OpenLLM-France/wikimedia huggingface dataset:
# Centered triangular number

A centered (or centred) triangular number is a centered figurate number that represents an equilateral triangle with a dot in the center and all its other dots surrounding the center in successive equilateral triangular layers.
This is also the number of points of a hexagonal lattice with nearest-neighbor coupling whose distance from a given point is less than or equal to $n$.
The following image shows the building of the centered triangular numbers by using the associated figures: at each step, the previous triangle (shown in red) is surrounded by a triangular layer of new dots (in blue).

## Properties

* The gnomon of the n-th centered triangular number, corresponding to the (n + 1)-th triangular layer, is:
       $C_{3,n+1}-C_{3,n}=3(n+1).$
* The n-th centered triangular number, corresponding to n layers plus the center, is given by the formula:
       $C_{3,n}=1+3{\frac {n(n+1)}{2}}={\frac {3n^{2}+3n+2}{2}}.$
* Each centered triangular number has a remainder of 1 when divided by 3, and the quotient (if positive) is the previous regular triangular number.
* Each centered triangular number from 10 onwards is the sum of three consecutive regular triangular numbers.
* For n > 2, the sum of the first n centered triangular numbers is the magic constant for an n by n normal magic square.

### Relationship with centered square numbers

The centered triangular numbers can be expressed in terms of the centered square numbers:
    $C_{3,n}={\frac {3C_{4,n}+1}{4}},$
where
    $C_{4,n}=n^{2}+(n+1)^{2}.$

## Lists of centered triangular numbers

The first centered triangular numbers (C$_{3,n}$ < 3000) are:
    1, 4, 10, 19, 31, 46, 64, 85, 109, 136, 166, 199, 235, 274, 316, 361, 409, 460, 514, 571, 631, 694, 760, 829, 901, 976, 1054, 1135, 1219, 1306, 1396, 1489, 1585, 1684, 1786, 1891, 1999, 2110, 2224, 2341, 2461, 2584, 2710, 2839, 2971, … (sequence A005448 in the OEIS).
The first simultaneously triangular and centered triangular numbers (C$_{3,n}$ = T$_N$ < 10$^9$) are:
    1, 10, 136, 1 891, 26 335, 366 796, 5 108 806, 71 156 485, 991 081 981, … (sequence A128862 in the OEIS).

## The generating function

If the centered triangular numbers are treated as the coefficients of the McLaurin series of a function, that function converges for all $|x|<1$, in which case it can be expressed as the meromorphic generating function
    $1+4x+10x^{2}+19x^{3}+31x^{4}+~...={\frac {1-x^{3}}{(1-x)^{4}}}={\frac {x^{2}+x+1}{(1-x)^{3}}}~.$
# Centralian tree frog

The Centralian tree frog (Ranoidea gilleni) is a large species of tree frog native to a small area in central Australia. It is closely related to the Australian green tree frog, and closely resembles it in appearance.

## Description

It is a large tree frog, reaching a length of 8 cm (3.1 in) in females and 6.2 cm (2.4 in) in males. The dorsal surface is green or olive green, while the ventral surface is white. A large fold covers the top portion of the tympanum, which is visible. The toe pads are large, the feet are webbed, and the hands are one-third webbed. The only physical feature which can distinguish the Centralian tree frog from the Australian green tree frog is numerous white spots on the dorsal surface.

## Ecology and behaviour

The habitat of the Centralian tree frog is rock gorges with water holes, either permanent or temporary. The frog will hide during the day beneath rocks, and hunt and mate during the cooler night. Its call is a slow barking call, similar to the Australian green tree frog.
It inhabits the MacDonnell Ranges in central Australia. This confined distribution is not inhabited by the Australian green tree frog, which allows easy identification.
# David Edward Lewis

David (Dafydd) Edward Lewis (7 March 1866 – 17 August 1941) was a Welsh-born businessman and philanthropist who emigrated to Australia and became well-known and successful there.
Lewis was born in Llanrhystud near Aberystwyth, Cardiganshire, Wales, the son of David Lewis, a farmer, and his wife Catherine, née Mason.
Lewis migrated to Melbourne, Australia, in 1890; opening a drapery shop in 1902 which became a successful business. In 1928 he donated £2000 to the engineering school of the University of Melbourne for laboratory extensions.

## Scholarship funds

Lewis bequeathed a £700,000 endowment that after his death established the Dafydd Lewis Trust. This provided scholarships for full-time degree courses (other than in theology, arts, music or education) at the University of Melbourne for boys from Victorian state schools whose parents could not afford to pay for a university education.
Although the original scholarships helped to support post-graduate education as well as a first degree, as of 2024 only undergraduate study is supported, for up to three years.
In 2004 a parallel scholarship fund, the Mary Jane Lewis Foundation was established to give scholarships to female university students in Victoria at the undergraduate level. The fund is named after Dafydd Lewis' second wife Mary Jane Jones Evans.
# Dave Penna

David Penna (January 11, 1958 – January 13, 2004) was an American jockey in thoroughbred horse racing who competed in the United States but had his greatest successes in Canada.
Born in Auburn, New York, he began his career as a professional rider in 1978 and three years later went to compete at Woodbine Racetrack in Toronto. In a career that spanned nineteen years, from 12,527 mounts he had 1,772 winners which earned purses totaling more than $39.5 million. Two of his most notable wins came in Canada's Triple Crown races.
One of the top riders in the 1980s and very popular with the Woodbine fans, Dave Penna rode primarily in Ontario at the Fort Erie Race Track in Fort Erie, and at Greenwood Raceway and Woodbine Racetrack, both in Toronto. In the 1990s, he began riding more frequently in the United States where he won important Graded stakes races at Keeneland Race Course in Kentucky and Gulfstream Park in Florida. In 1995 at Monmouth Park in New Jersey he won his last Grade I race, the Philip H. Iselin Handicap. A racing accident resulted in an injury that forced Penna to retire in 1996 and for a short time he turned to training horses at Gulfstream Park.
In 2004, Dave Penna died at age 46 in Saanich, British Columbia.
# Ceramic Fuel Cells

Ceramic Fuel Cells Ltd (ASX: CFU) was an Australian fuel cell technology company, based in Melbourne. The company produced the "BlueGen" gas-to-electricity generators. CFCL's developed solid oxide fuel cell (SOFC) technology to provide reliable, energy efficient, high quality, and low-emission electricity from natural gas and renewable fuels. CFCL was developing SOFC products for small-scale on-site micro combined heat and power (m-CHP) and distributed generation units that co-generate electricity and heat for domestic use. On 1 March 2015 it was announced that the company had appointed voluntary administrators.
Company De-Listed In accordance with section 3.4 of ASX Listing Rules "Guidance Note 33 Removal of Entities from the ASX Official List", Ceramic Fuel Cells Ltd was removed from the official list by the ASX under listing rule 17.12 from the commencement of trading on Monday 5 March 2018.

## History

Ceramic Fuel Cells Ltd was formed in 1992 by the Commonwealth Scientific and Industrial Research Organisation (CSIRO) and a consortium of energy and industrial companies. In 2009 a production facility opened in Noble Park, Melbourne and another one in Heinsberg, Germany, which won the North Rhine-Westphalia's economic development agency NRW.INVEST award for innovation.

## Products

The first marketed product of the company is "BlueGen" a solid oxide fuel cell which creates electricity and heat by passing natural gas over ceramic fuel cells. BlueGen is 85% efficient and is reported to cut the average Australian home's annual carbon dioxide emissions by 18 tonnes.

## Partners

CFCL has signed agreements with leading European utility customers and appliance partners in Europe and Japan to deploy micro-CHP units using CFCL's SOFC technology. These agreements give the Company access to a number of large and advanced European markets for m-CHP units. The company's utility partners in these markets have a total of more than 20 million gas and electricity customers.
# Karakaçak, Amasra

Karakaçak is a village in the Amasra District, Bartın Province, Turkey. Its population is 278 (2021).

## Geography

The village is 29 km from Bartın city center and 14 km from Amasra town centre.
# Centropyge heraldi

Centropyge heraldi, the yellow angelfish or Herald's angelfish is a species of marine ray-finned fish, a marine angelfish belonging to the family Pomacanthidae. It comes from the Pacific Ocean and sometimes makes its way into the aquarium trade.

## Etymology

The angelfish is named after Earl Stannard Herald. He died in Cabo San Lucas, Baja California, in a scuba diving accident.

## Description

Centropyge heraldi is a yellowish orange fish. There is a patch of darker olive, with some spots concolorous with the body, within it around the eye. The dorsal fin contains 15 spines and 15 soft rays while the anal fin has 3 spines and 17 soft rays. This species attains a maximum total length of 12 centimetres (4.7 in).

## Distribution

Centropyge heraldi has a wide range in the Western and Central Pacific Ocean. This range extends from southern Japan and Taiwan east as far as the Tuamotu Islands and south to Australia. In Australia it can be found along the Great Barrier Reef south to the Solitary Islands in New South Wales, as well as on some Coral Sea reefs.

## Habitat and biology

Centropyge heraldi is found at depths between 8 and 45 metres (26 and 148 ft) and is most commonly recorded on outer reef slopes, and occasionally on lagoon reefs. This species is usually found in small harems of a male and one to three females. Females may change to males when there is no male present. It is a herbivorous species which feeds on filamentous algae.

## Systematics

Centropyge heraldi was first formally described in 1953 by the Americans Loren Paul Woods (1914-1979) and Leonard Peter Schultz (1901-1986) with the type locality given as Bikini Atoll in the Marshall Islands. The specific name honours the American ichthyologist and public aquarium director Earl Stannard Herald (1914-1973) who assisted in the collection of the type. Within the genus Centropyge this species is considered, by some authorities, to be in the subgenus Centropyge.

## Utilisation

Centropyge heraldi sometimes appears in the aquarium trade.
# Ceres (1787 Ipswich ship)

Ceres was launched at Ipswich in 1787. Her career between 1787 and 1818 is currently obscure. From 1818 she made two voyages as a whaler in the British Southern Whale Fishery. On 28 August 1821 she was wrecked on the island of Tanameira, the South Pacific. The inhabitants murdered Captain Lancaster and seven of his crew.
1st whaling voyage (1818-1819): Ceres sailed in 1818. Reported 4 May 1819 at Rio de Janeiro on 11 January 1819.
Ceres appeared in the Register of Shipping (RS) in 1821 with Kingston, master, Wilkinson, owner, and trade London-South Seas. She had undergone a good repair in 1817.
2nd whaling voyage (1819): Ceres sailed from England on 28 April 1820. She was lost at Tonomia (Tongan Islands) [Hapaee i.e. Lifuka] in late 1822.

## Citations

* 1 2 RS (1821), Seq.№C337.
* ↑ Lloyd's List №5791.
* 1 2 British Southern Whale Fishery Database – Voyages: Ceres
# Karantaba Tenda

Karantaba Tenda is a small town in north-eastern Gambia. It is located in Sami District in the Central River Division. As of 2009, it has an estimated population of 1922.
The village is near to the site of the historic British trading post Pisania.
# Cephaloon bicolor

Cephaloon bicolor is a species of false longhorn beetle in the family Stenotrachelidae. It is found in North America.
# Cepheus (crater)

Cepheus is a lunar impact crater that is located in the northeastern part of the Moon, within one crater diameter of the larger crater Franklin to the southeast. To the north-north-east is the flooded crater Oersted. The proximity of this formation to the lunar limb means it appears oblong when viewed from the Earth due to foreshortening.
This is a relatively young formation, and the rim is still sharp and well-defined. The exception is an even younger, bowl-shaped crater that lies across the northeast rim. This is a satellite crater designated Cepheus A. The remaining rim is nearly circular, with outward bulges to the north and south. The inner wall is terraced in places, most notably along the northwest wall. There is a central peak formation at the midpoint of the floor which stretches somewhat to the north and south.

## Satellite craters

By convention these features are identified on lunar maps by placing the letter on the side of the crater midpoint that is closest to Cepheus.
| Cepheus | Latitude | Longitude | Diameter |
| A | 41.0° N | 46.5° E | 13 km |
# Karel Lidický

Karel Lidický (17 June 1900 – 21 May 1976) was a Czech sculptor. His work was part of the sculpture event in the art competition at the 1932 Summer Olympics.
# Cerdistus erythrurus

Cerdistus erythrurus is a species of robber fly in the subfamily Asilinae. It is the type species of the genus Cerdistus.

## Distribution

This species is present in Southern Europe (Austria, Bosnia and Herzegovina, Croatia, France, Greece, Italy, Switzerland and former Yugoslavia).

## Description

Cerdistus erythrurus can reach a body length of about 8–9 millimetres (0.31–0.35 in). These rather little robber flies are mainly black. Legs are black, with reddish tibiae. In males the modified last abdominal segment supporting the copulatory apparatus (hypopygium) may be partly reddish.
Adults can be found from May to July–August.
# Karijärve

Karijärve is a village in Elva Parish, Tartu County in eastern Estonia.
# David Grey Rattray

David Grey Rattray (6 September 1958 – 26 January 2007) was a South African historian of the 1879 Anglo-Zulu War in South Africa, also well known as a tour guide.

## Biography

Rattray was born in Johannesburg, matriculated from the St. Alban's College in Pretoria, and studied entomology (the study of insects) at the University of Natal, Pietermaritzburg, where he graduated in 1982. From 1983 to 1988 he managed the Mala Mala Game Reserve situated on the doorstep of Kruger National Park. In 1989 he and his family moved to their family farm at Rorke's Drift, where the Battle of Isandlwana and Battle of Rorke's Drift took place between the Zulus and British soldiers. He and his wife, Nicky, established and operated the Fugitives' Drift Lodge.
He gained considerable knowledge about the conflicts between the Zulus and British in South Africa as a child as he accompanied his father, an amateur historian himself, as he interviewed Zulus in the local community to obtain their accounts of the conflict, some of whose forebears had fought in those wars.
He provided tours of the historic battle sites of Isandlwana and Rorke's Drift, and his tours are estimated to have been attended by more than 60 000 visitors. He was a fellow of the Royal Geographical Society in London, and his annual lectures there are reported to have been always well attended.
Rattray, aged 48, was shot dead on his farm in KwaZulu-Natal on 26 January 2007 during an armed robbery attempt by six men. His funeral was held at Michaelhouse, a boarding school in Balgowan where two of his sons were scholars at the time, and his ashes are interred on the family property at Rorke's Drift in the Natal Midlands. Five of the gang, including the murderer, were subsequently arrested and sentenced to life imprisonment.
# Karl-Richard Koßmann

Karl-Richard Koßmann (26 June 1896 – 10 June 1969) was a German general during World War II. He was a recipient of the Knight's Cross of the Iron Cross.

## Awards and decorations

* Knight's Cross of the Iron Cross on 23 March 1945 as Oberst and commander of 74th Panzergrenadier Regiment
# 2013 UCI Women's Road World Cup

The 2013 UCI Women's Road World Cup is the 16th edition of the UCI Women's Road World Cup. The calendar retained the same races as the 2012 edition. Marianne Vos is the defending champion.

## Races

| Round | Date | Race | Country | Winner | Second | Third |
| 1 | 9 March | Ronde van Drenthe | Netherlands | Marianne Vos (NED) | Ellen van Dijk (NED) | Emma Johansson (SWE) |
| 2 | 25 March | Trofeo Alfredo Binda-Comune di Cittiglio | Italy | Elisa Longo Borghini (ITA) | Emma Johansson (SWE) | Ellen van Dijk (NED) |
| 3 | 31 March | Tour of Flanders | Belgium | Marianne Vos (NED) | Ellen van Dijk (NED) | Emma Johansson (SWE) |
| 4 | 17 April | La Flèche Wallonne Féminine | Belgium | Marianne Vos (NED) | Elisa Longo Borghini (ITA) | Ashleigh Moolman (RSA) |
| 5 | 12 May | Tour of Chongming Island World Cup | China | Tetyana Ryabchenko (UKR) | Giorgia Bronzini (ITA) | Amy Pieters (NED) |
| 6 | 16 August | Open de Suède Vårgårda TTT | Sweden | Specialized–lululemon Ellen van Dijk (NED) Evelyn Stevens (USA) Lisa Brennauer (GER) Trixi Worrack (GER) Carmen Small (USA) (+ 3' 46) Loren Rowney (AUS) (DNF) | Rabobank–Liv Giant Marianne Vos (NED) Annemiek van Vleuten (NED) Thalita de Jong (NED) Lucinda Brand (NED) Pauline Ferrand-Prévot (FRA) (+ 3") Roxane Knetemann (NED) (+ 3' 44") | Orica–AIS Emma Johansson (SWE) Amanda Spratt (AUS) Melissa Hoskins (AUS) Shara Gillow (AUS) Loes Gunnewijk (NED) (+ 5' 56") Jessie MacLean (AUS) (+ 5' 56") |
| 7 | 18 August | Open de Suède Vårgårda | Sweden | Marianne Vos (NED) | Emma Johansson (SWE) | Amy Pieters (NED) |
| 8 | 31 August | GP de Plouay | France | Marianne Vos (NED) | Emma Johansson (SWE) | Anna van der Breggen (NED) |
Source

## Points standings
### Individuals

World Cup individual standings after 8 of 8 races.
| | Cyclist | Team | World Cup points |
| 1 | Marianne Vos (NED) | Rabobank–Liv Giant | 429 |
| 2 | Emma Johansson (SWE) | Orica–AIS | 302 |
| 3 | Ellen van Dijk (NED) | Specialized–lululemon | 224 |
| 4 | Anna van der Breggen (NED) | Sengers Ladies Cycling Team | 158 |
| 5 | Elisa Longo Borghini (ITA) | Hitec Products UCK | 156 |
| 6 | Annemiek van Vleuten (NED) | Rabobank–Liv Giant | 101 |
| 7 | Amy Pieters (NED) | Argos-Shimano | 80 |
| 8 | Tetyana Ryabchenko (UKR) | Chirio Forno d'Asolo | 75 |
| 9 | Giorgia Bronzini (ITA) | Wiggle–Honda | 69 |
| 10 | Evelyn Stevens (USA) | Specialized–lululemon | 60 |
Source

### Teams

World Cup Team standings after 8 of 8 races.
| Place | UCI Code | Team Name | World Cup Points |
| 1 | RBW | Rabobank–Liv Giant | 695 |
| 2 | GEW | Orica–AIS | 500 |
| 3 | SLU | Specialized–lululemon | 394 |
| 4 | HPU | Hitec Products UCK | 291 |
| 5 | SLT | Sengers Ladies Cycling Team | 239 |
Source
# Talnique

Talnique is a municipality in the La Libertad department of El Salvador. The town is built atop a mountain with only one access road. The people rely on a combination of coffee farming and tourism.

## History

The town of Talnique has Pre-Columbian origins. In the year 1550 it had approx. 550 inhabitants.

## General information

The town has an area of about 11.5 sq mi and an altitude of roughly 2,900 ft. They celebrate Saint Luis King of France in the month of August. The name Talnique means "Hill of the Talnetes" or "The place of the wasps of the Earth." In years past Talnique was called "Terlinquetepeque" (1548), "San Luis Talnitepeque" (1740), "Talniquetet" (1770), and finally "Talnique" (1807).
# Nobanda railway station

Nobanda railway station is a railway station of Bankura–Masagram line under the Adra railway division of South Eastern Railway zone. It is situated at Makurgram, Nobanda in Bankura district in the Indian state of West Bengal.

## History

Old narrow-gauge Bankura–Damodar Railway (also called as Bankura Damodar River Railway) connecting Bankura and Rainagar in Bankura and Bardhaman districts was opened to traffic in sections between 1916 and 1917. In 2005, the 118 kilometers long railway section known as Bankura–Masagram line was converted to 1,676 mm (5 ft 6 in) broad gauge. The whole track including Nobanda railway station was electrified in 2018–19.
vteBankura–Masagram line :
Legend :
Sources: :
# Nemesis (2020 Swiss film)

Nemesis is a Swiss documentary film by Thomas Imbach from 2020. It premiered in April 2020 in competition in Nyon Visions du Réel. The international premiere took place at the International Documentary Film Festival Amsterdam 2020, where the film received the prize for Best Cinematography, awarded by Edward Lachman. The film was also shown at the "secret screenings" during Locarno Film Festival 2020, as well as 55th Karlovy Vary International Film Festival.

## Plot

Nemesis explores the destruction of a unique train station in Zurich, and the construction of a new prison and police centre in its place. From the perspective of the filmmaker's window, and with testimony from prisoners awaiting deportation, the film probes how we deal with the extinction of history, and its replacement with total security.

## Production

Nemesis was filmed exclusively from the filmmaker's window. Thomas Imbach's dismay at the agonizing death of the freight station prompts him to record the ongoing destruction, the years of standstill and the creation of the new concrete colossus, in order to compose a personal chronicle.

## Reception

Jamie Lang, Variety: "As the train station crumbles beneath the metal jaws of an excavator, Imbach tells stories from his past and the impact the station has had on his own life. The heartbreaking tales of confused and scared prisoners, not convicted of any crime yet serving sometimes years-long sentences, accompany construction until the city is no longer visible behind the stories-tall behemoth."
Wendy Ide, Screen Daily: "In terms of its methodology, the film couldn’t be more timely. … Shot on handsome 35 mm, sometimes through telephoto lenses which bring an uncomfortable intimacy with the unwitting subjects, sometimes through wide shots which seem to extend to the edge of the city and beyond, the film looks a treat."
# Eduard Fenzl

Eduard Fenzl (1808, in Krummnußbaum – 1879, in Vienna) was an Austrian botanist.

## Life and contributions

An obituary notes "[he] was Professor of Botany and Director of the Imperial Botanical Cabinet, a member of the Vienna Academy of Sciences, and Vice-President of the Vienna Horticultural Society."
Fenzl made contributions towards Karl Friedrich Philipp von Martius's Flora Brasiliensis and to Stephan Endlicher's Enumeratio plantarum quas in Novae Hollandiae, etc. He was the author of Pugillus plantarum novarum Syriæ et Tauri occidentalis primus (1842).
The plant genus Fenzlia is named in his honor.

## Works
### As author

* Dissertatio inauguralis medico-botanica sistens extensionem et distributionem geographicam Alsinearum familiae naturalis per terras arcticas partemque zonae temperatae orbis antiqui (1833)
* Sertum Cabulicum. Enumeratio Plantarum Quas in Itinere Inter Dera-Ghazee-Khan Et Cabul, Mensibus Majo Et Junio 1833 Collegit Dr Martin Honigberger. Accedunt Novarum Vel Minus Cognitarum Stirpium Icones Et Descriptiones Part 1 (1836)
* Novarum stirpium decas I-X (1839)
* Pugillus Plantarum novarum Syriae et Tauri occidentalis primus (1842)
* Illustrationes et descriptiones plantarum novarum Syriae et Tauri occidentalis (1843)
* Über die Stellung der Gattung Oxera im natürlichen Systeme (1843)
* Über die Blütezeit der Paulownia imperialis (1851)
* … Differential-Charaktere der Arten der Gattung Cyperus (1855)
* Bildliche Naturgeschichte des Pflanzenreiches in Umrissen nach seinen wichtigsten Ordnungen (1855)

### As editor

* Theodor Kotschy. Abbildungen und Beschreibungen neuer und seltener Thiere (1843)
* Franz Xaver Freiherr von Wulfen. Flora Norica Phanerogama (1858)