hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Tetrahedral number
A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron. The nth tetrahedral number, Ten, is the sum of the first n triangular numbers, that is,

The tetrahedral numbers are:

1, 4, 10, 20, 35, 56, 84, 120, 165, 220, ... (sequence A000292 in the OEIS)

Triangular number
A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The nth triangular number is the number of dots in the triangular arrangement with n dots on each side, and is equal to the sum of the n natural numbers from 1 to n. The first 100 terms sequence of triangular numbers, starting with the 0th triangular number, are

(sequence A000217 in the OEIS)
Foothills Trail
The Foothills Trail is a 76-mile (122 km) National Recreation Trail in South and North Carolina, United States, for recreational hiking and backpacking. It extends from Table Rock State Park to Oconee State Park. It passes through the Andrew Pickens Ranger District of the Sumter National Forest, Ellicott Rock Wilderness, Whitewater Falls, and Lake Jocassee.

The U.S. Forest Service built the section in the Sumter National Forest starting in 1968. Duke Power Company built the middle portion of the trail as a recreational resource in conjunction with its Bad Creek pumped storage hydroelectric project. The trail is maintained by the Foothills Trail Conference.

Upper Whitewater Falls
Upper Whitewater Falls is a waterfall in North Carolina on the Whitewater River.  As with most of North Carolina's waterfalls, it is in the mountainous area of the state. There is a cluster of falls in the area where the borders of Georgia and the Carolinas come together. Whitewater Falls is part of that group, very close to the South Carolina border.

According to the U.S. Forest Service, "With a 411-foot plunge, Upper Whitewater Falls in North Carolina is the highest waterfall east of the Rockies." However, this claim is likely exaggerated, and the actual height is likely closer to 350–400 feet. Furthermore, several other waterfalls have contended to be the highest waterfall east of the Rockies, including Crabtree Falls in Virginia, Amicalola Falls in Georgia, and Glassmine Falls in North Carolina, which depends on the way waterfalls are defined and categorized.
Ministry of Social Security (United Kingdom)
In 1966, the Supplementary Benefits Commission (part of the National Assistance Board) was merged with the Ministry of Pensions and National Insurance to form the new Ministry of Social Security, as part of the Ministry of Social Security Act 1966.

In November 1968, the Ministry of Health and the Ministry of Social Security were merged to create the new Department of Health and Social Security (DHSS).

Ministry of Pensions and National Insurance
The Ministry of Pensions and National Insurance (MPNI) was a British government ministry responsible for the administration and delivery of welfare benefits. It was headed by the Minister of Pensions and National Insurance.
The Young Doctors (film)
The Young Doctors is a 1961 American drama film directed by Phil Karlson and starring Ben Gazzara, Fredric March, Dick Clark, Ina Balin, Eddie Albert, Phyllis Love, Aline MacMahon, George Segal, and Dolph Sweet.

The film is based on the 1959 novel The Final Diagnosis by Arthur Hailey.  Ronald Reagan was the narrator in the film.

Ina Balin
Ina Balin  (née Rosenberg; November 12, 1937 – June 20, 1990) was an American stage, film, and television actress. She is best known for her role in the film From the Terrace (1960), for which she received two Golden Globe Award nominations and won one for Most Promising Newcomer – Female.
Eberhard I, Duke of Württemberg
Eberhard I of Württemberg also known as Eberhard im Bart (Eberhard the bearded) (11 December 1445 – 24 February 1496) was the first Duke of Württemberg. After the death of his older brother in 1459 he became the Count of Württemberg-Urach as Eberhard V. In 1482 he signed the Treaty of Münsingen with his cousin Eberhard VI of Württemberg-Stuttgart reuniting Württemberg-Urach with Württemberg-Stuttgart under his rule. In exchange his cousin was designated as his heir. He moved the capital to Stuttgart and in July 1495 he was elevated to Duke of Württemberg by Emperor Maximilian I.

Eberhard was acquainted with a number of scholars and held education in high esteem. In 1477 he founded the University of Tübingen.

Eberhard died in 1496 and was succeeded by his cousin Duke Eberhard II (formerly Eberhard VI of Württemberg-Stuttgart).

Treaty of Münsingen
The Treaty of Münsingen was signed on 14 December 1482. This accord officially reunited the divided County of Württemberg after it was divided by the Treaty of Nürtingen in 1442. The hereditary dispute between the Stuttgart part and the part of Urach were settled after 40 years. Residing in Urach, Count Eberhard V, later Duke Eberhard I of Württemberg, obtained rule and moved the capital to Stuttgart. The succession was laid down for the ruling count in the Stuttgart part of the country, Eberhard VI. With this treaty, that was worked out with collaboration of the council of Württembergian subjects, the indivisibility of Württemberg and the primogeniture became contractual. The treaty prevented the division of Württemberg and thus was an important step to the exaltation to a duchy in 1495. The original document is stored in the main public record office in Stuttgart.
Meghan Camarena
Meghan Channing Camarena (born July 17, 1987), known by her online pseudonym Strawburry17, is an American YouTube personality, television host, actress, and comic book writer. She has worked on a number of videos, web series, and films, gaining popularity as a YouTube star, and participating as a contestant with fellow YouTuber Joey Graceffa on The Amazing Race 22 and The Amazing Race: All-Stars. She was an on-screen host for video content at Teen.com and was the backstage correspondent for season 2 of the TruTV talent contest Fake Off. In 2017, she and fellow YouTuber Jimmy Wong co-hosted the video game themed variety show Polaris Primetime which was part of Disney's inaugural "D | XP" summer programming block on Disney XD. She's also the co-writer of the Radiant Pink miniseries.

Fake Off
Fake Off is an American reality competition television series. The show features groups of performers who recreate and reimagine moments from pop culture (e.g. movies, events, television series) in spectacular 90-second routines. The teams use a diverse range of stage disciples including black light theatre, projection mapping, puppetry, and dance. The term "Faking" is used to describe the act of recreating an iconic moment. It debuted on TruTV on October 27, 2014, and is produced by Shine America. TruTV renewed the show for a second season, which was also its last.
For the Fallen Dreams
For the Fallen Dreams is an American metalcore band from Lansing, Michigan, formed in 2003. The band originally signed to Rise Records but produced one album under Artery Recordings in 2012. After the departure of then vocalist Dylan Richter and the return of vocalist Chad Ruhlig in 2013, the band started producing music under Rise Records once again until 2022.

They have released three demos (their first being in the genre of deathcore), a self-titled extended play, and seven full-length albums: Changes (2008), Relentless (2009), Back Burner (2011), Wasted Youth (2012), Heavy Hearts (2014), Six (2018) and For the Fallen Dreams (2023). Relentless charted at number 29 on the Billboard Top Heatseekers.

Relentless (For the Fallen Dreams album)
Relentless is the second studio album by American metalcore band For the Fallen Dreams. It is the first album to feature vocalist Dylan Richter. It was released on July 21, 2009, through Rise Records and was produced by the band themselves and Joey Sturgis. The album charted at number 29 on the Billboard Top Heatseekers chart.
G. Samantha Rosenthal
Gregory Samantha Rosenthal (born January 24, 1983) is an American historian, activist, and author. She serves on the faculty, as associate professor of History and Coordinator of the Public History Concentration, at Roanoke College in Salem, Virginia. She is the co-founder of the Southwest Virginia LGBTQ+ History Project. Rosenthal has written two books, Beyond Hawaiʻi: Native Labor in the Pacific World and Living Queer History: Remembrance and Belonging in a Southern City. She serves on the governing board of the Committee on Lesbian, Gay, Bisexual, and Transgender History and on the editorial board of The Public Historian.

Roanoke College
Roanoke College is a private liberal arts college in Salem, Virginia. It has approximately 2,000 students who represent approximately 40 states and 30 countries. The college offers 35 majors, 57 minors and concentrations, and pre-professional programs. Roanoke awards bachelor's degrees in arts, science, and business administration and is one of 280 colleges with a chapter of the Phi Beta Kappa honor society.

Roanoke is an NCAA Division III school competing in the Old Dominion Athletic Conference. The college fields varsity teams in eleven men's and ten women's sports. Roanoke's athletic nickname is Maroons and the mascot is Rooney, a maroon-tailed hawk.
California State Parks
California State Parks is the state park system for the U.S. state of California. The system is administered by the California Department of Parks and Recreation, a department under the California Natural Resources Agency. The California State Parks system is the largest state park system in the United States.

California State Parks administers 279 separate park units on 1.4 million acres (5,700 km2), with over 280 miles (450 km) of California coastline; 625 miles (1,006 km) of lake and river frontage; nearly 15,000 campsites; and 3,000 miles (4,800 km) of hiking, biking, and equestrian trails. Headquartered in Sacramento, park administration is divided into 21 districts.

California Natural Resources Agency
The California Natural Resources Agency (CNRA) is a state cabinet-level agency in the government of California. The institution and jurisdiction of the Natural Resources Agency is provided for in California Government Code sections 12800 and 12805, et seq. The agency has six departments, 10 conservancies, 17 boards and commissions, three councils, and one urban park in Los Angeles that consists of two museums, the California Science Center and the California African American museum. Through its 25 departments, conservancies and commissions, the Natural Resources Agency is responsible for protecting prehistory history, natural landscapes and cultural sites, monitoring and stewarding state lands and waterways, and regulating fish and game use, as well as private lands and the intersection with federal lands and waters.

The current Secretary for Natural Resources is Wade Crowfoot, a member of Governor Gavin Newsom's cabinet.
Legend of the Naga Pearls
Legend of the Naga Pearls (Chinese: 鲛珠传) is a 2017 Chinese fantasy adventure film directed by Yang Lei, starring Wang Talu, Zhang Tianai and Sheng Guansen. It is the first film to be set in the fictional world of Novoland. The film was released on August 11, 2017 in China.

Zhang Tian'ai
Zhang Tian'ai (Chinese: 张天爱; born 28 October 1988), also known by her English name Crystal Zhang, is a Chinese actress and model. She is best known for her breakout role in the 2015 hit web-drama Go Princess Go.
Stanisław Kutrzeba
Stanisław Marian Kutrzeba (1876–1946) was a Polish historian and politician who was Professor of the Jagiellonian University from 1908, and then until the end of his life the Chair of Studies in Polish law. He was chair of the Law Department (1913/1914, 1920/1921), university's rector (1932/33), General Secretary of Polish Academy of Learning (1926–39) and its president (1939–1946). He was one of many professors of Jagiellonian University arrested by Nazis during Sonderaktion Krakau in 1939 and imprisoned in the Sachsenhausen concentration camp. After being freed in 1940, he took part in the underground education. In 1945, he was deputy to the State National Council.

His works in the area of history were centered on the history of Polish law, the history of Poland from 14th to 18th centuries and the history of Kraków.

Polish Academy of Arts and Sciences
The Polish Academy of Arts and Sciences or Polish Academy of Learning (Polish: Polska Akademia Umiejętności, PAU), headquartered in Kraków and founded in 1872, is one of two institutions in contemporary Poland having the nature of an academy of sciences (the other being the Polish Academy of Sciences, headquartered in Warsaw).

The Polish Academy of Arts and Sciences is co-owner of the Polish Library in Paris.
Paradise (Paint It Black album)
Paradise is the second full-length album from Philadelphia's Paint It Black, which followed up the band's  debut LP from 2003, CVA. It features a more melodic hardcore sound than previous releases from the band, and was met with a slightly more positive critical reception than CVA.

CVA (album)
CVA is the debut full-length album from Philadelphia, PA's Paint It Black. It features much shorter and arguably more aggressive songs than their follow-up album, Paradise, two and a half minutes shorter despite sporting three more tracks. The song "Womb Envy" was featured on the soundtrack of the 2003 skateboarding video game Tony Hawk's Underground.
FC Winterthur
FC Winterthur is a Swiss football club based in Winterthur, Canton of Zürich. They play in the Swiss Super League, the first tier of Swiss football, and appeared regularly in the Nationalliga A during the 20th century. Their home is the Stadion Schützenwiese.

Stadion Schützenwiese
Stadion Schützenwiese is a football stadium in Winterthur, Switzerland. It has been the home ground of FC Winterthur since the club's inception in 1896. It has a capacity of 8,550, more specifically 1,100 covered seats, 800 uncovered seats and 6,650 standing places.

The field received its first, wooden stands in 1922 on the western side, which were completely replaced in 1957/58 to contain changing rooms, a kiosk, and underground gyms. In 1968 the stadium received funding to build floodlights.

To match the Swiss Football League's license requirements introduced in the 2012/13 season, the stadium was modernized in three stages. The first stage contained improvements to the lighting, security, and catering systems, completed by 2013. This was followed by a rebuild of the eastern standing terrace in 2015, and finally a renovation of the main stands.
England men's national ice hockey team
The English national ice hockey team was the national ice hockey team of England. The club last participated in an international game in 1994, a 6–5 win against Scotland. While England still participates in junior hockey tournaments, in most IIHF tournaments, English players are part of the Great Britain national ice hockey team.

Scotland national ice hockey team
The Scottish national ice hockey team was the national ice hockey team of Scotland. The club last participated in an international game in 1994, a 5–6 loss to England. Scottish players are part of the Great Britain national ice hockey team.
Alfred Brehm
Alfred Edmund Brehm (German pronunciation: [ˈalfʁeːt ˈʔɛtmʊnt ˈbʁeːm]; 2 February 1829 – 11 November 1884) was a German zoologist and writer. His multi-volume book Brehms Tierleben, which he co-authored with Eduard Pechuël-Loesche, Wilhelm Haacke, and Richard Schmidtlein, became a household word for popular zoological literature. He was the first director of the Zoological Garden of Hamburg.

Zoological Garden of Hamburg
The Zoological Garden of Hamburg (German: Zoologischer Garten zu Hamburg) was a zoo in Hamburg, Germany that operated from 1863 until 1930.  Its aquarium, which opened in 1864, was among the first in the world.
Abie's Irish Rose (1928 film)
Abie's Irish Rose is a 1928 American early sound (part-talkie) comedy film directed by Victor Fleming and starring Charles "Buddy" Rogers, Nancy Carroll, Jean Hersholt, and J. Farrell MacDonald. In addition to sequences with audible dialogue or talking sequences, the film features a synchronized musical score and sound effects along with English intertitles. The soundtrack was recorded using the Western Electric sound-on-film system. The film based on the 1922 play Abie's Irish Rose by Anne Nichols. The film was later remade in 1946. In the 1930s, author Nichols revealed that her deal with Paramount brought her $300,000 plus half the film's profits.

Abie's Irish Rose (1946 film)
Abie's Irish Rose is a 1946 American comedy film directed by A. Edward Sutherland based on a play by Anne Nichols. The film stars Michael Chekhov, Joanne Dru, Richard Norris, J. M. Kerrigan, George E. Stone, Vera Gordon, and Emory Parnell. The film was released on December 27, 1946, by United Artists. It was a remake of the 1928 film that was based on the 1922 play Abie's Irish Rose by Anne Nichols. The film drew criticism for stereotyping and additional cuts were made after complaints.
Trygve Olsen
Trygve Jens Asbjørn Olsen (11 November 1921 – 17 April 1979) was a Norwegian politician for the Centre Party.

He was born in Måsøy Municipality in Finnmark, Norway.

Trygve Olsen was the son of Parliament member Johannes Olai Olsen, but was not elected to parliament himself. Instead, he worked as a fisherman starting in 1939. He served on the board of Norges Råfisklag from 1958 to 1966, and was chairman of Fiskebåtredernes forbund from 1977 to 1979. He was the Minister of Fisheries from 1972–1973 during the cabinet Korvald.

Olsen was active in local politics, serving as mayor of Måsøy Municipality from 1968 to 1972. During the same period, he was also a member of the Finnmark county council.

Johannes Olai Olsen
Johannes Olai Olsen (3 October 1895 – 16 January 1974) was a Norwegian fisher and politician for the Labour Party.

He was born in Måsøy Municipality.

He was elected to the Norwegian Parliament from Finnmark in 1945, and was re-elected on four occasions.

Olsen was mayor of Måsøy Municipality between 1928 and 1946, with the exception of a period between 1940 and 1945, during the German occupation of Norway. He was also a long-time member of Finnmark county council.

His son Trygve Olsen later became mayor of Måsøy, as well as a cabinet member.
Elisabeth Troy
Elisabeth Troy Antwi is a British singer and songwriter.

She appeared on several top 40 hit singles in the UK, including MJ Cole's "Crazy Love" and "Hold On to Me" in 2000 and B.Traits' "Fever" in 2012. She also co-wrote and performed the 1996 song "Headstrong", which was featured on the soundtrack of the film Mars Attacks!.

She also co-wrote and sang the duet "Incomplete" (as Elisabeth Antwi) with Fish from his 1999 solo album Raingods with Zippos, and provided backing vocals on his 2013 album A Feast of Consequences.

She toured with Clean Bandit from 2013 until 2016.

Fever (B.Traits song)
"Fever" is the debut single performed by Canadian DJ and producer B.Traits. It was released on 23 March 2012 as a digital download in the United Kingdom. The song features vocals from British singer Elisabeth Troy. It peaked at number 36 on the UK Singles Chart.
Colin Fox (actor)
Colin R. Fox (November 20, 1938 – April 5, 2025) was a Canadian actor, who appeared in various Canadian and American films and television series. His best known roles included Jean Paul Desmond / Jacques Eloi Des Mondes on Strange Paradise (1969–70), Professor Anton Hendricks on PSI Factor: Chronicles of the Paranormal (1996–2000), and Fritz Brenner on A Nero Wolfe Mystery (2001–02).

Fox also provided voiceover work for animated projects like The Legend of Zelda (1989), Rupert (1991–97), X-Men: The Animated Series (1996), and Atomic Betty (2004–08). The latter earned him a Gemini Award for Best Performance in an Animated Program or Series.

Strange Paradise
Strange Paradise is a Canadian Gothic soap opera of 195 episodes, initially launched in syndication in the United States on September 8, 1969, and later broadcast on CBC Television from October 20, 1969, to July 22, 1970. The production was the brainchild of producer Steve Krantz, in an attempt to capitalize on the phenomenal success of ABC's daytime serial Dark Shadows in America. To develop the series, Krantz hired actor-writer Ian Martin and veteran TV and radio producer Jerry Layton, both of whom were given screen credit for the creation of Strange Paradise.  With the CBC and American broadcasters Metromedia and Kaiser Broadcasting handling distribution and co-production, the series was filmed in Ottawa, Ontario, at CTV affiliate CJOH-TV and aired for 39 weeks, presenting three separate 13-week story arcs.
Siegfried Matthus
Siegfried Matthus (13 April 1934 – 27 August 2021) was a German composer, conductor, and festival founder and manager. Some of his operas, such as Judith, were premiered at the Komische Oper Berlin in East Berlin. In 1991, he founded the chamber opera festival Kammeroper Schloss Rheinsberg and directed it until 2018. In 2005, he composed a Te Deum for the reopening of the Dresden Frauenkirche. Matthus is considered one of Germany's most often performed contemporary composers.

Komische Oper Berlin
The Komische Oper Berlin is a German opera company based in Berlin. The company produces operas, operettas and musicals.

The opera house is located on Behrenstraße, near Unter den Linden. Since 2004, the Komische Oper Berlin, along with the Berlin State Opera, the Deutsche Oper Berlin, the Berlin State Ballet, and the Bühnenservice Berlin (Stage and Costume Design), has been a member of the Berlin Opera Foundation.
Plateau–Rayleigh instability
In fluid dynamics, the Plateau–Rayleigh instability, often just called the Rayleigh instability, explains why and how a falling stream of fluid breaks up into smaller packets with the same total volume but less surface area per droplet. It is related to the Rayleigh–Taylor instability and is part of a greater branch of fluid dynamics concerned with fluid thread breakup.   This fluid instability is exploited in the design of a particular type of ink jet technology whereby a jet of liquid is perturbed into a steady stream of droplets.

The driving force of the Plateau–Rayleigh instability is that liquids, by virtue of their surface tensions, tend to minimize their surface area.  A considerable amount of work has been done recently on the final pinching profile by attacking it with self-similar solutions.

Rayleigh–Taylor instability
The Rayleigh–Taylor instability, or RT instability (after Lord Rayleigh and G. I. Taylor), is an instability of an interface between two fluids of different densities which occurs when the lighter fluid is pushing the heavier fluid. Examples include the behavior of water suspended above oil in the gravity of Earth, mushroom clouds like those from volcanic eruptions and atmospheric nuclear explosions, supernova explosions in which expanding core gas is accelerated into denser shell gas, merging binary quantum fluids in metastable configuration, instabilities in plasma fusion reactors and inertial confinement fusion.