to the large number of sea passengers, Helsinki

7308-440: The Baltic Sea". One of Tallinn's sister cities is the Silicon Valley town of Los Gatos, California . Skype is one of the best-known of several Estonian start-ups originating from Tallinn. Many start-ups have originated from the Institute of Cybernetics . In recent years, Tallinn has gradually been becoming one of the main IT centres of Europe, with the Cooperative Cyber Defence Centre of Excellence (CCD COE) of NATO , eu-LISA ,

7434-409: The EU Digital Agency and the IT development centres of large corporations, such as TeliaSonera and Kuehne + Nagel being based in the city. Tallinn receives 4.3 million visitors annually, a figure that has grown steadily over the past decade. The Finns are especially a common sight in Tallinn; on average, about 20,000–40,000 Finnish tourists visit the city between June and October. Most of

7560-552: The European Union. According to Eurostat , in 2004, Tallinn had one of the largest number of non-EU nationals of all EU member states' capital cities. Ethnic Russians are a significant minority in Tallinn, as around a third of the city's residents are first and second generation immigrants from Russia and other parts of the former Soviet Union; a majority of the Soviet-era immigrants now hold Estonian citizenship. Ethnic Estonians made up over 80% of Tallinn's population before World War II. As of 2022, ethnic Estonians made up over 53% of

7686-400: The Kansallisromantiikka ( romantic nationalism ) trend, designed in the early 20th century and strongly influenced by Kalevala , which was a common theme of the era. Helsinki's Art Nouveau style is also featured in central residential districts, such as Katajanokka and Ullanlinna . An important architect of the Finnish Art Nouveau style was Eliel Saarinen , whose architectural masterpiece

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7812-457: The Quaternary deposits are valuable as they constitute aquifers , or as in the case of gravels and sands, are used as construction materials. The Quaternary deposits are the fill of valleys that are now buried. The buried valleys of Tallinn are carved into older rock likely by ancient rivers to be later modified by glaciers. While the valley fill is made up of Quaternary sediments the valleys themselves originated from erosion that took place before

7938-428: The Quaternary. The substrate into which the buried valleys were carved is made up of hard sedimentary rock of Ediacaran , Cambrian and Ordovician age. Only the upper layer of Ordovician rocks protrudes from the cover of younger deposits, cropping out in the Baltic Klint at the coast and at a few places inland. The Ordovician rocks are made up from top to bottom of a thick layer of limestone and marlstone , then

8064-505: The Societies Executive Committee, which welcomes self-nominations of individuals who have worked on OpenMath-related issues in research or application. As of 2007, Michael Kohlhase is president of the OpenMath society. He succeeded Arjeh M. Cohen, who was the first president. The well-known quadratic formula : would be marked up like this in OpenMath (the representation is an expression tree made up from functional elements like OMA for function application or OMV for variables): In

8190-407: The Sveaborg fortress during the war, and about a quarter of the city was destroyed in a fire in 1808. Emperor Alexander I of Russia moved the capital of Finland from Turku to Helsinki on 8 April 1812 to reduce Swedish influence in Finland and bring the capital closer to St Petersburg . After the Great Fire of Turku in 1827, the Royal Academy of Turku , the only university in the country at

8316-485: The Teutonic Knights in 1346. Reval was arguably the most significant medieval port in the Gulf of Finland. Reval enjoyed a strategic position at the crossroads of trade between the rest of western Europe and Novgorod and Muscovy in the east. The city, with a population of about 8,000, was very well fortified with city walls and 66 defence towers . The city wall has been described as an outstanding example of German Medieval fortification architecture. A weather vane ,

8442-400: The area was settled by Christians from Sweden. They came mainly from the Swedish coastal regions of Norrland and Hälsingland , and their migration intensified around 1100. The Swedes permanently colonised the Helsinki region's coastline in the late 13th century, after the successful 'crusade' to Finland that led to the defeat of the Tavastians. In the Middle Ages, the Helsinki area was

8568-452: The area. Christianity does not gain a significant foothold in Finland before the 11th century. After that, a number of crosses and other objects related to Christianity can be found in archaeological material. According to the traditional view, the Kingdom of Sweden made three crusades to Finland, thanks to which the region was incorporated into both Christianity and the Swedish Empire. Recent research has shown that these expeditions, to

8694-416: The beginning of the 19th century. The construction of the naval fortress of Sveaborg ( Viapori in Finnish, now also called Suomenlinna ) in the 18th century helped to improve Helsinki's status. However, it wasn't until Russia defeated Sweden in the Finnish War and annexed Finland as the autonomous Grand Duchy of Finland in 1809 that the city began to develop into a substantial city. The Russians besieged

8820-405: The cities of Espoo , Vantaa and Kauniainen —and surrounding commuter towns, including the neighbouring municipality of Sipoo to the east —Helsinki forms a metropolitan area . This area is often considered Finland's only metropolis and is the world's northernmost metropolitan area with over one million inhabitants. Additionally, it is the northernmost capital of an EU member state . Helsinki

8946-463: The cities of the capital region and ten surrounding municipalities: Hyvinkää , Järvenpää , Kerava , Kirkkonummi , Nurmijärvi , Sipoo , Tuusula , Pornainen , Mäntsälä and Vihti . The Metropolitan Area covers 3,697 square kilometres (1,427 sq mi) and has a population of about 1.6 million, or about a fourth of the total population of Finland. The metropolitan area has a high concentration of employment: approximately 750,000 jobs. Despite

9072-431: The city centre to Helsinki's northern border, is an important recreational area for residents. The City of Helsinki has about 11,000 boat moorings and over 14,000 hectares (35,000 acres; 54 square miles) of marine fishing waters adjacent to the capital region. About 60 species of fish are found in this area, and recreational fishing is popular. Helsinki's main islands include Seurasaari , Lauttasaari and Korkeasaari –

9198-495: The city hosted the 2002 Eurovision Song Contest . Tallinn was the 2011 European Capital of Culture , and is the recipient of the 2023 European Green Capital Award . The city has pledged to cut greenhouse gas emissions by 40% by 2030 and takes pride in its biodiversity and high air quality. But critics say that the award was received on false promises since it won the title with its " 15-minute city " concept, according to which key facilities and services should be accessible within

9324-512: The country's largest private energy company, Alexela Group , all have their headquarters in Tallinn. Tallinn is the financial centre of Estonia and also an important economic centre in the Baltoscandian region. Many major banks, such as SEB , Swedbank , and Nordea , have their local offices in Tallinn. LHV Pank , an Estonian investment bank, has its corporate headquarters in Tallinn. Tallinn Stock Exchange , part of NASDAQ OMX Group ,

9450-511: The country's second largest city, Tartu ; however, only 80 km (50 mi) south of Helsinki , Finland , also 320 km (200 mi) west of Saint Petersburg , Russia , 300 km (190 mi) north of Riga , Latvia , and 380 km (240 mi) east of Stockholm , Sweden . From the 13th century until the first half of the 20th century, Tallinn was known in most of the world by variants of its other historical name Reval . Tallinn received Lübeck city rights in 1248; however,

9576-481: The downtown area include Malmi ( Swedish : Malm ), located in the northeastern part of city, and Itäkeskus ( Swedish : Östra centrum ), in the eastern part of city. Carl Ludvig Engel , appointed to plan a new city centre on his own, designed several neoclassical buildings in Helsinki. The focal point of Engel's city plan was the Senate Square . It is surrounded by the Government Palace (to

9702-478: The driest months, averaging about 35 to 37 mm (1.4 to 1.5 in), while July and August are the wettest months with 82 to 85 mm (3.2 to 3.3 in) of precipitation. The average humidity is 81%, ranging from a high of 89% to a low of 69% in May. Tallinn has an average windspeed of 3.3 m/s (11 ft/s) with winters being the windiest (around 3.7 m/s (12 ft/s) in January) and summers being

9828-504: The earliest evidence of human population in the area dates back nearly 5,000 years. The medieval indigenous population of what is now Tallinn and north Estonia was one of the last " pagan " civilisations in Europe to adopt Christianity following the Papal -sanctioned Livonian Crusade in the 13th century. The first recorded claim over the place was laid by Denmark after a successful raid in 1219 led by King Valdemar II , followed by

9954-459: The early parts of autumn, temperatures commonly reach 16.1 °C (61.0 °F) and at least one day above 21 °C (70 °F) in September. In late autumn, snowfall can occur in October and freezing temperatures become more common in November. Tallinn receives 700 mm (28 in) of precipitation annually, which is evenly distributed throughout the year although March, April and May are

10080-461: The east), the main building of Helsinki University (to the west), and (to the north) the large Helsinki Cathedral , which was finished in 1852, twelve years after Engel's death. Helsinki's epithet , "The White City of the North", derives from this construction era. Most of Helsinki's older buildings were built after the 1808 fire; before that time, the oldest surviving building in the center of Helsinki

10206-486: The eastern district of Vuosaari : the 87-meter, 26-story Cirrus was completed in 2006, the 24-story, 85-meter-tall Hyperion was completed in 2023 and the 33-story, 288-apartment, 120-meter-tall Atlas is due to be completed in late 2024. Skyscrapers have also be planned in the Pasila area, with a handful of over-100-meter-tall towers in various stages of planning or early construction as of 2024. In Jätkäsaari ,

10332-464: The expression tree above symbols—i.e. elements like <OMS cd="arith1" name="times"/> —stand for mathematical functions that are applied to sibling expressions in an OMA which are interpreted as arguments. The OMS element is a generic extension element that means whatever is specified in the content dictionary referred to in the cd attribute (this document can be found at the URI specified in

10458-468: The extent that there were even three of them, were not the crusades that had been imagined. Later, the conquest of Finland was justified in terms of "civilisation" and "christianisation", and the myth of the Crusades was developed. It is more likely that it was a multidimensional combination of economic, cultural and political power ambitions. The early settlements were raided by Vikings until 1008, and

10584-627: The figure of an old warrior called Old Thomas , was put on top of the spire of the Tallinn Town Hall in 1530. Old Thomas later became a popular symbol of the city. In the early years of the Protestant Reformation , the city converted to Lutheranism . In 1561, Reval (Tallinn) became a dominion of Sweden. During the 1700–1721 Great Northern War , plague - stricken Tallinn along with Swedish Estonia and Livonia capitulated to Tsardom of Russia (Muscovy) in 1710, but

10710-475: The fortress. Helsinki was also the most important cattle-breeding area in Uusimaa. With the help of trade, Helsinki became one of the wealthiest cities in Finland and Uusimaa. Thanks to trade and travel, e.g. to Reval, people could speak several languages, at least helpfully. Depending on the situation, Finnish, Swedish, Latin or Low German could be heard in the Helsinki area. Written chronicles from 1417 mention

10836-902: The fountain sculpture Havis Amanda (1908), the Paavo Nurmi statue (1925), the Three Smiths Statue (1932), the Aleksis Kivi Memorial (1939), the Eino Leino Statue (1953), the Equestrian statue of Marshal Mannerheim (1960) and the Sibelius Monument (1967). As is the case with all Finnish municipalities , Helsinki's city council is the main decision-making organ in local politics, dealing with issues such as urban planning , schools, health care, and public transport . The council

10962-414: The glass-walled Sanomatalo (1999). There have been many plans to build highrise buildings in Helsinki since the 1920s when architect Eliel Saarinen proposed the 85-meter-tall Kalevalatalo in 1921, but few tall buildings were built until the 21st century. In 1924 Oiva Kallio won Etu-Töölö competition with his plan (several 14- to 16-story buildings). A 32-story city hall was also proposed. Other plans of

11088-874: The headquarters of the paper company Stora Enso and the concert venue Finlandia Hall , have been subject to divided opinions from the citizens. Functionalist buildings in Helsinki by other architects include the Olympic Stadium , the Tennis Palace , the Rowing Stadium , the Swimming Stadium , the Velodrome , the Glass Palace , the Töölö Sports Hall , and Helsinki-Malmi Airport . The sports venues were built to serve

11214-543: The highest number of startup companies per person among all capitals and larger cities in Europe. Tallinn is the birthplace of many international high-technology companies, including Skype and Wise . The city is home to the headquarters of the European Union 's IT agency, and to the NATO Cyber Defence Centre of Excellence . In 2007, Tallinn was listed among the top-10 digital cities in

11340-547: The innermost cdbase attribute dominating the respective OMS element. In the example above, all symbols come from the content dictionary for arithmetics ( arith1 , see below), except for the plusminus , which comes from a non-standard place, hence the cdbase attribute here. Content Dictionaries are structured XML documents that define mathematical symbols that can be referred to by OMS elements in OpenMath Objects. The OpenMath 2 standard does not prescribe

11466-412: The intensity of land use, the region also has large recreational areas and green spaces. The Helsinki metropolitan area is the world's northernmost urban area with a population of over one million people, and the northernmost EU capital city. The Helsinki urban area is an officially recognized urban area in Finland , defined by its population density. The area stretches throughout 11 municipalities, and

11592-404: The latitude, the days around the winter solstice are 5 hours and 48 minutes long, with the sun very low (at noon the sun is just over 6 degrees in the sky), and the cloudy weather at this time of year exacerbates the darkness. Conversely, Helsinki enjoys long days in summer, with 18 hours and 57 minutes of daylight around the summer solstice . The average maximum temperature from June to August

11718-497: The latter is home to Finland's largest zoo, Korkeasaari Zoo . The former military islands of Vallisaari and Isosaari are now open to the public, but Santahamina is still in military use. The most historic and remarkable island is the fortress of Suomenlinna (Sveaborg). The island of Pihlajasaari is a popular summer resort, comparable to Fire Island in New York City . There are 60 nature reserves in Helsinki with

11844-408: The least windy at around 2.7 m/s (8.9 ft/s) in August. Extremes range from −32.2 °C (−26.0 °F) on 31 December 1978 to 34.3 °C (93.7 °F) on 30 July 1994. According to a 2021 study commissioned by the British price comparison site Uswitch.com, Tallinn is the most unpredictable of European capitals in terms of weather conditions, with a total score of 69/100; the high score

11970-620: The local self-government institutions ( Magistracy of Reval and Estonian Knighthood ) retained their cultural and economical autonomy within Imperial Russia as the Governorate of Estonia . The Magistracy of Reval was abolished in 1889. The 19th century brought industrialisation of the city and the port kept its importance. On 24 February 1918, the Estonian Declaration of Independence was proclaimed in Tallinn. It

12096-451: The main source of the city's drinking water. Lake Harku is the second-largest lake within the borders of Tallinn and its area is 1.6 km (0.6 sq mi). The only significant river in Tallinn nowadays is the Pirita river, in the eponymous Pirita city district. Historically, a smaller river, called Härjapea , flowed from Lake Ülemiste through the town into the sea, but the river

12222-409: The majority of workers were Finnish-speaking. The local Helsinki slang (or stadin slangi ) developed among Finnish children and young people from the 1890s as a mixed Finnish-Swedish language, with influences from German and Russian , and from the 1950s the slang began to become more Finnish. A landmark event was the 1952 Olympic Games , which were held in Helsinki. Finland's rapid urbanisation in

12348-538: The maker of the internationally-known Vana Tallinn liqueur, is similarly based in Tallinn. The headquarters of Kalev , a confectionery company and part of the industrial conglomerate Orkla Group , is located in Lehmja , near the city's southeastern boundary. Estonia is ranked third in Europe in terms of shopping centre space per inhabitant, ahead of Sweden and being surpassed only by Norway and Luxembourg . Institutions of higher education and science include: Tallinn

12474-471: The most populous municipality in Finland and the third in the Nordics . The Helsinki region is the largest urbanised area in Finland with 1,603,170 inhabitants. The city of Helsinki is home to 12% of Finland's population. 19.9% of the population has a foreign background, which is twice above the national average. However, it is lower than in the major Finnish cities of Espoo or Vantaa . At 53 percent of

12600-467: The northern location would suggest, with an average of −4 °C (25 °F) in January and February. Winters in Helsinki are significantly warmer than in the north of Finland, and the snow season in the capital is much shorter due to its location in the extreme south of Finland and the urban heat island effect. Temperatures below −20 °C (−4 °F) occur only a few times a year. However, due to

12726-458: The population of the city nearly doubled from 275,000 to 525,600. In the 1960s, the population growth of Helsinki began to decrease, mainly due to a lack of housing. Some residents began to move to the neighbouring cities of Espoo and Vantaa, resulting in increased population growth in both municipalities. Espoo's population increased ninefold in sixty years, from 22,874 people in 1950 to 244,353 in 2009. Vantaa saw an even more dramatic change in

12852-458: The population, women form a greater proportion of Helsinki residents than the national average of 51 percent. Helsinki's population density of 3,147 people per square kilometre makes Helsinki the most densely-populated city in Finland. The life expectancy for men and women is slightly below the national averages: 75.1 years for men as compared to 75.7 years, 81.7 years for women as compared to 82.5 years. Helsinki has experienced strong growth since

12978-522: The population. Tallinn was one of the urban areas with industrial and military significance in northern Estonia that during the period of Soviet occupation underwent extensive changes in its ethnic composition due to large influx of immigrants from Russia and other parts of the former USSR. Whole new city districts were built where the main intent of the then Soviet authorities was to accommodate Russian-speaking immigrants: Mustamäe, Väike-Õismäe, Pelguranna, and most notably, Lasnamäe, which in 1980s became, and

13104-539: The railway and industrialisation were key factors in the city's growth. By the 1910s, Helsinki's population was already over 100,000, and despite the turbulence of Finnish history in the first half of the 20th century, Helsinki continued to grow steadily. This included the Finnish Civil War and the Winter War , both of which left their mark on the city. At the beginning of the 20th century, there were roughly equal numbers of Finnish and Swedish speakers in Helsinki;

13230-667: The rest ( Paleoproterozoic age) and do not crop out anywhere in Estonia. Tallinn has a humid continental climate ( Köppen climate classification Dfb ) with warm, rainy summers and cold, snowy winters. Winters are cold, but mild for its latitude, owing to its coastal location. The average temperature in February, the coldest month, is −3.6 °C (25.5 °F). During the winters, temperatures tend to hover close to freezing, but mild spells of weather can push temperatures above 0 °C (32 °F), occasionally reaching above 5 °C (41 °F) while cold air masses can push temperatures below −18 °C (0 °F) an average of 6 days

13356-647: The right shows the distribution of religion in Tallinn as of 2021. Religion in Tallinn (2021) [1] Tallinn has a highly diversified economy with particular strengths in information technology, tourism and logistics. More than half of Estonia's GDP is created in Tallinn. In 2008, the GDP per capita of Tallinn stood at 172% of the Estonian average. In addition to longtime functions as seaport and capital city, Tallinn has seen development of an information technology sector; in its 13 December 2005, edition, The New York Times characterised Estonia as "a sort of Silicon Valley on

13482-481: The rule of the Russian Empire , Helsinki was known as Gel'singfors ( Гельсингфорс ) in Russian, because the main and official language of Grand Duchy of Finland was Swedish. In Helsinki slang , the city is called Stadi (from the Swedish word stad , meaning 'city'). Abbreviated form Hesa is equally common, but its use is associated with people of rural origin ("junantuomat", lit. "brought by

13608-607: The same time span: from 14,976 in 1950 to 197,663 in 2009, a thirteenfold increase. These population changes prompted the municipalities of metropolitan area into more intense cooperation in areas such as public transportation – resulting in the foundation of HSL – and waste management. The increasing scarcity of housing and the higher costs of living in the capital region have pushed many daily commuters to find housing in formerly rural areas, and even further, to cities such as Lohja , Hämeenlinna , Lahti , and Porvoo . Tallinn, Estonia Tallinn ( / ˈ t æ l ɪ n / )

13734-667: The shore of the Gulf of Finland and is the seat of southern Finland's Uusimaa region. About 684,000 people live in the municipality, with 1.26 million in the capital region and 1.6 million in the metropolitan area . As the most populous urban area in Finland, it is the country's most significant centre for politics, education, finance, culture, and research. Helsinki is 80 kilometres (50 mi) north of Tallinn, Estonia , 400 kilometres (250 mi) east of Stockholm, Sweden , and 300 kilometres (190 mi) west of Saint Petersburg, Russia . Helsinki has significant historical connections with these three cities. Together with

13860-478: The site dates to about 3000 BCE and corded ware pottery to around 2500 BCE. Around 1050 AD, a fortress was built in what is now central Tallinn, on the hill of Toompea . As an important port on a major trade route between Novgorod and western Europe, it became a target for the expansion of the Teutonic Knights and the Kingdom of Denmark during the period of Northern Crusades in the beginning of

13986-519: The small set of mathematical concepts defined in Content MathML, the non-presentational subset of MathML. OpenMath has been developed in a long series of workshops and (mostly European) research projects that began in 1993 and continues through today. The OpenMath 1.0 Standard was released in February 2000, and revised as OpenMath 1.1 in October 2002. Two years later, the OpenMath 2.0 Standard

14112-584: The time, such as Helsingør in Denmark and Helsingborg in Sweden. When a town was founded in the village of Forsby (later Koskela ) in 1548, it was called Helsinge fors , 'Helsinge rapids'. The name refers to the Vanhankaupunginkoski  [ fi ] rapids at the mouth of the river. The town was commonly known as Helsinge or Helsing , from which the modern Finnish name

14238-492: The time, was also moved to Helsinki and eventually became the modern University of Helsinki. The move consolidated the city's new role and helped set it on a path of continuous growth. This transformation is most evident in the city centre, which was rebuilt in the neoclassical style to resemble St. Petersburg, largely according to a plan by the German-born architect C. L. Engel . As elsewhere, technological advances such as

14364-515: The village of Koskela near the rapids at the mouth of the River Vantaa , where Helsinki was to be founded. Helsinki was founded by King Gustav I of Sweden on 12 June 1550 as a trading town called Helsingfors to rival the Hanseatic city of Reval (now Tallinn ) on the southern shore of the Gulf of Finland . To populate the new town at the mouth of the Vantaa River , the king ordered

14490-553: The visitors come from Europe, though Tallinn has also become increasingly visited by tourists from the Asia-Pacific region. Tallinn Passenger Port is one of the busiest cruise destinations on the Baltic Sea, it served more than 520,000 cruise passengers in 2013. The state-owned energy company Eesti Energia , the nationwide electric power transmission system operator Elering , the natural gas distributor Eesti Gaas , and

14616-422: The world, and in 2022, Tallinn was listed among the top-10 "medium-sized European cities of the future". The name Tallinn(a) Estonian: [ˈtɑlʲːinː] is Estonian . It has been widely considered a historical derivation of Taani-linna , meaning "Danish-castle" ( Latin : Castrum Danorum ), conceivably because the Danish invaders built the castle in place of the Estonian stronghold after

14742-658: Was a European Capital of Culture for 2011, along with Turku , Finland. Tallinn is home to more than 60 museums and galleries. Most of them are located in Kesklinn , the central district of the city, and cover Tallinn's rich history. One of the most visited historical museums in Tallinn is the Estonian History Museum , located in Great Guild Hall at Vanalinn , the old part of the city. It covers Estonia's history from prehistoric times up until

14868-563: Was diverted into underground sewerage system in the 1930s and has since completely disappeared from the cityscape. References to it still remain in the street names Jõe (from jõgi , river) and Kivisilla (from kivi sild , stone bridge). The length of the seaside coast is 46 km (29 mi), comprising three larger ( Kopli , Paljassaare , and Kakumäe ) peninsulas . The city has a number of public beaches, including those at Pirita, Stroomi, Kakumäe, Harku, and Pikakari. The highest point in Tallinn, at 64 m (about 200 ft) above sea level,

14994-485: Was established in 1948. Helsinki's official plant is the Norway maple and its official animal is the red squirrel . The Helsinki capital region ( Finnish : Pääkaupunkiseutu , Swedish : Huvudstadsregionen ) comprises four municipalities: Helsinki, Espoo , Vantaa , and Kauniainen . The Helsinki urban area is considered to be the only metropolis in Finland . It has a population of about 1.26 million, and

15120-524: Was followed by Imperial German occupation until the end of World War I in November 1918, after which Tallinn became the capital of independent Estonia. During World War II , Estonia was first occupied by the Soviet army and annexed into the USSR in the summer of 1940, then occupied by Nazi Germany from 1941 to 1944. During the German occupation Tallinn suffered from many instances of aerial bombing by

15246-549: Was not possible. Some of them, including The Kremlin Letter (1970), Reds (1981), and Gorky Park (1983). was possible due to such Russian cities as Leningrad and Moscow also having similar neoclassical architecture. At the same time due to Cold War and Finnish relations with the USSR the government secretly instructed Finnish officials not to extend assistance to such film projects. There are some films where Helsinki has been represented on its own in films, most notably

15372-501: Was recorded in the description of the world on the world map ( Tabula Rogeriana ) commissioned by the Norman King Roger II of Sicily and compiled by Arab cartographer Muhammad al-Idrisi , who described it as "a small town like a large castle" among the towns of 'Astlanda'. It has been suggested that one possible transcription, 'Qlwn', may have denoted a predecessor of the modern city and may somehow be related to

15498-585: Was released in June 2004. OpenMath 1 fixed the basic language architecture, while OpenMath2 brought better XML integration, structure sharing and liberalized the notion of OpenMath Content dictionaries. The OpenMath Effort is governed by the OpenMath Society, based in Helsinki , Finland . The Society brings together tool builders, software suppliers, publishers and authors. Membership is by invitation of

15624-517: Was still a small fleet of oceangoing trawlers that operated out of Tallinn. Tallinn's industries include shipbuilding, machine building, metal processing, electronics, textile manufacturing. BLRT Grupp has its headquarters and some subsidiaries in Tallinn. Air Maintenance Estonia and AS Panaviatic Maintenance , both based in Tallinn Airport, provide MRO services for aircraft, largely expanding their operations in recent years. Liviko ,

15750-795: Was the Helsinki Central Station . Opposite the Bank of Finland building is the Renaissance Revivalish the House of the Estates (1891). The only visible public buildings of the Gothic Revival architecture in Helsinki are St. John's Church (1891) in Ullanlinna, which is the largest stone church in Finland, and its twin towers rise to 74 meters and have 2,600 seats. Other examples of neo-Gothic include

15876-454: Was the first regional center in the 1980s. Efforts have also been made to protect Helsinki in the late 20th century, and many old buildings have been renovated. Modern architecture is represented, for example, by the Museum of Contemporary Art Kiasma , which consists of two straight and curved-walled parts, though this style strongly divided the opinions from the citizens. Next to Kiasma is

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