hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Half-side formula
In spherical trigonometry, the half side formula relates the angles and lengths of the sides of spherical triangles, which are triangles drawn on the surface of a sphere and so have curved sides and do not obey the formulas for plane triangles.

For a triangle  on a sphere, the half-side formula is

where a, b, c are the angular lengths (measure of central angle, arc lengths normalized to a sphere of unit radius) of the sides opposite angles A, B, C respectively, and  is half the sum of the angles. Two more formulas can be obtained for  and  by permuting the labels

The polar dual relationship for a spherical triangle is the half-angle formula,

where semiperimeter  is half the sum of the sides. Again, two more formulas can be obtained by permuting the labels

Central angle
A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B. Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one (measured in radians). The central angle is also known as the arc's angular distance. The arc length spanned by a central angle on a sphere is called spherical distance.

The size of a central angle Θ is  0° < Θ < 360°  or   0 < Θ < 2π (radians). When defining or drawing a central angle, in addition to specifying the points A and B, one must specify whether the angle being defined is the convex angle (<180°) or the reflex angle (>180°). Equivalently, one must specify whether the movement from point A to point B is clockwise or counterclockwise.
Mazama (steamboat)
Mazama was a small steamboat driven by twin propellers that operated on upper Klamath Lake starting in 1909. Mazama was, reportedly, the only craft ever to navigate the Wood River, a tributary of upper Klamath Lake.  For a few years, until the construction of a rail line, Mazama was an important link in transportation system linking Fort Klamath to Klamath Falls.

Fort Klamath
Fort Klamath was a military outpost near the western end of the Oregon Trail, between Crater Lake National Park and Upper Klamath Lake in Klamath County, Oregon, United States. The Fort Klamath Site, about a mile southeast of the present community of Fort Klamath, Oregon, is listed on the U.S. National Register of Historic Places
Ich zähle täglich meine Sorgen
Ich zähle täglich meine Sorgen [I Daily Count My Sorrows] is a 1960 West German musical comedy film directed by Paul Martin and starring Peter Alexander, Ingeborg Schöner and Gunther Philipp.

The film's sets were designed by the art directors Dieter Bartels, Mathias Matthies and Ellen Schmidt. It was shot at the Bendestorf Studios outside Hamburg.

Bendestorf
Bendestorf is a municipality in Lower Saxony in Germany. It is situated ca. 30 km south of Hamburg and belongs to the Landkreis (district) Harburg and the Samtgemeinde of Jesteburg.

The first mentioning of Bendestorf dates back to the year 970. The current population ist approximately 2300 (2022). In the post-war era Bendestorf was well known for its film-studios where movies starring Hildegard Knef (a.k.a. Hildegard Neff) and other famous German actors were produced.
Pane di Laterza
Pane di Laterza is a traditional bread of Laterza, a municipality (comune) in the province of Taranto, Italy. It is made with durum wheat flour with water, salt, and sourdough. It is mainly produced in Laterza, but it can be also found in neighbouring comuni. It has been recognised by the Italian Ministry of the Agriculture, Food and Forestry Policies as a prodotto agroalimentare tradizionale (PAT) of Apulia.

Province of Taranto
The province of Taranto (Italian: provincia di Taranto; Tarantino: provìnge de Tarde; Salentino: provincia ti Tàrantu), previously known as the province of the Ionian, is a province in the Apulia region of Italy. Its capital is the city of Taranto. It has an area of 2,437 square kilometres (941 sq mi), and a total population of 581,092 (2017). The province contains 29 comuni (sg.: comune). The coat of arms of the province contains a scorpion, which Pyrrhus is thought to have seen when looking down at Taranto.
Aleksandr Ryazantsev
Aleksandr Aleksandrovich Ryazantsev (Russian: Александр Александрович Рязанцев, born 5 September 1986) is a Russian former footballer.
He scored the first goal for Rubin Kazan on 20 October 2009, a thunderous 30-yard strike in their shock 2–1 away victory at the Camp Nou against Barcelona in a Champions League group stage match. The goal against Barcelona was described as a "heavenly thunderbolt" by many of his teammates and was remembered as one of the goals of the tournament.

Russian Super Cup
The Russian Super Cup (Russian: Суперкубок России) is a one-match football annual competition. Its official sponsored name is OLIMPBET Russian Supercup (Russian: ОЛИМПБЕТ Суперкубок России). The two participating clubs are the Russian Premier League champions and the Russian Cup winners. If the Premier League and the Cup are won by the same team, then the other participant is the league runners-up. The match is played at the beginning of the season, typically in July.

The trophy has been contested since 2003.
Finally Karen
Finally Karen is the debut solo album of gospel singer Karen Clark Sheard of the Clark Sisters, released on November 4, 1997. The live portion of the album was recorded at Bailey Cathedral in Detroit, Michigan, on November 15, 1996. The album was Grammy-nominated for Best Contemporary R&B Gospel Album in 1998. The song "The Will of God" launched the gospel career of her daughter Kierra "Kiki" Sheard, who won her first Stellar award from the strength of her vocal performance. Finally Karen also won the Lady of Soul award for Best Gospel Album the same year.

Stellar Awards
A Stellar Award is an award presented by the Stellar Awards Gospel Music Academy (SAGMA) to recognize achievements in the gospel music industry. The annual presentation ceremony features performances by prominent gospel artists, and the presentation of those awards that have a more popular interest. The Stellars were the first major gospel music awards held annually.

The first Stellar Awards ceremony was held on 1984, to honor and respect the musical accomplishments by gospel performers for the year 1983. Following the 2018 ceremony, SAGMA overhauled a few Stellar Award categories for 2019.

In 2020, the awards show was canceled due to the COVID-19 pandemic. The ceremony was aired virtually on August 23, 2020.
2023 Vero Beach International Tennis Open
The 2023 Vero Beach International Tennis Open was a professional tennis tournament played on outdoor clay courts. It was the fourth edition of the tournament and was part of the 2023 ITF Women's World Tennis Tour. It took place in Vero Beach, United States between 16 and 22 January 2023.

Quinn Gleason
Quinn Gleason (born November 10, 1994) is an American professional tennis player.
She has career-high WTA ranking of No. 60 in doubles and No. 323 in singles. Gleason has won two WTA Tour, four WTA 125 doubles titles and 15 on the ITF Circuit as well as one singles title.

She first played college tennis at the University of Notre Dame.
Brad Edelman
Brad M. Edelman (born September 3, 1960) is an American former professional football player who was a guard for the New Orleans Saints of the National Football League (NFL). Edelman played college football for the Missouri Tigers.

Missouri Tigers football
The Missouri Tigers football program represents the University of Missouri (often referred to as Mizzou) in college football, the Tigers are members in Southeastern Conference (SEC) of the Football Bowl Subdivision (FBS) part of the National Collegiate Athletic Association (NCAA).
True to Self
True to Self is the second studio album by American singer-songwriter Bryson Tiller. It was released on May 26, 2017, by RCA Records. Recording sessions took place from 2016 to 2017, while the production was handled by several producers from Teddy Walton, J-Louis, Mahxie, NES, Boi-1da, Frank Dukes, Illmind, Hollywood Hot Sauce, Keyz, Soundz, T-Minus and Wondagurl, among others.

The album was supported by the two singles: "Somethin Tells Me" and "Run Me Dry". In August 2017, Tiller started the Set It Off tour to promote the album. True to Self debuted at number one on the Billboard 200 (Tiller's only album to debut within that position), selling 107,000 album-equivalent units and 47,000 copies in the first week.

Ghost Kid
Paul Dawson, best known as Ghost Kid, formally known as Hot Sauce or Hollywood Hot Sauce, is an American music producer and songwriter based in Los Angeles, California. In short, Paul has written, produced and/or co-produced singles including Rihanna's "As Real As You and Me", Ariana Grande's "Hands on Me", Young Jeezy's "Shady Life", Robin Thicke's "Sex Therapy", New Boyz's "Spot Right There", and Usher's "Hot Tottie".
January 2046 lunar eclipse
A partial lunar eclipse will occur at the Moon’s descending node of orbit on Monday, January 22, 2046, with an umbral magnitude of 0.0550. A lunar eclipse occurs when the Moon moves into the Earth's shadow, causing the Moon to be darkened. A partial lunar eclipse occurs when one part of the Moon is in the Earth's umbra, while the other part is in the Earth's penumbra. Unlike a solar eclipse, which can only be viewed from a relatively small area of the world, a lunar eclipse may be viewed from anywhere on the night side of Earth. Occurring about 1.1 days before perigee (on January 23, 2046, at 14:00 UTC), the Moon's apparent diameter will be larger.

Magnitude of eclipse
The magnitude of eclipse is the fraction of the angular diameter of a celestial body being eclipsed. This applies to all celestial eclipses. The magnitude of a partial or annular solar eclipse is always between 0.0 and 1.0, while the magnitude of a total solar eclipse is always greater than or equal to 1.0, and has a theoretically maximum value of around 1.12.

This measure is strictly a ratio of diameters and should not be confused with the covered fraction of the apparent area (disk) of the eclipsed body. Neither should it be confused with the astronomical magnitude scale of apparent brightness.
Connecticut's 32nd House of Representatives district
Connecticut's 32nd House of Representatives district elects one member of the Connecticut House of Representatives. It consists of the towns of Cromwell and Portland. It has been represented by Republican Christie Carpino since 2011.

Cromwell, Connecticut
Cromwell (/ˈkrɑːmwɛl/ CRAHM-wel) is a town in Middlesex County, Connecticut, United States, located within the Lower Connecticut River Valley Planning Region. The population was 14,225 at the 2020 census.
Fort Armstrong (Alabama)
Fort Armstrong was a stockade fort built in present-day Cherokee County, Alabama during the Creek War. The fort was built to protect the surrounding area from attacks by Red Stick warriors but was also used as a staging area and supply depot in preparation for further military action against the Red Sticks.

Cherokee County, Alabama
Cherokee County, Alabama is a county located in the northeastern part of the U.S. state of Alabama. As of the 2020 census, the population was 24,971. Its county seat is Centre. The county is named for the Cherokee tribe.
Nivaclé language
Nivaclé ([niβaˈq͡le]) is a Matacoan language spoken in Paraguay and  in Argentina by the Nivaclé. It is also known as Chulupí and Ashluslay, and in older sources has been called Ashluslé, Suhin, Sujín, Chunupí, Churupí, Choropí, and other variant spellings of these names. Nivaclé speakers are found in the Chaco, in Paraguay in Presidente Hayes Department, and Boquerón Department, and in Argentina in Salta Province.

Nivaclé is complex both in its phonology and morphology. Much of what is handled in syntactic constructions in many other languages is signalled in Nivaclé by its rich bound morphology and clitics. Nivaclé has several linguistic traits that are rare elsewhere in the world or even unique.

Presidente Hayes Department
Presidente Hayes (Spanish pronunciation: [pɾesiˈðente ˈaʝes]) is a department in Paraguay. The capital is the city of Villa Hayes. The department was named after U.S. President Rutherford B. Hayes, who awarded the territory to Paraguay while arbitrating a boundary dispute between Paraguay and Argentina after the Paraguayan War.
FC Caleta Coloso a Aguas Blancas
The Ferrocarril Caleta Coloso a Aguas Blancas (Aguas Blancas Railway) was a 2 ft 6 in (762 mm) narrow gauge railway operating in the Antofagasta region of Chile, and was built to serve the nitrate workings southeast of Antofagasta. Opened in 1902 it was taken over by the Ferrocarril de Antofagasta a Bolivia in 1909. Never converted to 1,000 mm (3 ft 3+3⁄8 in) metre gauge like its parent, it retained 2 ft 6 in (762 mm) gauge track until it closed in 1961. Total length was 111 miles (179 km), and in 1958 it possessed 6 locomotives, 3 coaches, and 362 freight cars.

2 ft 6 in gauge railways
2 ft 6 in (762 mm) gauge railways are narrow gauge railways with track gauge of 2 ft 6 in (762 mm). That gauge was particularly promoted by Thomas Hall and Everard Calthrop during the second half of the nineteenth century, especially in colonies of the British Empire.

Several Bosnian-gauge railways with 760 mm (2 ft 5+15⁄16 in) are found in south-eastern Europe. 760 mm (29.92 in) is well within engineering tolerance of 762 mm (30.0 in).
Acanthus (son of Autonous)
In Greek mythology, Acanthus (Ancient Greek: Ακανθος Akanthos means 'thorn') was the son of Autonous (son of Melaneus) and Hippodamia. He was the brother of Acanthis, Erodius, Anthus and Schoeneus. The bird he turned into has been identified as the siskin, the linnet, the blue tit or other birds, but with little certainty. Perhaps he is supposed to be the male of the bird his sister Acanthis turned into.

Common linnet
The common linnet (Linaria cannabina) is a small passerine bird of the finch family, Fringillidae. It derives its common name and the scientific name,  Linaria, from its fondness for hemp seeds and flax seeds—flax being the English name of the plant from which linen is made.
Sepeko
Sepeko is an administrative ward in the Monduli District of the Arusha Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 13,550 people in the ward, from 16,720 in 2012.

National Bureau of Statistics (Tanzania)
The National Bureau of Statistics is a branch of the Government of Tanzania which has the mandate to provide official statistics to the Government of Tanzania, business community and the public at large. It is based in Dodoma and obtains a wide range of economic, social and demographic statistics about the country. The bureau compiled data on every village in Tanzania for the censuses of 2002, 2012 and 2022, but also provides the results of the previous censuses of 1967, 1978 and 1988.
Anne Brunila
Anne Maritta Brunila (born 31 August 1957) was the Executive Vice President, Corporate Relations and Sustainability at Fortum Corporation from 2009 to 2013. She has a P.h.D in Economics and Business Administration from Helsinki School of Economics. Brunila has been described as "one of the most influential women in the Finnish economy."

Fortum
Fortum Oyj is a Finnish state-owned energy company located in Espoo, Finland. It mainly focuses on the Nordic region. Fortum operates power plants, including co-generation plants, and generates and sells electricity and heat. The company also sells waste services such as recycling, reutilisation, final disposal solutions and soil remediation and environmental constructions services, and other energy-related services and products e.g. consultancy services for power plants and electric vehicle charging. Fortum is listed on the Nasdaq Helsinki stock exchange.

As of 2023 Fortum was the third-largest power generator in the Nordics.
Arun Kumar Upreti
Arun Kumar Upreti is an Indian politician. He was elected to the Sikkim Legislative Assembly from Arithang in the 2019 Sikkim Legislative Assembly election as a member of the Sikkim Krantikari Morcha. He has served his tenure as Minister of Urban & Housing development, Food & Civil supplies and Consumer affairs from 2019 to 2022 in P. S. Golay Cabinet. He was the Speaker of Sikkim State Legislative Assembly.

Sikkim Krantikari Morcha
Sikkim Krantikari Morcha (translation: Sikkim Revolutionary Front) is a political party in the Indian state of Sikkim which is the ruling party of Sikkim since 2019.

P.S. Golay, a member of the Sikkim Legislative Assembly, was one of the prominent figures of the Sikkim Democratic Front (SDF) and was a minister in the government of Sikkim. Since December 2009 he has been a vocal critic of Pawan Kumar Chamling, the President of the SDF and the former chief minister of Sikkim. He started the party Sikkim Krantikari Morcha on 4 February 2013. Golay became the Chief Minister of Sikkim on 28 May 2019, thus ending Chamling’s 25-year-rule. In the 2024 general elections the Sikkim Krantikari Morcha party won a landslide victory of 31 seats out of 32; in July 2024 the sole MLA of the opposition Sikkim Democratic Front, Tenzing Norbu Lamtha defected to Sikkim Krantikari Morcha, resulting in the Sikkim Legislative Assembly having no opposition.
Malea (Arcadia)
Malea (Ancient Greek: Μαλέα) was a town in the district of Aegytis in ancient Arcadia, the inhabitants of which were transferred to Megalopolis upon the foundation of the latter city (371 BCE). Its territory was called the Maleatis (ἡ Μαλεᾶτις). Xenophon describes Leuctra as a fortress situated above the Maleatis. The place Midea (Μιδέα) mentioned by Xenophon may be a corrupt form of Malea.

Its site is tentatively located south of the modern Voutsaras.

Arcadia (region)
Arcadia (/ɑːrˈkeɪdiə/; Greek: Ἀρκαδία, romanized: Arkadía) is a region in the central Peloponnese, Greece. It takes its name from the mythological character Arcas, and in Greek mythology it was the home of the gods Hermes and Pan. In European Renaissance arts, Arcadia was celebrated as an unspoiled, harmonious wilderness; as such, it was referenced in popular culture.

The modern regional unit of the same name more or less overlaps with the historical region, but is slightly larger.
Carex caespititia
Carex caespititia, also known as cong sheng tai cao, is a tussock-forming species of perennial sedge in the family Cyperaceae. It is native to parts of Asia from Assam in northern India in the west to central China in the east.

The sedge has a long rhizome and slender culms with a triangular cross-section that are 15 to 20 cm (5.9 to 7.9 in) that have a rough texture above. The green leaves are usually shorter than the culms and have a linear blade with a width of 3 to 4 mm (0.12 to 0.16 in) with rough margins.

The species was first described by the botanist Christian Gottfried Daniel Nees von Esenbeck in 1834 as a part of the Robert Wight work Contributions to the Botany of India.

Culm (botany)
A culm is the aerial (above-ground) stem of a grass or sedge. It is derived from the Latin word culmus, meaning "stalk". It originally referred to the stem of any type of plant.

In horticulture or agriculture, it is especially used to describe the stalk or woody stems of bamboo, cane or grain grasses.
James M. Collins
James Mitchell Collins (April 29, 1916 – July 21, 1989) was an American businessman and a Republican politician who represented the Third Congressional District of Texas from 1968 to 1983. The district was based at the time around Irving in Dallas County.

Irving, Texas
Irving is a city in Dallas County, Texas, United States. It is part of the Mid-Cities region of the Dallas–Fort Worth metroplex and is an inner city suburb of Dallas.  The city had a population of 256,684 according to the 2020 United States census, making it the twelfth-most populous city in Texas, and the 90th most populous in the U.S. Irving includes the Las Colinas mixed-use master-planned community and part of the Dallas Fort Worth International Airport.
Loop Creek (West Virginia)
Loop Creek, also known by the spelling Loup Creek, is a tributary of the Kanawha River, 20 miles (32 km) long, in southern West Virginia in the United States.  Via the Kanawha and Ohio rivers, it is part of the watershed of the Mississippi River, draining an area of 49.6 square miles (128 km2) in a coal mining region on the unglaciated portion of the Allegheny Plateau.

Loop Creek flows for its entire length in western Fayette County.  It rises in the city of Oak Hill and flows initially west-northwestward through the unincorporated communities of Lick Fork, Wriston, Ingram Branch, and Hamilton; then northward through the unincorporated communities of Kincaid, Page, North Page, and Robson, to Deep Water, where it flows into the Kanawha River.

In addition to Loup Creek, the Geographic Names Information System lists "Loops Creek" as a historical variant name for the creek. Loop Creek was so named on account of its irregular, looping course, according to local history.

Deep Water, West Virginia
Deep Water, also known historically as Deepwater, is a census-designated place on the Kanawha River in Fayette County, West Virginia, United States. As of the 2020 census, its population was 183 (down from 280 at the 2010 census). It is best known as the starting point of the Deepwater Railway founded in 1898 by William N. Page, which was merged to create the Virginian Railway in 1907.

Located near the head of navigation of the Kanawha River just a short distance downstream from Kanawha Falls, it may have been named for that reason. However, according to local legend, as recounted by H. Reid in The Virginian Railway (Kalmbach, 1961), it was named by Squire James Galsepy Kincaid and other locals on a rainy day in 1871 as a commentary on the standing groundwater outside the new post office along Loup Creek.
Atabek Azisbekov
Atabek Azisbekov (born 6 November 1995) is a Kyrgyz Greco-Roman wrestler. He is two time Asian Championships silver medalist

He represented Kyrgyzstan at the 2020 Summer Olympics in the men's Greco-Roman 87 kg weight class.

He competed in the 87 kg event at the 2022 World Wrestling Championships held in Belgrade, Serbia.

Asian Wrestling Championships
Asian Wrestling Championships is the Wrestling Asian Championship organized by the Asian Associated Wrestling Committee (AAWC).

The men's tournament began in 1979 and The women's tournament was first staged in 1996, and it has been held every year.
23 Camelopardalis
23 Camelopardalis is a star in the northern circumpolar constellation of Camelopardalis, located 433 light years away from the Sun. It is just visible to the naked eye as a dim, yellow-hued star with an apparent visual magnitude of 6.17. The object is moving closer to the Sun with a heliocentric radial velocity of −2.5 km/s.

With a stellar classification of G5 III:, 23 Camelopardalis appears to be an aging giant star that has exhausted the hydrogen at its core and evolved away from the main sequence, although the ':' denotes some uncertainty about the classification. It is a red clump giant, which indicates it is on the horizontal branch and is generating energy through helium fusion at its core. The star is 1.5 billion years old with more than double the mass of the Sun and almost 10 times the Sun's radius. It is radiating 60 times the Sun's luminosity from its enlarged photosphere at an effective temperature of 5,183 K.

Red clump
The red clump is a clustering of red giants in the Hertzsprung–Russell diagram at around 5,000 K and absolute magnitude (MV) +0.5, slightly hotter than most red-giant-branch stars of the same luminosity.  It is visible as a denser region of the red-giant branch or a bulge towards hotter temperatures.  It is prominent in many galactic open clusters, and it is also noticeable in many intermediate-age globular clusters and in nearby field stars (e.g. the Hipparcos stars).

The red clump giants are cool horizontal branch stars, stars originally similar to the Sun which have undergone a helium flash and are now fusing helium in their cores.