OpenLLM-France/wikimedia huggingface dataset:
# Poncelet's closure theorem

In geometry, Poncelet's closure theorem, also known as Poncelet's porism, states that whenever a polygon is inscribed in one conic section and circumscribes another one, the polygon must be part of an infinite family of polygons that are all inscribed in and circumscribe the same two conics. It is named after French engineer and mathematician Jean-Victor Poncelet, who wrote about it in 1822; however, the triangular case was discovered significantly earlier, in 1746 by William Chapple.
Poncelet's porism can be proved by an argument using an elliptic curve, whose points represent a combination of a line tangent to one conic and a crossing point of that line with the other conic.

## Statement

Let C and D be two plane conics. If it is possible to find, for a given n > 2, one n-sided polygon that is simultaneously inscribed in C (meaning that all of its vertices lie on C) and circumscribed around D (meaning that all of its edges are tangent to D), then it is possible to find infinitely many of them. Each point of C or D is a vertex or tangency (respectively) of one such polygon.
If the conics are circles, the polygons that are inscribed in one circle and circumscribed about the other are called bicentric polygons, so this special case of Poncelet's porism can be expressed more concisely by saying that every bicentric polygon is part of an infinite family of bicentric polygons with respect to the same two circles.$^{:p.94}$

## Proof sketch

View C and D as curves in the complex projective plane P$^2$. For simplicity, assume that C and D meet transversely (meaning that each intersection point of the two is a simple crossing). Then by Bézout's theorem, the intersection C ∩ D of the two curves consists of four complex points. For an arbitrary point d in D, let ℓ$_d$ be the tangent line to D at d. Let X be the subvariety of C × D consisting of (c,d) such that ℓ$_d$ passes through c. Given c, the number of d with (c,d) ∈ X is 1 if c ∈ C ∩ D and 2 otherwise. Thus the projection X → C ≃ P$^1$ presents X as a degree 2 cover ramified above 4 points, so X is an elliptic curve (once we fix a base point on X). Let $\sigma$ be the involution of X sending a general (c,d) to the other point (c,d′) with the same first coordinate. Any involution of an elliptic curve with a fixed point, when expressed in the group law, has the form x → p − x for some p, so $\sigma$ has this form. Similarly, the projection X → D is a degree 2 morphism ramified over the contact points on D of the four lines tangent to both C and D, and the corresponding involution $\tau$ has the form x → q − x for some q. Thus the composition $\tau \sigma$ is a translation on X. If a power of $\tau \sigma$ has a fixed point, that power must be the identity. Translated back into the language of C and D, this means that if one point c ∈ C (equipped with a corresponding d) gives rise to an orbit that closes up (i.e., gives an n-gon), then so does every point. The degenerate cases in which C and D are not transverse follow from a limit argument.
# Porcia, Friuli-Venezia Giulia

Porcia (pronounced) is a comune (municipality) in the Regional decentralization entity of Pordenone, in the Italian region of Friuli-Venezia Giulia, located about 100 kilometres (62 mi) northwest of Trieste and about 3 kilometres (1.9 mi) west of Pordenone.

## Main sights

* The castle, residence from the 12th century of the Porcia family (Counts, later Princes)
* Torre dell'Orologio ("Watch Tower")
* Villa Correr-Dolfin (late 17th – early 18th centuries)
* Church of St. George, known from 1262. It has a 44-metre (144 ft) standing unfinished bell tower.

## International relations
### Twin towns — sister cities

Porcia is twinned with:
* Spittal an der Drau, Austria
* Berettyóújfalu, Hungary
# Wesleyan Christian Academy (Cayman Islands)

Wesleyan Christian Academy is a private Christian school in West Bay, Grand Cayman, Cayman Islands. It serves grade levels K4-12. As of 2016 there are 130 students. The school was established in 1977.
# Harald Beyer (politician)

Harald Ricardo Beyer Burgos (born April 2, 1964) is a Chilean economist and researcher. Former member of the Presidential Advisory Councils of Education under the government of Michelle Bachelet. He served as Minister of Education of Chile from December 29, 2011 to April 17, 2013, when he was impeached because of his failure to address for-profit activity in universities (which is illegal). He subsequently became executive director of the Centro de Estudios Públicos, a right-wing think tank in Santiago under the presidency of Eliodoro Matte. He is now vice-chancellor of the Adolfo Ibáñez University.
# Gowland

Gowland is an English surname. Notable people with the surname include:
* Daniel Gowland (1798–1883), English merchant and banker
* Don Gowland (born 1940), Australian sports shooter
* Gibson Gowland (1877–1951), English film actor
* Lance Gowland (1935–2008), Australian activist
* Peter Gowland (1916–2010), American photographer and actor
* Ralph Gowland (c. 1722 – c. 1782), British politician
* Sam Gowland (born 1995), English television personality
* Thomas Gowland (1768–1833), English trader
* Tony Gowland (born 1945), English track cyclist
* William Gowland (1842–1922), English mining engineer
* Frederick Gowland Hopkins (1861–1947), English biochemist
# Dynaflex

The DynaFlex can refer to
* Dynaflex (RCA) a thin, lightweight vinyl phonograph record developed by RCA Records
* DynaFlex International, a company that manufactures Gyroscopic Exercise tools
# Graham Creek

Graham Creek may refer to:
* Graham Creek (Alberta), a stream in Saskatchewan and Alberta
* Graham Creek (Sonoma County, California), a stream in California
* Graham Creek (Rogue River tributary), a stream in Oregon
* Graham Creek (Manitoba), a river in Saskatchewan and Manitoba
* Grahams Creek, Queensland, a rural locality in the Fraser Coast Region, Queensland, Australia
# Dysbiota

Dysbiota is a genus of flies in the family Stratiomyidae.

## Species

* Dysbiota parvula Lindner, 1958
* Dysbiota peregrina (Hutton, 1901)
# Graeme Turner (cricketer)

Graeme John Turner (born 5 August 1964) is a Rhodesian-born South African former cricketer.
Turner was born in August 1964 at Bulawayo, Southern Rhodesia, later moving to South Africa to study at university. He made his debut in first-class cricket for Western Province B against Boland in the 1984–85 Castle Bowl. His second first-class match, played in December 1984, came for the combined South African Universities against Transvaal. He played first-class cricket for Western Province and their B team until the 1986–87 season, making sixteen appearances. He scored 678 runs in these matches, at an average of 24.21 and a high score of 69 not out. It was for Western Province that he made his debut in List A one-day cricket in the 1984–85 Benson and Hedges Series against Transvaal, with Turner making two further List A appearances for Western Province in the 1986–87 Nissan Shield. Toward the end of the 1986–87 Castle Bowl, Turner moved to Northern Transvaal B, where he represented the team in seven first-class matches until January 1988. He scored 259 runs in these matches, at an average of 21.58 and a high score of 58. He made a first-class appearance for the South African Defence Force cricket team against Natal in December 1988, while conscripted in the South African Defence Force.
He travelled to England in 1989 to study at the University of Oxford, where he attended St Anne's College. While studying at Oxford, he made sixteen first-class appearances for Oxford University in 1990–91, scoring 607 runs at an average of 38.93. He made his only first-class century while playing for Oxford, scoring 101 not out against Lancashire in 1991. With his right-arm off break bowling, he took 19 wickets for Oxford with best figures of 3 for 32. He also made a single first-class appearance for the combined Oxford and Cambridge Universities cricket team against the touring New Zealanders in 1900, where he featured alongside fellow South African and St Anne's College attendee Willem van der Merwe. In addition to playing first-class cricket while at Oxford, he also appeared in three List A matches for the Combined Universities cricket team in the 1991 Benson & Hedges Cup. Returning to South Africa, he later made two first-class appearances for Transvaal in the 1993–93 Castle Cup.
# William Gough (disambiguation)

William Gough may refer to:

## People

* William Gough (1929–1978), New Zealand cricketer
* William Gough (antiquarian) (1654?–1682), English antiquarian
* William Venn Gough (1842–1918), English architect
# Graincourt-lès-Havrincourt

Graincourt-lès-Havrincourt is a commune in the Pas-de-Calais department in the Hauts-de-France region of France.

## Geography

A farming village situated 22 miles (35 km) southeast of Arras, at the junction of the D15 and C5 roads. The A26 autoroute junction with the A2 autoroute is only half a mile from the commune.

## Places of interest

* The church of St.Martin, rebuilt along with the rest of the village after World War I.
* The Commonwealth War Graves Commission cemetery.
# Dəlləkli, Tovuz

40°42′N 45°38′E﻿ / ﻿40.700°N 45.633°E﻿ / 40.700; 45.633
Dəlləkli (also, Dellekli and Dellyakli) is a village in the Tovuz Rayon of Azerbaijan. The village forms part of the municipality of Qəribli.
# Dəllər, Shamkir

Dəllər (also, Dəlilər, Dallyar, and Dolyar) is a village and municipality in the Shamkir Rayon of Azerbaijan. It has a population of 4,284.
# Dəlləklər

40°26′42″N 46°59′31″E﻿ / ﻿40.44500°N 46.99194°E﻿ / 40.44500; 46.99194
Dəlləklər (also, Dellyaklyar and Delleklyar) is a village in the Yevlakh Rayon of Azerbaijan. The village forms part of the municipality of Qaramanlı.
# Graham Gardner (cricketer)

Graham Edward Gardner (born 1 June 1966) is an English-born Scottish former first-class cricketer.
Gardner was born in June 1966 at Brighton. Moving to Scotland as a child, he was educated at Graeme High School in Falkirk and Larbert High School at Larbert. A club cricketer for Stenhousemuir Cricket Club, Gardner made a single appearance for Scotland in first-class cricket against Ireland at Linlithgow in 1996. Batting once in the match from the middle order, he scored an unbeaten 2 runs in the Scottish second innings. With his medium pace bowling, he took a wicket apiece in both Irish innings', dismissing Kyle McCallan in their first innings and Andrew Patterson in their second. In 2005, Gardner featured in a minor match between Clackmannan and Warwickshire as part of Dougie Brown's benefit year, with Gardner being instrumental in a surprise 8 wicket victory for Clackmannan.
# Passo della Limina

The Passo della Limina is a mountain pass in Calabria, southern Italy. It marks the natural boundary between the Aspromonte and the Serre Calabresi massifs.
It has an altitude of 822 m.
38°23′34″N 16°11′18″E﻿ / ﻿38.39278°N 16.18833°E﻿ / 38.39278; 16.18833
* This Calabrian location article is a stub. You can help Wikipedia by expanding it.
* v
* t
* e
# Anaciaeschna jaspidea

Anaciaeschna jaspidea is a species of dragonfly in the family Aeshnidae, commonly known as the Australasian duskhawker and Rusty darner. It is widely distributed from India through Australia to the Pacific.

## Description and habitat

Anaciaeschna jaspidea is a large brown dragonfly with blue eyes. Its thorax is reddish-brown, with two broad greenish-yellow stripes on each side. Wings are transparent with pterostigma, reddish-brown. Abdomen is reddish-brown, marked with azure-blue, white, and yellow. Abdomen segment 1 has a large pale yellow spot on each side. Abdomen segment 2 has white marks on the sides and azure-blue on the dorsum with a broad spot of reddish-brown on mid-dorsum. Abdomen segments 3 to 7 are brown on dorsum with black apical annules. Abdomen segments 8 to 10 are darker on dorsum with a pair of dorsal apical spots. Anal appendages are dark reddish-brown. Female appears similar to the male.
Anaciaeschna jaspidea is a crepuscular species, flies during dawn and dusk. It is common in marshes surrounded by woods where it breeds.

## Gallery

* Male, Bengaluru, India
* Female, Bengaluru, India
* Female, Atiu, Cook Islands
* Female wings
* Male wings

## Note

The Australasian duskhawker, Anaciaeschna jaspidea, should not be confused with almost-similarly named Australian duskhawker, Austrogynacantha heterogena, a different species of Aeshnid dragonfly.
# Ongare Point

Ongare Point is a rural settlement in the Western Bay of Plenty District and Bay of Plenty Region of New Zealand's North Island. It is on a headland on the eastern side of Tauranga Harbour, southeast of Katikati Entrance and opposite Matakana Island.
A coastal walkway through a reserve connects Ongare Point to Kauri Point. There is a small sandy beach.
Ngāi Te Rangi's Ōngare Pā was attacked in 1842 by a war party of 50 men led by Tāraia Ngākuti Te Tumuhuia. The local chief Te Whanake and several followers were killed.

## Demographics

Ōngare Point-Kauri Point is defined by Statistics New Zealand as a rural settlement. Ongare Point covers 0.55 km$^2$ (0.21 sq mi). It is part of the wider Tahawai statistical area.
Ongare Point had a population of 117 at the 2018 New Zealand census, an increase of 15 people (14.7%) since the 2013 census, and an increase of 15 people (14.7%) since the 2006 census. There were 54 households, comprising 63 males and 51 females, giving a sex ratio of 1.24 males per female. The median age was 59.6 years (compared with 37.4 years nationally), with 9 people (7.7%) aged under 15 years, 12 (10.3%) aged 15 to 29, 54 (46.2%) aged 30 to 64, and 42 (35.9%) aged 65 or older.
Ethnicities were 94.9% European/Pākehā, 10.3% Māori, 2.6% Pacific peoples, and 5.1% Asian. People may identify with more than one ethnicity.
Although some people chose not to answer the census's question about religious affiliation, 64.1% had no religion, 25.6% were Christian, and 2.6% were Muslim.
Of those at least 15 years old, 24 (22.2%) people had a bachelor's or higher degree, and 21 (19.4%) people had no formal qualifications. The median income was $30,300, compared with $31,800 nationally. 15 people (13.9%) earned over $70,000 compared to 17.2% nationally. The employment status of those at least 15 was that 39 (36.1%) people were employed full-time, 15 (13.9%) were part-time, and 3 (2.8%) were unemployed.
# Villa Giusti

45°22′15″N 11°50′34″E﻿ / ﻿45.37083°N 11.84278°E﻿ / 45.37083; 11.84278
Villa Giusti or Villa Giusti del Giardino is a villa in Mandria, outside of Padua in Northern Italy. It is notable for being the site of the signing of the Armistice of Villa Giusti that ended the First World War on the Italian Front.
Fully restored in the nineteenth century, the villa was owned at the time of the armistice by the Count Vettor Giusti del Giardino, of a Veneto noble family. Giusti del Giardino was the mayor of Padua in the 1890s and a senator of the Kingdom of Italy from 1915.
Before the armistice, the villa was the temporary residence of King Victor Emmanuel III, who came back from the front and wanted to avoid the aerial bombardment of Padua's city centre. He established his command and stayed there from November 1917 until January 1918.
The Armistice of Villa Giusti ended warfare between Italy and Austria-Hungary on the Italian Front during the First World War. The armistice was signed on 3 November 1918 and took effect 24 hours later. In the room where the negotiations were conducted and the armistice was signed, the furniture remains just as it was on that day.
# Villevallier

Villevallier (French pronunciation:) is a commune in the Yonne department in Bourgogne-Franche-Comté in north-central France.
# Villa Hortensia (Rosario)

Villa Hortensia is a mansion in the city of Rosario, province of Santa Fe, Argentina. It is located on 1917 Warnes St. in Barrio Alberdi, in the north-eastern part of Rosario. It was built in 1890 by architect Boyd Walker for José Nicolás Puccio, founder of Alberdi. It was then sold to Ciro Echesortu, and then in turn to Alfredo Rouillon, married to María Hortensia Echesortu (from whom the house got its name). The wealthy Rouillon family employed Villa Hortensia as a summer residence, taking advantage of its proximity to the Paraná River and its large, tree-shadowed gardens.
Maintenance of the mansion was neglected until, in 1989, it was declared a National Historic Monument. At the time it was under a serious threat of being condemned. The Villa was acquired by the Municipality of Rosario on 30 May 1996 in order to transform it into an administrative center, as part of an official decentralisation plan. Villa Hortensia was restored, emphasizing the original plans and materials, and was re-opened as the first Municipal District Center on 13 October 1997.
Villa Hortensia hosts a citizen assistance office, a delegation of the Municipal Bank of Rosario, and offices of the water, natural gas and power companies, where the neighbors of the North District can pay for these services, place requests, etc. The mansion also has a marriage office. This allows for citizens to carry out administrative business near their homes, instead of travelling downtown to the main municipal offices (a 40-minute bus ride). A survey conducted a month after the inauguration of Villa Hortensia found that the citizens of the North District used to travel an average of 8 km for administrative business before, a distance which has been reduced to only 1.5 km. Eighty percent of the citizens surveyed also consider the service in Villa Hortensia better than the one formerly provided in the downtown offices.

## Sources

* (in Spanish) Municipality of Rosario - Information on the North District Municipal Center.
* (in Spanish) Rosario.com.ar - Directions and a location map for Villa Hortensia.
* (in Spanish) Villa Hortensia, un palacio del siglo XIX. Tourism Office of Rosario.
* (in Spanish) Ciudades para un futuro más sostenible. Descentralización y transformación estructural en Rosario (Argentina). 5 July 2000.
# Villers-le-Château

Villers-le-Château (French pronunciation:) is a village and commune in the Marne département of north-eastern France.
# Funky Squad

Funky Squad was a short-lived 1995 Australian comedy television series which satirised 1970s-era U.S. police television dramas, such as The Mod Squad. Only seven half-hour episodes were produced, which were broadcast on the ABC. Real television commercials from the 1970s were shown during the program's "commercial breaks".
The show featured four "funky" undercover detectives: undetectable as police, given their "hipness". The conclusion of each episode was deliberately designed to be incredibly predictable: usually the perpetrator of the crime under investigation could be identified within the first few minutes of the episode.
Before the television series, Funky Squad originally aired as a series of episodes on radio station Triple M. Rob Sitch, who played Grant, was replaced by Tim Ferguson when the series went to television.

## Characters

In a metafictional setting, the characters were played by "actors" whose "names" were displayed in the opening credits of the program. These "real names" were also satirical, poking fun at the names of actors who appeared in American 1970s cop shows.

### "Stix": Joey Alvarez

* Played by Santo Cilauro
* Had a large afro.

### "Grant": Blair Steele

* Played by Tim Ferguson
* The leader of the group; the cool guy.

### "Poncho": Harvey Zdalka Jr

* Played by Tom Gleisner
* Mute, as a bullet had hit his tongue. The joke was that this was a ridiculous plot device to get around having accidentally hired an actor with poor English.

### "Cassie": Verity Svensön-Hart

* Played by Jane Kennedy
* The token female; a stereotypical 1970s feminist.

### The Chief: Baldwin Scott

* Played by Barry Friedlander
* The tough cop to whom the Funky Squad reported.

## Production

The program was created and written by Australian comedians Santo Cilauro, Jane Kennedy, Tom Gleisner, and Rob Sitch of Frontline and The Late Show fame. Cilauro, Kennedy and Gleisner also co-directed the series. Sitch was originally to star but was replaced by Ferguson due to study commitments overseas.
The show was given a meagre production budget of A$1,000 per episode, so many of the costumes were acquired by wardrobe director Kitty Stuckey (best known for her work on Kath & Kim) at local Melburnian Salvation Army stores.

## Merchandise including video and DVD release

In 1995 The Funky Squad Annual was published. Unlike many TV show tie-ins this was not a behind-the-scenes work or analysis of the show but was a parody of annuals for TV shows in the 1970s. As such it addressed a child readership and included many pictures, features, puzzles and comic strips.
A VHS video containing three episodes of the series ("A Degree in Death", "Wrong Side of the Tracks" and "The Carnival is Over") was released in 1996. A DVD set of all seven episodes of the series was released in Australia on 7 November 2007. The DVDs were marked as Region 4, but appear to be region-free.
# Frédérique Lenger

Frédérique Papy-Lenger (August 12, 1921 – January 9, 2005) was a Belgian mathematician and mathematics educator active in the New Math movement of the 1960s and 1970s.

## Early life and education

Frédérique Lenger was born on August 12, 1921, in Arlon, Belgium, one of three daughters of a lawyer. After studying classics in the Lycée Royal d’Arlon, she studied for a licentiate in mathematics at the Université libre de Bruxelles from 1939 to 1943. The University officially closed in 1941 to prevent its takeover by the German occupation, and her studies continued underground.
In 1968, she completed a doctorate with a two-part thesis, one part on mathematics education and the other on geometric transformation groups.

## Career

From 1947 to 1950, Lenger taught mathematics at the l’Ecole Decroly, while working as an assistant to mathematician Paul Libois, who suggested that she perform research involving projective geometry and triality. This became a precursor to the work of another student of Libois, Jacques Tits. In 1950, Lenger joined the mathematics faculty of the Lycée Royal d’Arlon; in 1957, she was appointed prefect at Arlon and director of the State Normal School in Arlon.
She became a professor of mathematics at the Berkendael State Normal School in Brussels in 1960. In 1961, with several other mathematicians, she became one of the founders of the Centre Belge de Pédagogie de la Mathématique (Belgian Center for the Pedagogy of Mathematics). From 1974 to 1980 she worked in the US, at the Comprehensive School Mathematics Program in St. Louis, Missouri. She returned to Berkendael in 1980. She retired in 1981 but continued to work as a volunteer at the French school in Nivelles until 1992.

## Contributions

Lenger began her work on developing a modern school mathematics curriculum in 1958, working with Willy Servais and in consultation with Georges Papy, whom she married in 1960. With Madeleine Lepropre, Lenger ran an experimental training program for kindergarten teachers based on the new curriculum in 1958–1959, and was encouraged by the enthusiasm the kindergarten students showed for the material. With Papy, in the mid-1960s, she developed a six-volume high-school mathematics program based on the principles of set theory and abstract algebra.
She was an invited plenary speaker at the first International Congress on Mathematical Education, speaking there on the "minicomputer" method for teaching binary number arithmetic to schoolchildren. She became the founding president of the International Research Group in Mathematical Pedagogy in 1971.
Her books include L'enfant et les graphes (Didier, 1968), Mathématique moderne (Didier, 1970), Modern mathematics (two vols., Collier, 1968 and 1969), Graph Games (Crowell, 1971), and Graphs and the Child (Harvard University Press, 1979). She also produced many educational booklets through the Belgian Center for the Pedagogy of Mathematics and the Comprehensive School Mathematics Program.

## Legacy

The rue Frédérique Lenger in Arlon is named after her.