hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Erdős–Mordell inequality
In Euclidean geometry, the Erdős–Mordell inequality states that for any triangle ABC and point P inside ABC, the sum of the distances from P to the sides is less than or equal to half of the sum of the distances from P to the vertices. It is named after Paul Erdős and Louis Mordell. Erdős (1935) posed the problem of proving the inequality; a proof was provided two years later by Mordell and D. F. Barrow (1937). This solution was however not very elementary. Subsequent simpler proofs were then found by Kazarinoff (1957), Bankoff (1958), and Alsina & Nelsen (2007).

Barrow's inequality is a strengthened version of the Erdős–Mordell inequality in which the distances from P to the sides are replaced by the distances from P to the points where the angle bisectors of  ∠APB, ∠BPC, and ∠CPA cross the sides. Although the replaced distances are longer, their sum is still less than or equal to half the sum of the distances to the vertices.

Barrow's inequality
In geometry, Barrow's inequality is an inequality relating the distances between an arbitrary point within a triangle, the vertices of the triangle, and certain points on the sides of the triangle. It is named after David Francis Barrow.
Musashi Imperial Graveyard
Musashi Imperial Graveyard (武蔵陵墓地, Musashi ryōbochi) is a mausoleum complex of the Japanese Emperors in Nagabusa-machi, Hachiōji, Tokyo, Japan. Located within a forest in the western suburbs of Tokyo and named for the ancient Musashi Province, the site contains the mausolea of Emperor Taishō and Emperor Shōwa, as well as those of their wives, Empress Teimei and Empress Kōjun.

Empress Teimei
Sadako Kujō (九条節子, Kujō Sadako; 25 June 1884 – 17 May 1951), posthumously honoured as Empress Teimei (貞明皇后, Teimei Kōgō), was the wife of Emperor Taishō and the mother of Emperor Shōwa. Her posthumous name, Teimei, means "enlightened constancy". She was also the paternal grandmother of Emperor Emeritus Akihito, and the paternal great-grandmother of Emperor Naruhito.
BAE Systems Land Systems South Africa
BAE Systems Land Systems South Africa (LSSA) was a South African defence company that operated as a subsidiary of BAE Systems Land Systems. On 28 April 2015, BAE Systems announced the sale of its 75% stake in the company to the state-owned defence group Denel. Denel acquired the stake for R641 million in cash, with the total acquisition costing R855 million after it also purchased the remaining 25% from the company's Black Economic Empowerment (BEE) partner, DGD Technologies. Following the acquisition, LSSA was rebranded as Denel Vehicle Systems (DVS).

BAE Systems Platforms & Services
BAE Systems Platforms & Services is a wholly owned subsidiary of BAE Systems Inc. and is a large provider of tracked and wheeled armored combat vehicles, naval guns, naval ship repair and modernization, artillery and missile launching systems, advanced precision strike munitions and ordnance, and other technologies for US and international customers.

It was created on 24 June 2005, following the completion of BAE Systems' acquisition of United Defense in 2004 and its merger with BAE Systems Land Systems. In 2007, BAE Systems acquired Armor Holdings adding to the size of Land & Armaments significantly.

Until April 2003, BAE Systems was a relatively small player in the land systems industry.  As a result of the acquisitions, it is now one of the largest land systems defence contractors in the world.
Battle of Trangen
The Battle of Trangen took place on 25 April 1808 at Trangen in Flisa, Hedemarkens Amt, between Swedish and Norwegian troops, as a part of the Dano-Swedish War of 1808–1809. The invading Swedish troops, led by Colonel Carl Pontus Gahn, were surrounded and forced to surrender by the Norwegian troops under the command of Bernhard Ditlef von Staffeldt. Gahn and around 450 of his troops were captured.

Dano-Swedish War (1808–1809)
The Dano-Swedish War of 1808–1809 was a war between Denmark–Norway and Sweden due to Denmark–Norway's alliance with France and Sweden's alliance with the United Kingdom during the Napoleonic Wars. Neither Sweden nor Denmark-Norway had wanted war to begin with but once pushed into it through their respective alliances, Sweden made a bid to acquire Norway by way of invasion while Denmark-Norway made ill-fated attempts to reconquer territories lost to Sweden in the 17th century. Peace was concluded on grounds of status quo ante bellum on 10 December 1809.
Riparian water rights
Riparian water rights (or simply riparian rights) is a system for allocating water among those who possess land along its path.  It has its origins in English common law.  Riparian water rights exist in many jurisdictions with a common law heritage, such as Canada, Australia, New Zealand, and states in the eastern United States.

Common land ownership can be organized into a partition unit, a corporation consisting of the landowners on the shore that formally owns the water area and determines its use.

Water right
In water law, water right is the right of a user to use water from a water source, e.g., a river, stream, pond or source of groundwater. In areas with plentiful water and few users, such systems are generally not complicated or contentious. In other areas, especially arid areas where irrigation is practiced, such systems are often the source of conflict, both legal and physical. Some systems treat surface water and ground water in the same manner, while others use different principles for each.
West Vancouver Schools
West Vancouver Schools, also known as WVS or School District 45 West Vancouver, is a school district in British Columbia. It is immediately north of Vancouver and includes the Municipality of West Vancouver, the community of Lions Bay and Bowen Island.

West Vancouver
West Vancouver is a district municipality in the province of British Columbia, Canada. A member municipality of the Metro Vancouver Regional District, West Vancouver is situated on the north shore of Burrard Inlet to the northwest of the city of Vancouver. With the District of North Vancouver and the City of North Vancouver, West Vancouver is part of a regional grouping known as the North Shore municipalities. It is among the wealthiest municipalities in Canada by average household net worth.

West Vancouver is home to the Horseshoe Bay ferry terminal, one of the main transportation hubs connecting the British Columbia mainland and Vancouver Island, and to much of Cypress Provincial Park.
Johnston, Iowa
Johnston is a city in Polk County, Iowa, United States. The population was 24,064 in the 2020 census, a large increase from the 8,649 population in 2000. It is part of the Des Moines–West Des Moines Metropolitan Statistical Area.

Johnston is the location of the headquarters of Pioneer Hi-Bred Seeds, Iowa Public Television, and The Gardeners of America/Men's Garden Clubs of America. Also located here are the Camp Dodge Military Reservation as well as the Paul J. and Ida Trier House, a private residence designed by architect Frank Lloyd Wright, and the Des Moines Weather Forecast Office of the National Weather Service.

Des Moines metropolitan area
The Des Moines metropolitan area, officially known as the Des Moines–West Des Moines, IA Metropolitan Statistical Area (MSA) is located at the confluence of the Des Moines River and the Raccoon River. Des Moines serves as the capital and largest city of the U.S. state of Iowa. The metro area consists of six counties in central Iowa: Polk, Dallas, Warren, Madison, Guthrie, and Jasper. The Des Moines–Ames–West Des Moines Combined Statistical Area (CSA) encompasses the separate metropolitan area of Ames (Story County), and the separate micropolitan area of Boone (Boone County). The Des Moines area is a fast-growing metro area.
Bernezzo
Bernezzo (Occitan, Bernès) is a comune (municipality) in the Province of Cuneo in the Italian region Piedmont, located about 80 kilometres (50 mi) southwest of Turin and about 9 kilometres (6 mi) west of Cuneo.

Bernezzo borders the following municipalities: Caraglio, Cervasca, Rittana, Roccasparvera, and Valgrana.

Rittana
Rittana is a comune (municipality) in the Province of Cuneo in the Italian region Piedmont, located about 80 kilometres (50 mi) southwest of Turin and about 13 kilometres (8 mi) southwest of Cuneo.

Rittana borders the following municipalities: Bernezzo, Gaiola, Monterosso Grana, Roccasparvera, Valgrana, and Valloriate.
Catan
Catan (/kəˈtæn, -ɑːn/), previously known as The Settlers of Catan or simply Settlers, is a multiplayer board game designed by Klaus Teuber. It was first published in 1995 in Germany by Franckh-Kosmos Verlag (Kosmos) as Die Siedler von Catan (German: [diː ˈziːdlɐ fɔn kaˈtaːn]). Players take on the roles of settlers, each attempting to build and develop holdings while trading and acquiring resources. Players gain victory points as their settlements grow and the first to reach a set number of victory points, typically 10, wins. The game and its many expansions are also published by Catan Studio, Filosofia, GP, Inc., 999 Games, Κάισσα (Káissa), and Devir. Upon its release, The Settlers of Catan became one of the first Eurogames to achieve popularity outside Europe. As of 2020, more than 32 million boxed sets in 40 languages had been sold.

Asmodee
Asmodee (formerly known as Asmodée Editions) is a French publisher of board games, card games and role-playing games (RPGs). Founded in 1995 to develop their own games and to publish and distribute for other smaller game developers, they have since acquired numerous other board game publishers. A division, Twin Sails Interactive (formerly Asmodee Digital), publishes video game adaptations of Asmodee games.
Cyrus McCormick Farm
The Cyrus McCormick Farm and Workshop is on the family farm of inventor Cyrus Hall McCormick known as Walnut Grove. Cyrus Hall McCormick improved and patented the mechanical reaper, which eventually led to the creation of the combine harvester.

The farm is near Steele's Tavern and Raphine, close to the northern border of Rockbridge and Augusta counties in the U.S. state of Virginia, and is currently a museum run by the Virginia Agricultural Experimental Station of Virginia Tech. The museum has free admission and covers 5 acres (2.0 ha) of the initial 532-acre (215.3 ha) farm.

Cyrus McCormick
Cyrus Hall McCormick (February 15, 1809 – May 13, 1884) was an American inventor and businessman who founded the McCormick Harvesting Machine Company, which became part of the International Harvester Company in 1902. Originally from the Blue Ridge Mountains of Virginia, he and many members of the McCormick family became prominent residents of Chicago.

McCormick always claimed credit as the single inventor of the mechanical reaper. He was, however, one of several designing engineers who produced working models in the 1830s. His efforts built on more than two decades of work by his father Robert McCormick Jr., with the aid of Jo Anderson, an enslaved African-American man held by the family. He also successfully developed a modern company, with manufacturing, marketing, and a sales force to market his products.
Bream Bay
Bream Bay is an embayment and area south-east of Whangārei, on the east coast of New Zealand. The bay runs from Bream Head, at the mouth of Whangārei Harbour, 22 kilometres south to the headland of Bream Tail, east of Langs Beach and north of Mangawhai. It was named by Captain James Cook. The Bream Bay area includes the towns of Ruakākā, One Tree Point and Waipu. A group of nature reserve islands lie outside Bream Bay: the Hen and Chicken Islands and Sail Rock.

Whangārei
Whangārei is the northernmost city in New Zealand and the largest settlement of the Northland Region. It is part of the Whangarei District, created in 1989 from the former Whangarei City, Whangarei County and Hikurangi Town councils to administer both the city and its hinterland. The city population was estimated to be 56,100 in June 2025, an increase from 47,000 in 2001.
Battle of Wadi (1916)
The Battle of Wadi, occurring on 13 January 1916, was an unsuccessful attempt by British forces fighting in Ottoman Iraq during World War I to relieve beleaguered forces under Sir Charles Townshend then under siege by the Ottoman Sixth Army at Kut-al-Amara.

Pushed by regional British Commander-in-Chief Sir John Nixon, General Fenton Aylmer launched an attack against Ottoman defensive positions on the banks of the Wadi River. The Wadi was a steep valley of a stream that ran from the north into the River Tigris, some 6 miles (9.7 km) upstream towards Kut-al-Amara from Sheikh Sa'ad. The attack is generally considered as a failure, as although Aylmer managed to capture the Wadi, it cost him 1,600 men. The British failure led to Townshend's surrender, along with 10,000 of his men, in the largest single surrender of British troops up to that time. However, the British recaptured Kut in February 1917, on their way to the capture of Baghdad sixteen days later on 11 March 1917.

George Kemball
Major-General Sir George Vere Kemball KCMG CB DSO (1 October 1859 – 10 January 1941) was a British Army officer of the 19th and early 20th century. He was a career officer in the British Army spending most of his career in India and Nigeria.
Ellmauer Tor
The Ellmauer Tor is a 2,000-metre high rock saddle in the middle of the Kaisergebirge in the Austrian state of Tyrol.

It is the deepest saddle on the main ridge of the Wilder Kaiser between the Ostkaiser's Ackerlspitze in the East Kaiser and the Ellmauer Halt in the Central Kaiser mountains. Because there is a well-used route across the Ellmauer Tor with its unique setting, it is often referred to as the "heart of the Kaiser". From the south, seen from the general direction of Ellmau or Going, it is the distinctive notch in the Kaisergebirge between the Karlspitzen and the Goinger Halt.

Goinger Halt
The Goinger Halt is a mountain in the Kaisergebirge range in the Northern Limestone Alps in Austria. It has a double summit: a northern top to the rear, the Hintere Goinger Halt (2,192 metres), and a higher, southern top in front, the Vordere Goinger Halt (2,242 metres). The name "Halt" means something like Alpine meadow and refers therefore to the peak over the meadow areas, that belong to the parish of Going (cf. Ellmauer Halt).
Stroud News & Journal
The Stroud News & Journal is a weekly paid-for newspaper based in Stroud, Gloucestershire. It is published every Wednesday in a tabloid format by Newsquest and covers a large portion of the Stroud district, including the towns of Stroud, Minchinhampton, Nailsworth, Stonehouse, Painswick and Chalford, and their surrounding villages.

Minchinhampton
Minchinhampton is a Cotswolds market town and a civil parish in the Stroud District of Gloucestershire, South West England. The town is located on a hilltop, 4 miles (6.4 km) south-east of Stroud. Minchinhampton Common offers wide views over the Severn Estuary into Wales and further into the Cotswolds. It is an ancient town which was recorded in the Domesday Book.
Étale cohomology
In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil conjectures. Étale cohomology theory can be used to construct ℓ-adic cohomology, which is an example of a Weil cohomology theory in algebraic geometry. This has many applications, such as the proof of the Weil conjectures and the construction of representations of finite groups of Lie type.

Tate module
In mathematics, a Tate module of an abelian group, named for John Tate, is a module constructed from an abelian group A. Often, this construction is made in the following situation: G is a commutative group scheme over a field K, Ks is the separable closure of K, and A = G(Ks) (the Ks-valued points of G). In this case, the Tate module of A is equipped with an action of the absolute Galois group of K, and it is referred to as the Tate module of G.
OneBeat (music program)
OneBeat in an annual international music exchange program that gathers musicians to share and collaborate on musical ideas and projects. The program was an initiative of the U.S. Department of State's Bureau of Educational and Cultural Affairs in partnership with and produced by Bang on a Can's Found Sound Nation.

The program selects around 25 musicians from hundreds of international applicants to participate in a two-week artist residency, where they experiment with sounds, record and produce tracks, and implement workshops through brainstorming with local educators, organizers, and entrepreneurs. These compositions and workshops are taken on the road for a two-week-long tour of performances, youth workshops and public music.

In addition to the U.S.-based program, OneBeat launched OneBeat Abroad hosted in partnership with global alumni, as well as OneBeat Virtual, OneBeat Institute and OneBeat Accelerator, a micro-granting program.

Found Sound Nation
Found Sound Nation (FSN) is a New York-based creative agency and nonprofit organization that uses music-making to connect people across cultural and societal divides. FSN is composed of musicians and artists who use collaborative sound-making as a tool of music diplomacy to help enhance communities and build bonds both locally and internationally.
Kyriakos Stamatopoulos
Kyriakos Stamatopoulos (born 28 August 1979) is a Greek Canadian former professional soccer goalkeeper who is the head goalkeeper coach for AIK. In addition to his role as goalkeeping coach, he continues to be registered as a player on the roster, dressing as the substitute goalkeeper on the bench when needed.

He is nicknamed "Stam" (/stæm/) and he is also often referred to as Kenny Stamatopoulos.

Greek Canadians
Greek Canadians (Greek: Ελληνοκαναδοί) are Canadian citizens who have full or partial Greek heritage or people who emigrated from Greece and reside in Canada. According to the 2021 Census, there were 262,140 Canadians who claimed Greek ancestry.
Ust-Orda Buryat constituency
The Ust-Orda Buryat constituency (No.220) was a Russian legislative constituency in the Ust-Orda Buryat Autonomous Okrug in 1993–2007. It encompassed the entire territory of Ust-Orda Buryat Autonomous Okrug. The seat was last occupied by United Russia deputy Valery Maleyev, former Governor of Ust-Orda Buryat Autonomous Okrug, who won a by-election in 2006.

The constituency was dissolved in 2007 when State Duma adopted full proportional representation for the next two electoral cycles. In 2008 Ust-Orda Buryat Autonomous Okrug was merged with Irkutsk Oblast. Currently the territory of the former Ust-Orda constituency is split between Irkutsk and Angarsk constituencies.

Irkutsk constituency
The Irkutsk constituency (No.93) is a Russian legislative constituency in Irkutsk Oblast. The constituency covers part of Irkutsk on the right bank of Angara as well as sparsely populated central Irkutsk Oblast.

The constituency has been vacant since September 23, 2025, following the resignation of two-term Communist deputy Mikhail Shchapov, who was appointed Auditor of the Accounts Chamber of Russia.
Our Lady of La Vang Parish
Our Lady of La Vang Parish (Vietnamese: Giáo Xứ Đức Mẹ La Vang, Spanish: Iglesia Católica Nuestra Señora de La Vang), formerly Saint Patrick Proto-Cathedral Parish, is a Vietnamese national parish and former cathedral of the Roman Catholic Diocese of San Jose in California. The proto-cathedral is located in Downtown San José, one block north of San José State University. It is named after Our Lady of La Vang. The Daughters of Charity of Saint Vincent de Paul sponsor St. Patrick Elementary School which is located on the church grounds.

Diocese of San José in California
The Diocese of San José in California (Latin: Diœcesis Sancti Josephi in California) is a diocese of the Catholic Church in Santa Clara County in California in the United States. The mother church is the Cathedral Basilica of St. Joseph in San Jose.
Edwina Lau
Edwina Lau Chi-wai, PMSM (Chinese: 劉賜蕙; Jyutping: lau4 ci3 wai6, born 29 July 1965) is a Hong Kong law enforcement administrator currently serving as the head of the National Security Department of the Hong Kong Police Force while also sitting on the Committee for Safeguarding National Security.

Committee for Safeguarding National Security
The Committee for Safeguarding National Security of the Hong Kong Special Administrative Region is a national security committee established by the Government of Hong Kong under the Article 12 of the Hong Kong national security law. The committee is supervised and accountable to the Central People's Government of China.

The committee is chaired by the Chief Executive, as stated in the Article 13 of the law. The committee's other members are the Chief Secretary for Administration, the Financial Secretary, the Secretary for Justice, the Secretary for Security, the Commissioner of Police, the head of the National Security Department of the Hong Kong Police Force, the Director of Immigration, the Commissioner of Customs and Excise, and the Director of the Chief Executive's Office.
Buglio in Monte
Buglio in Monte is a comune (municipality) in the Province of Sondrio in the Italian region Lombardy, located about 90 kilometres (56 mi) northeast of Milan and about 14 kilometres (9 mi) west of Sondrio. As of 31 December 2004, it had a population of 2,066 and an area of 27.8 square kilometres (10.7 sq mi).

Buglio in Monte borders the following municipalities: Ardenno, Berbenno di Valtellina, Chiesa in Valmalenco, Colorina, Forcola, Torre di Santa Maria, Val Masino.

Colorina
Colorina is a comune (municipality) in the Province of Sondrio in the Italian region Lombardy, located about 90 kilometres (56 mi) northeast of Milan and about 10 kilometres (6 mi) west of Sondrio. As of 31 December 2004, it had a population of 1,468 and an area of 18.0 square kilometres (6.9 sq mi).

The municipality of Colorina contains the frazioni (subdivisions, mainly villages and hamlets) Valle, Piona, and Selvetta.

Colorina borders the following municipalities: Berbenno di Valtellina, Buglio in Monte, Forcola, Fusine.
Bob McKillop
Robert McKillop (born July 13, 1950) is an American college basketball coach who is the former head coach of the Davidson Wildcats men's team of the Atlantic 10 Conference. He had a 100 percent graduation rate for his players during a 33-year tenure.

John M. Belk Arena
John M. Belk Arena is a 5,295-seat multi-purpose arena, located on the campus of Davidson College, in Davidson, North Carolina, United States. It is named for Davidson alumnus and benefactor John M. Belk (1920–2007), class of 1943.

As the centerpiece of the Baker Sports Complex, it is home to the Davidson Wildcats men's and women's basketball teams, the Davidson Wildcats wrestling team, and the women's volleyball team.

The playing surface is named McKillop Court in honor of former men's basketball coach Bob McKillop, who has coached the most victories in the school's history.

Bob Dylan performed at the arena during his 2006 North American Tour on May 2, 2006.
1982 Toronto municipal election
The 1982 Toronto municipal election was held on November 8, 1982, in Metropolitan Toronto, Ontario, Canada. Mayors, controllers, city councillors and school board trustees were elected in the municipalities of Toronto, York, East York, North York, Etobicoke and Scarborough.

Art Eggleton was re-elected as Mayor of Toronto, and Mel Lastman was re-elected as Mayor of North York.

1988 Toronto municipal election
The 1988 Toronto municipal election was held to elect members of municipal councils, school boards, and hydro commissions in the six municipalities that made up Metropolitan Toronto, Ontario, Canada. The election was held  November 14, 1988. This election also marked the abolition of Boards of Control in North York, Etobicoke, Scarborough, and York. The Toronto Board of Control had been abolished in 1969.