hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Euler's formula
Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number x, one has

where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively. This complex exponential function is sometimes denoted cis x ("cosine plus i sine"). The formula is still valid if x is a complex number, and is also called Euler's formula in this more general case.

Euler's formula is ubiquitous in mathematics, physics, chemistry, and engineering. The physicist Richard Feynman called the equation "our jewel" and "the most remarkable formula in mathematics".

When x = π, Euler's formula may be rewritten as eiπ = −1 or eiπ + 1 = 0, which is known as Euler's identity.

Complex plane
In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the horizontal x-axis, called the real axis, is formed by the real numbers, and the vertical y-axis, called the imaginary axis, is formed by the imaginary numbers.

The complex plane allows for a geometric interpretation of complex numbers. Under addition, they add like vectors. The multiplication of two complex numbers can be expressed more easily in polar coordinates: the magnitude or modulus of the product is the product of the two absolute values, or moduli, and the angle or argument of the product is the sum of the two angles, or arguments. In particular, multiplication by a complex number of modulus 1 acts as a rotation.

The complex plane is sometimes called the Argand plane or Gauss plane.
Puerto Rican cuisine
Puerto Rican cuisine consists of the cooking style and traditional dishes original to Puerto Rico. It has been primarily a fusion influenced by the ancestors of the Puerto Rican people: the indigenous Taínos, Spanish Criollos and sub-Saharan African slaves. As a territory of the United States, the culinary scene of Puerto Rico has also been moderately influenced by American cuisine.

Eryngium foetidum
Eryngium foetidum is a tropical perennial herb in the family Apiaceae. Common names include culantro (Costa Rica and Panama) (/kuːˈlɑːntroʊ/ or /kuːˈlæntroʊ/), cimarrón, recao (Puerto Rico), chardon béni (Martinique), Mexican coriander, samat, ban dhaniya, wide coriander, Burmese coriander, sawtooth coriander, Shadow Beni (Trinidad and Tobago), and ngò gaicode: vie promoted to code: vi  (Vietnam). It is native to Mexico, the Caribbean, and Central and South America, but is cultivated worldwide, mostly in the tropics as a perennial, but sometimes in temperate climates as an annual. In India it is called "Nagadhonia", specifically in the Northeast.

In the United States, the common name culantro sometimes causes confusion with cilantro, a common name for the leaves of Coriandrum sativum (also in Apiaceae but in a different genus), of which culantro is said to taste like a stronger version.
Nida (river)
The Nida pronounced [ˈɲida] is a river in central Poland, a left tributary of the Vistula river, into which it flows near Nowy Korczyn). The Nida has a length of 154 kilometres and a basin area of 3,844 km2. This includes the protected area called Nida Landscape Park.

The Nida itself is made up of two smaller rivers, the White Nida and the Black Nida, which merge in the village of Brzegi (near Checiny). It is a typical lowland river, with little difference in the water level. The valley of the Nida is wide, and covered with meadows. At its narrowest, the river is only 6 m wide, while at its widest spot, the Nida is 79 m across. The depth ranges from 0,4 to 2,6 m. The Nida is one of the warmest rivers of Poland; in the summer, its temperature reaches up to 27 degrees C.

Nida Landscape Park
Nida Landscape Park (Nadnidziański Park Krajobrazowy) is a Polish Landscape Park designated protected area, located in Świętokrzyskie Voivodeship of south-central Poland. Within the Solec Basin, gypsum outcrops are common, forming rocky cliffs. Examples of karst formations include numerous caves, ponors, wywierzyski, karst lakes and rock gates. They are found in the vicinity of Gacek, Wiślica and Busk-Zdrój. There are karst gullies in Gorysławice. The karst forms found in Nadnidziański Park are unique in the country.  Among the most valuable are large-crystalline (glassy) gypsums. The crystals of which they are composed reach a length of 3.5 meters.
Three Little Words (film)
Three Little Words is a 1950 American biographical musical comedy film directed by Richard Thorpe from a screenplay by George Wells. It stars Fred Astaire as lyricist Bert Kalmar and Red Skelton as composer Harry Ruby, along with Vera-Ellen and Arlene Dahl as their wives, with Debbie Reynolds in a small but notable role as singer Helen Kane and Gloria DeHaven as her own mother, Mrs. Carter DeHaven.

The film was produced by Jack Cummings and released by Metro-Goldwyn-Mayer. Ruby served as a consultant on the project and appears in a cameo role as a baseball catcher. The third in a series of MGM biopics about Broadway composers, it was preceded by Till the Clouds Roll By (1946) and Words and Music (1948) and followed by Deep in My Heart (1954).

Vera-Ellen
Vera-Ellen (born Vera-Ellen Rohe; February 16, 1921 – August 30, 1981) was an American dancer, actress, and singer. She is remembered for her solo performances as well as her work with partners Fred Astaire, Gene Kelly, Danny Kaye, and Donald O'Connor. She is best known for her starring roles in On the Town (1949) with Kelly and White Christmas (1954) with Kaye.
My Chick Bad
"My Chick Bad" is a song by American rapper Ludacris. The song features Nicki Minaj, who co-wrote the song with Ludacris, Samuel Lindley, and Derrelle Davidson. The track was produced by the Legendary Traxster. "My Chick Bad" serves as the second single from Ludacris' eighth album, Battle of the Sexes. An official remix to the song was also released, featuring female rappers Diamond, Eve, and Trina.

The song was a commercial success, peaking at number 11 on the Billboard Hot 100. The song reached number two on the Hot R&B/Hip-Hop Songs and Rap Songs charts, and also appeared on the Pop Songs without an official release to pop radio. "My Chick Bad" was nominated for a 2011 Grammy Award in the category Best Rap Performance by a Duo or Group. The accompanying music video for both versions of the song take place in a dungeon during the filming of a movie, with Minaj portraying a Freddy Krueger-esque character, an early incarnation of her alter-ego, Roman Zolanski.

Battle of the Sexes (album)
Battle of the Sexes is the eighth studio album by American rapper Ludacris, released March 9, 2010 on Disturbing tha Peace and Def Jam South. The album was recorded during 2008 to 2010 and its production was handled by several producers, including T-Minus, Bangladesh, Swizz Beatz, The Neptunes, and The Runners.

Upon its release, Battle of the Sexes received generally positive reviews from most music critics.
Shastri (2005 film)
Shastri (also known as Darshan Shastri)  is a 2005 Kannada-language  action film written and directed by P. N. Sathya and produced by Anaji Nagaraj for Namana films. The film stars Darshan and Manya. The musical score is by Sadhu Kokila.

P. N. Sathya
P. N. Sathya (died 5 May 2018) was an Indian film director, writer and actor working in Kannada cinema. He was known for writing and directing crime drama films. He debuted with the crime film Majestic (2002) which introduced actor Darshan in the lead role and went on to direct many such films like Don (2003), Daasa (2003), Shashtri (2005), Thangigagi (2006), Sugreeva (2010) and Shivajinagar (2014).
Bahamas at the 1972 Summer Paralympics
The Bahamas made its Paralympic Games début at the 1972 Summer Paralympics in Heidelberg, West Germany. The country's delegation consisted in a single athlete, John Sands. Sands competed in one event: the men's 60m wheelchair sprint, in category 1B. He completed his race in 34.8s, which placed him 22nd overall in the heats, and did not enable him to advance to the final. The event was ultimately won by West German athlete Baumgartner (full name not recorded), in 19s.

1972 Summer Paralympics
The 1972 Summer Paralympics (German: Paralympische Sommerspiele 1972), the fourth edition of the Paralympic Games, were held in Heidelberg, West Germany, from 2 to 11 August 1972. Organised under the guidance of the International Stoke Mandeville Games Federation (ISMGF), they were known as the 21st International Stoke Mandeville Games at the time. The games ended 15 days before the 1972 Summer Olympics held in Munich, also in West Germany.
Tulips (film)
Tulips  is a 1981 Canadian-American comedy-drama film starring Gabe Kaplan and Bernadette Peters. The director was officially credited as "Stan Ferris", but the film was actually directed by Rex Bromfield, Mark Warren and Al Waxman.

Rex Bromfield
Rex Bromfield is a Canadian film, retired television director and writer. He is best known for his 1982 film Melanie, which garnered seven Genie Award nominations at the 4th Genie Awards in 1983, including a nod for Bromfield as Best Director.

He has directed five feature films and numerous episodes of Canadian television series. He subsequently left the film business to start a software company, but in 2004 he briefly returned to film as co-writer with Jackson Davies of the screenplay for The Wild Guys. He has since published several works of fiction as ebooks on Smashwords.

He is the brother of comedians Valri Bromfield and Lois Bromfield who appeared in the 1990s, Bromfield with Chris Aable in her first television interview, on Hollywood Today.
St Mary Magdalene, Richmond
St Mary Magdalene, Richmond, in the Anglican Diocese of Southwark, is a Grade II* listed parish church on Paradise Road, Richmond, London.  The church, dedicated to Jesus' companion Mary Magdalene, was built in the early 16th century but has been greatly altered so that, apart from the tower, the visible parts of the church date from the 18th, 19th and early 20th centuries.

Since 1996 St Mary Magdalene's has been part of the Richmond Team Ministry, which also includes the churches of St John the Divine and St Matthias. It has a strong musical tradition and offers choral services each Sunday.

Edmund Kean
Edmund Kean (4 November 1787 – 15 May 1833) was a British Shakespearean actor, who performed, among other places, in London, Belfast, New York, Quebec, and Paris. He was known for his short stature, tumultuous personal life, and controversial divorce.
Wolfgang Kubin
Wolfgang Kubin (Chinese: 顾彬; pinyin: Gù Bīn; born December 17, 1945, in Celle) is a German poet, essayist, sinologist and translator of literary works. He is the former director of the Institute for Oriental and Asian Studies at the University of Bonn, Germany. Kubin has frequently been a guest professor at universities in China, for instance at Beijing Foreign Studies University, but also in Madison, Wisconsin, and in Jerusalem. Since 1989, Kubin has been the editor of the journals ORIENTIERUNGEN: Zeitschrift zur Kultur Asiens and Minima sinica: Zeitschrift zum chinesischen Geist.

Celle
Celle (German pronunciation: [ˈtsɛlə] ⓘ) is a town and capital of the district of Celle in Lower Saxony, in north-central Germany. The town is situated on the banks of the river Aller, a tributary of the Weser, and has a population of about 71,000. Celle is the southern gateway to the Lüneburg Heath, has a castle (Schloss Celle) built in the Renaissance and Baroque styles and a picturesque old town centre (the Altstadt) with more than 400 timber-framed houses, making Celle one of the most remarkable members of the German Timber-Frame Road. From 1378 to 1705 Celle was the official residence of the Lüneburg branch of the dukes of Brunswick-Lüneburg (House of Welf), who had been banished from their original ducal seat by its townsfolk.
George A. French (Minnesota politician)
George A. French (March 19, 1901 – February 8, 1992) was an American lawyer and politician.

French was born in Hartford, Connecticut and graduated from West High School in Minneapolis, Minnesota. French received his bachelor's degree in engineering from the University of Minnesota and his law degree from University of Minnesota Law School in 1927. He was admitted to the Minnesota bar and practiced law in Minneapolis. French lived in Minneapolis with his wife and family. He served in the Minnesota House of Representatives from 1941 to 1966 and was a Republican. French died from a heart attack at Memorial Hospital in St. Louis Park, Minnesota. The funeral and burial was in Minneapolis.

West High School (Minneapolis, Minnesota)
West High School (1908–1982) was a public high school in Minneapolis, Minnesota. Edward Stebbins designed the school building. Built in 1908 on what had recently been farmland, the school had a student capacity of 1,600 by 1917. Minneapolis Public Schools closed Central, West and Marshall-University high schools in 1982.
The Amazon (film)
The Amazon (German: Die Amazone) is a 1921 German silent film directed by Richard Löwenbein and starring Eva May, Rudolf Forster, and Olga Engl.

The film's sets were designed by the art director Robert Neppach.

Eva May
Eva Maria Mandl (29 May 1902 – 10 September 1924), known professionally as Eva May, was an Austrian actress. She was the daughter of the film director Joe May and his wife actress Mia May. In 1924, she committed suicide by gunshot.
Pechora Radar Station
Pechora Radar Station (Russian: Печорская радиолокационная станция, romanized: Pechorskaya radiolokatsionnaya stantsiya) is an early warning radar near Pechora in the Komi Republic, northern Russia. It is a key part of the Russian early warning system against missile attack and was built by the Soviet Union, becoming operational in 1984. It is run by the Russian Space Forces.

Pechora
Pechora (Russian: Печо́ра; Komi: Печӧра, romanized: Pećöra) is a town in the Komi Republic, Russia, located on the Pechora River, west of and near the northern Ural Mountains. The area of the town is 28.9 square kilometres (11.2 mi2).  Population:  43,105 (2010 census); 48,700 (2002 census); 64,746 (1989 Soviet census).
Devario quangbinhensis
Devario quangbinhensis (Vietnamese: cá phong nha) is a species of freshwater ray-finned fish belonging to the family Danionidae. This species is found only in Phong Nha-Kẻ Bàng National Park, Quảng Bình Province, North Central Coast, Vietnam. It is sometimes found in the ornamental fish trade.

Quảng Bình province
Quảng Bình was formerly a southern coastal province in the North Central Coast region, the Central of Vietnam. It borders Hà Tĩnh to the north, Quảng Trị to the south, Khammouane of Laos to the west and the Gulf of Tonkin (South China Sea) to the east.

On June 12, 2025, Quảng Bình was merged into Quảng Trị.
Madriz Department
Madriz (Spanish pronunciation: [maˈðɾis]) is a department in Nicaragua. It covers an area of 1,708 km2 and has a population of 176,920 (2021 estimate). The capital is Somoto.

Madriz was created from Nueva Segovia department in 1936, and named after President José Madriz.

The Madriz flag is extremely similar to the flag of France. It has the same proportions, but the blue and red are slightly different shades.

José Madriz
José Madriz Rodríguez (21 July 1867 – 14 May 1911) was the President of Nicaragua from 21 December 1909 to 20 August 1910.

Madriz was born on 21 July 1867, in León, Nicaragua. He was president of the Nicaraguan Congress 1896, 1896-1905 and 1909-1910. After President José Santos Zelaya resigned on December 21, 1909 in the face of an armed Counter-Revolution and United States opposition, Madriz assumed the presidency as a designate by the congress. Madriz attempted to establish an Anti-Imperialist struggle against USA interests, but active North American intervention in favor of the Oligarchic politicians proved insurmountable, and he went into exile in August 1910. He died in Mexico City on 14 May 1911.

In 1936, the newly created Madriz Department was named in his honor.
Maxwell Institute
The Neal A. Maxwell Institute for Religious Scholarship, or Maxwell Institute, is a research institute at Brigham Young University (BYU). The institute consists of faculty and visiting scholars who study religion, primarily the Church of Jesus Christ of Latter-day Saints (LDS Church). The institute is named after a former LDS Church apostle, known for his writings and sermons.

The LDS Church identifies the Maxwell Institute as one of several third-party church affiliates offering gospel study resources.

Neal A. Maxwell
Neal Ash Maxwell (July 6, 1926 – July 21, 2004) was an American scholar, educator, and religious leader who served as a member of the Quorum of the Twelve Apostles of the Church of Jesus Christ of Latter-day Saints (LDS Church) from 1981 until his death in 2004.
2023–24 Wagner Seahawks men's basketball team
The 2023–24 Wagner Seahawks men's basketball team represented Wagner College during the 2023–24 NCAA Division I men's basketball season. The Seahawks, led by second-year head coach Donald Copeland, played their home games at the Spiro Sports Center in Staten Island, New York as members of the Northeast Conference. They finished the season 17–16, 7–9 in NEC play to finish in sixth place. As the No. 6 seed in the NEC Tournament, they defeated Sacred Heart, Central Connecticut, and Merrimack to win the NEC tournament championship, as a result, they received the conference's automatic bid to the NCAA tournament for the second time in school history and the first time since 2003. As a No. 16 seed in the West region, they defeated to Howard in the First Four, before losing to North Carolina in the First Round.

2024 Northeast Conference men's basketball tournament
The 2024 Northeast Conference Men's Basketball Tournament was the postseason men's basketball tournament for the Northeast Conference for the 2023–24 NCAA Division I men's basketball season. The tournament took place on three dates between March 6 and 12, 2024, and all tournament games were played in the home arenas of the higher-seeded school. The winner, Wagner, received the conference's automatic bid to the 2024 NCAA tournament.

Merrimack was the defending champion. Due to Merrimack's ineligibility as a team transitioning from Division II, Fairleigh Dickinson represented the conference in the 2023 NCAA tournament and advanced to the second round.
Special Operations Command Pacific
The Special Operations Command Pacific, known as SOCPAC or USSOCPAC, is a sub-unified command of the United States Department of Defense for special operations forces in the United States Indo-Pacific Command (USINDOPACOM) area of responsibility.

David P. Fridovich
David P. Fridovich is a retired lieutenant general and Green Beret in the United States Army. His position at the time of retirement was deputy commander of the U.S. military's United States Special Operations Command that directs special operations campaigns.

Fridovich is a 1974 graduate of Knox College where he was a member of Tau Kappa Epsilon. He received his master's degree in political science from Tulane University in 1976.
Donets
The Seversky Donets (Russian: Северский Донец) or Siverskyi Donets (Ukrainian: Сіверський Донець), usually simply called the Donets (Russian: Донец, lit. 'Don + - ets, suffix'), is a river on the south of the East European Plain. It originates in the Central Russian Upland, north of Belgorod, flows south-east through Ukraine (Kharkiv, Donetsk and Luhansk Oblasts) and then again through Russia (Rostov Oblast) to join the river Don, about 100 km (62 mi) from the Sea of Azov. The Donets is the fourth-longest river in Ukraine, and the largest in eastern Ukraine, where it is an important source of fresh water. It gives its name to the Donets Basin, known commonly as the Donbas, an important coal-mining and industrial region in Ukraine.

Eastern Ukraine
Eastern Ukraine or East Ukraine (Ukrainian: Східна Україна, romanized: Skhidna Ukrayina; Russian: Восточная Украина, romanized: Vostochnaya Ukraina) is primarily the territory of Ukraine east of the Dnipro (or Dnieper) river, particularly Kharkiv, Luhansk and Donetsk oblasts (provinces). Dnipropetrovsk and Zaporizhzhia oblasts are often also regarded as "eastern Ukraine".

Almost a third of the country's population lives in the region, which includes several cities with population of around a million. Within Ukraine, the region is the most highly urbanized, particularly portions of central Kharkiv Oblast, south-western Luhansk Oblast, central, northern and eastern areas of Donetsk Oblast.
Obelisks of Nectanebo II
51°31′10″N 0°7′37″W﻿ / ﻿51.51944°N 0.12694°W﻿ / 51.51944; -0.12694

The Obelisks of Nectanebo II are a pair of monumental obelisks that were found in Cairo during the period of Ottoman Egypt, but were originally erected in the ancient city of Hermopolis (modern Al-Ashmunayn), in central Egypt. The fragmentary monoliths were recovered by French scholars as part of Napoleon's 1798 expedition to Egypt but, after the capitulation of French forces, they were confiscated by the British, along with a number of antiquities including the Rosetta Stone, and transported to England]. They can now be seen in the Great Court of the British Museum.

Queen Elizabeth II Great Court
51°31′10″N 0°7′37″W﻿ / ﻿51.51944°N 0.12694°W﻿ / 51.51944; -0.12694

The Queen Elizabeth II Great Court, commonly referred to simply as the Great Court, is the covered central quadrangle of the British Museum in London. It was redeveloped during the late 1990s to a design by Foster and Partners, from a 1970s design by Colin St John Wilson. The court was opened by Queen Elizabeth II in 2000.
Washburn, Iowa
Washburn is an unincorporated town and census-designated place (CDP) in Black Hawk County, Iowa, United States. Washburn lies south of Waterloo on U.S. Route 218. Other towns near Washburn are Gilbertville and La Porte City. The community is part of the Waterloo–Cedar Falls Metropolitan Statistical Area.

U.S. Route 218
U.S. Highway 218 (US 218) is an original United States Highway that was created in 1926. Although technically a spur of US 18, US 218 neither begins nor ends at US 18, but overlaps US 18 for eight miles (13 km) near Charles City, Iowa. US 218 begins at U.S. 136 in downtown Keokuk and ends 319 miles (513 km) away at Interstate 35 (I-35) and US 14 at Owatonna, Minnesota. A large portion of US 218 in Iowa is part of the Avenue of the Saints, which connects St. Louis, Missouri, and Saint Paul, Minnesota.
Calliophis salitan
Calliophis salitan is a species of venomous snake in the family Elapidae. It is endemic to  the Philippines and known from Dinagat Island and Mindanao; the former is based on a small number of recent records whereas the latter is based on a museum specimen from 1887.

It is unique for its large size as well as its body coloration of a black head & neck with black & white bands along the width of the body, terminating at a bright orange tail. It is distinct from any other coral snake species in the Philippines or Sundas, but is most closely related to the blue coral snake complex (C. bivirgatus & C. intestinalis) of the Sunda Shelf. While it is known only from Dinagat Island and possibly Mindanao, it may also occur or have formerly occurred on other islands in the Sulu Archipelago.

Coral snake
Coral snakes are a large group of elapid snakes that can be divided into two distinct groups, the Old World coral snakes and New World coral snakes. There are 27 species of Old World coral snakes, in three genera (Calliophis, Hemibungarus, and Sinomicrurus), and 83 recognized species of New World coral snakes, in two genera (Micruroides and Micrurus). Phylogenetic studies suggest that the group originated in the Old World. While new world species of both genera are venomous, their bites are seldom lethal; as of 2018, only two confirmed fatalities had been documented in the United States in the preceding 100 years from the genus Micrurus. Meanwhile, snakes of the genus Micruroides have never caused a medically significant bite.