OpenLLM-France/wikimedia huggingface dataset:
# Pedal triangle

In plane geometry, a pedal triangle is obtained by projecting a point onto the sides of a triangle.
More specifically, consider a triangle △ABC, and a point P that is not one of the vertices A, B, C. Drop perpendiculars from P to the three sides of the triangle (these may need to be produced, i.e., extended). Label L, M, N the intersections of the lines from P with the sides BC, AC, AB. The pedal triangle is then △LMN.
If △ABC is not an obtuse triangle and P is the orthocenter, then the angles of △LMN are 180° − 2A, 180° − 2B and 180° − 2C.
The quadrilaterals PMAN, PLBN, PLCM are cyclic quadrilaterals.
The location of the chosen point P relative to the chosen triangle △ABC gives rise to some special cases:
* If P is the orthocenter, then △LMN is the orthic triangle.
* If P is the incenter, then △LMN is the intouch triangle.
* If P is the circumcenter, then △LMN is the medial triangle.
* If P is on the circumcircle of the triangle, △LMN collapses to a line (the pedal line or Simson line).
The vertices of the pedal triangle of an interior point P, as shown in the top diagram, divide the sides of the original triangle in such a way as to satisfy Carnot's theorem:
$|AN|^{2}+|BL|^{2}+|CM|^{2}=|NB|^{2}+|LC|^{2}+|MA|^{2}.$

## Trilinear coordinates

If P has trilinear coordinates p : q : r, then the vertices L, M, N of the pedal triangle of P are given by ${\begin{array}{ccccccc}L&=&0&:&q+p\cos C&:&r+p\cos B\\[2pt]M&=&p+q\cos C&:&0&:&r+q\cos A\\[2pt]N&=&p+r\cos B&:&q+r\cos A&:&0\end{array}}$

## Antipedal triangle

One vertex, L', of the antipedal triangle of P is the point of intersection of the perpendicular to BP through B and the perpendicular to CP through C. Its other vertices, M' and N', are constructed analogously. Trilinear coordinates are given by ${\begin{array}{ccrcrcr}L'&=&-(q+p\cos C)(r+p\cos B)&:&(r+p\cos B)(p+q\cos C)&:&(q+p\cos C)(p+r\cos B)\\[2pt]M'&=&(r+q\cos A)(q+p\cos C)&:&-(r+q\cos A)(p+q\cos C)&:&(p+q\cos C)(q+r\cos A)\\[2pt]N'&=&(q+r\cos A)(r+p\cos B)&:&(p+r\cos B)(r+q\cos A)&:&-(p+r\cos B)(q+r\cos A)\end{array}}$
For example, the excentral triangle is the antipedal triangle of the incenter.
Suppose that P does not lie on any of the extended sides BC, CA, AB, and let P$^{−1}$ denote the isogonal conjugate of P. The pedal triangle of P is homothetic to the antipedal triangle of P$^{−1}$. The homothetic center (which is a triangle center if and only if P is a triangle center) is the point given in trilinear coordinates by
$ap(p+q\cos C)(p+r\cos B)\ :\ bq(q+r\cos A)(q+p\cos C)\ :\ cr(r+p\cos B)(r+q\cos A)$
The product of the areas of the pedal triangle of P and the antipedal triangle of P$^{−1}$ equals the square of the area of △ABC.

## Pedal circle

The pedal circle is defined as the circumcircle of the pedal triangle. Note that the pedal circle is not defined for points lying on the circumcircle of the triangle.

### Pedal circle of isogonal conjugates

For any point P not lying on the circumcircle of the triangle, it is known that P and its isogonal conjugate P* have a common pedal circle, whose center is the midpoint of these two points.
# Vesa Mäkäläinen

Vesa Mäkäläinen (born September 3, 1986) is a Finnish former professional basketball player. Standing at 6 ft 6.7 in (2.00 m), he usually played as forward.

## Career statistics
### National team

| Team | Tournament | Pos. | GP | PPG | RPG | APG |
| Finland | EuroBasket 2011 | 9th | 8 | 0.3 | 0.9 | 0.4 |
# Ville Pekkola

Ville Valtteri Pekkola (born January 31, 1989, in Lahti) is a Finnish basketball player. 190 cm tall shooting guard/small forward Pekkola plays for Tampereen Pyrintö in Korisliiga. Alongside Finnish competitions, Pekkola has represented Pyrintö in Baltic Basketball League. He is known of his good defensive abilities.
Pekkola won Finnish championship with Tampereen Pyrintö in 2014 and with Namika Lahti in 2009. Moreover, he has achieved Finnish cup championship in 2013 and cup silver medal in 2012.

## Trophies and awards

* Finnish championship in 2009 and 2014
* Finnish Cup in 2013
** Finnish Cup runner-up in 2012
* Baltic League: fourth in 2014
* Super Mario Shanghai Cup 2019- Defending Title

## Sources

* Ville Pekkola Finnish Basketball Association
* Ville Pekkola Eurobasket.com
* Ville Pekkola Baltic Basketball League
# Þorsteinn Gauti Hjálmarsson

Þorsteinn Gauti Hjálmarsson is an Icelandic-Finnish handball player who currently plays for Fram of the Icelandic top-tier Úrvalsdeild karla. In December 2022, he was called into the Finnish national handball team training group.

## Personal life

Þorsteinn holds a dual Icelandic-Finnish citizenship due to his grandmother being born in Finland.
# Coolgardie safe

The Coolgardie safe is a low-tech food storage unit, using evaporative cooling to prolong the life of whatever edibles are kept in it. It applies the basic principle of heat transfer which occurs during evaporation of water (see latent heat and heat of evaporation). It was named after the place where it was invented – the small mining town of Coolgardie, Western Australia, near Kalgoorlie-Boulder.

## History

Coolgardie was the site of a gold rush in the early 1890s, before the Kalgoorlie-Boulder gold rush.
For the prospectors who had rushed here to find their fortune, one challenge was to extend the life of their perishable foods – hence the invention of the Coolgardie safe.
The safe was invented in the late 1890s by Arthur Patrick McCormick, who used the same principle as explorers and travellers in the Outback used to cool their canvas water bags: when the canvas bag is wet the fibres expand and it holds water. Some water seeps out and evaporates. It is most effective when air continually moves past it, such as when in a moving vehicle or when exposed to a breeze.
This technology is commonly thought to have been adopted by explorer and scientist Thomas Mitchell, who had observed the way some Indigenous Australians used kangaroo skins to carry water.

## Principles of operation

The Coolgardie safe was made of wire mesh, hessian, a wooden frame and had a hot dip galvanised iron tray on top. The galvanised iron tray was filled with water. The hessian bag was hung over the side with one of the ends in the tray to soak up the water.
Gradually the hessian bag, acting as a wick, would draw water from the tray by the process of capillary action. When a breeze came it would pass through the wet bag and evaporate the water. This would cool the air inside the safe, and in turn cool the food stored in the safe. This cooling is due to the water in the hessian needing energy to change state and evaporate. This energy is taken from the interior of the safe (metal mesh), thus making the interior cooler. There is a metal tray below the safe to catch excess water from the hessian.
Some modern tests have shown that the interior of the safe would achieve temperatures 3–9 °C (dependant on breeze) cooler than the atmospheric temperature during the middle of the day.
It was usually placed on a veranda where there was a breeze. The Coolgardie safe was a common household item in Australia until the mid-twentieth century. Safes could be purchased ready-made or easily constructed at home. Some of the metal panel safes are highly decorated.
# Luis Sarmento

Luis Sarmento was the Imperial ambassador to Portugal in 1536. He represented Charles V, Holy Roman Emperor and King of Spain.
# Research to Prevent Blindness

Research to Prevent Blindness (RPB) is a nonprofit organization created in 1960 by Jules Stein, the founder of Music Corporation of America, to stimulate research to eliminate blinding diseases. It supports eye research directed at the prevention, treatment or eradication of all diseases that threaten vision.
In pursuit of this objective, RPB has committed hundreds of millions of dollars in grants to support high-impact vision research. RPB's grant-making programs provide major eye research funding to leading scientific institutions in the U.S. and support the work of hundreds of talented vision scientists engaged in a diverse range of disease-oriented research.
RPB's far-reaching activities are planned and carried out with the expert advice and guidance of a Scientific Advisory Panel composed of distinguished leaders in the field of medical science.

## Mission statement

   RPB's mission is to preserve and restore vision by supporting research to develop treatments, preventives and cures for all conditions that damage and destroy sight.

## Eye diseases researched

Eye diseases addressed by grants from RPB include macular degeneration, cataracts, glaucoma, diabetic retinopathy, dry eye, corneal diseases, uveitis, low vision, amblyopia and strabismus, retinitis pigmentosa, color blindness and ocular cancers.

## History

Shortly after it was founded, RPB conducted the first comprehensive survey of the state of eye research in the United States. Among the findings was strong support within the eye research community for a separate National Eye Institute as part of the National Institutes of Health. RPB then led the movement that caused Congress in 1968 to establish the National Eye Institute. In the following years, RPB became a major influence in stimulating legislative interest and support for the work of the National Eye Institute.
Another finding was lack of sufficient laboratory space—across the country—for eye research. Over a span of years, RPB organized capital campaigns for the construction of modern eye research centers in large population areas: University of California, Los Angeles, Johns Hopkins University, Columbia University, University of Louisville, Medical College of Wisconsin, Baylor College of Medicine and Oregon Health Sciences University, Portland.
Through a grants program, Research to Prevent Blindness has channeled more than $407 million into eye research.

## Grants

RPB works with medical institutions throughout the United States to strengthen their programs in eye research. Unrestricted grant programs are intended to produce new scientific investigations, accelerate the pace of research and complement government grants.
Research to Prevent Blindness also provides individual grants, which are directed toward investigators working across all areas of vision science, on ground-breaking science.
Since its founding, RPB grant support has been identified with virtually every major scientific advance in eye research including the development of laser surgery for eye conditions, new drugs that prevent blindness, and refinements to the intraocular lenses used in cataract surgery.
# Aham Okeke

Aham Okeke (born 19 August 1969 in Nigeria) is a Nigerian-born Norwegian former sprinter, who represented the clubs IK Tjalve, IL i BUL and IF Hellas. He has won the 100 metres national championship six times. He set the national record on 100 metres five times, with a personal best of 10.26 seconds. His personal record in the 200 metres, also national record at the time, was 20.75 seconds.
Okeke competed at the 1987 European Junior Championships, the 1990 European Championships, the 1994 European Indoor Championships, the 2000 European Indoor Championships, the 2001 World Championships, the 2002 European Indoor Championships and the 2002 European Championships (interchangeably in the 60 metres, 100 metres, 200 metres or the 4x100 metres relay) without reaching the final round in any of the events.
Okeke tested positive for doping on two occasions in the 1990s, receiving bans of 1 month and 30 months respectively. In 2006, Okeke came out of retirement to qualify for the 2006 European Championships, when the Norwegian Anti-Doping Agency claimed a test taken on 20 July contained 20 times the highest allowed level of testosterone. He was given a lifetime ban from all sports.
# Aloysius Atuegbu

Aloysious Ikem Atuegbu (29 April 1953 – 25 May 2008) was a Nigerian football player. Nicknamed "Blockbuster" for his ferocious shots, he was a stalwart on the Super Eagles offense from 1975 until 1981, winning 60 caps.
After retirement he got into coaching, including a stint with the Nigeria under-17 national football team. At his death he was coaching Keffi United FC.
# Anthony Andeh

Anthony Andeh (16 August 1945 – 12 May 2010) was a Nigerian boxer. He competed in the men's featherweight event at the 1964 Summer Olympics, and then won the gold medal in the lightweight event at the 1966 Commonwealth Games in Kingston, Jamaica. At the 1964 Summer Olympics, he defeated Badawi El-Bedewi of Egypt, before losing to Tin Tun of Burma.
# Blessing Onoko

Blessing Onoko (born 15 December 1969) is a Nigerian boxer. He competed in the men's lightweight event at the 1988 Summer Olympics.
# Chidi Imoh

Chukwudi "Chidi" Imoh (born 27 August 1965) is a former sprinter from Nigeria who won an Olympic silver medal in the 4 x 100 metres relay at the 1992 Summer Olympics. He also won a silver medal in the 100 metres at the 1986 Goodwill Games, finished behind Ben Johnson and ahead of Carl Lewis. He won a 60 metres bronze medal at the 1991 World Indoor Championships, and he became African champion in 1984 and 1985.
In 1986 he posted the world leading time for that year in the 100 metres.
He won the 100 metres race in the 1987 All-Africa Games.
Imoh is also a former runner for the University of Missouri in Columbia. He holds the records there in the 200 m outdoor with a time of 19.9, the 100 m outdoor with a time of 10.00 and in the 55 m indoor with a time of 6.10.

## Personal bests

* 100 metres - 10.00 (1986)
* 200 metres - 21.04 (1985)
# Christopher Okonkwo

Christopher Okonkwo (born 29 April 1941) is a Nigerian athlete. He competed in the men's shot put at the 1972 Summer Olympics.
# Eddie Ndukwu

Eddie Ndukwu (born 1 June 1950) is a Nigerian amateur and professional bantam/super bantam/featherweight boxer of the 1960s, '70s and '80s who as an amateur won the gold medal at bantamweight in the Boxing at the 1966 British Empire and Commonwealth Games in Kingston, Jamaica, won the silver medal at featherweight at the 1973 All-Africa Games, won the featherweight class at the 1974 British Commonwealth Games, and represented Nigeria in the 1974 World Amateur Boxing Championships losing to eventual gold medal winner Howard Davis, Jr. of the United States. As a professional, he won the Nigerian Featherweight title, and Commonwealth featherweight title, his professional fighting weight varied from 118 lb (54 kg; 8 st 6 lb), i.e. bantamweight to 124+3⁄4 lb (56.6 kg; 8 st 12.8 lb), i.e. featherweight.
As a professional, Ndukwu was undefeated until he fought Wilfredo Gomez at the Puerto Rican's hometown of San Juan. The World Boxing Council wanted to design this a world featherweight championship eliminator fight but they were dissuaded once Gomez was not able to make the Featherweight division's limit, so the fight was fought without their sanctioning. On Sunday, April 4, 1980, Ndukwu lost to the International Boxing Hall of Fame member by a fourth-round technical knockout at San Juan's Hiram Bithorn Stadium.
# Fidelis Onye Som

Fidelis Onye Som (born 5 March 1945) is a Nigerian boxer. He competed in the men's welterweight event at the 1968 Summer Olympics. At the 1968 Summer Olympics, he lost to Donato Paduano of Canada.
# Pink ODI

The Pink ODI is an annual One Day International cricket match held at the Wanderers Stadium in Johannesburg, South Africa. The match features the South African national cricket team and a touring international side, typically during the southern hemisphere summer.
The Pink Day ODI has been recognized as one of South Africa's major sporting events, comparable to the Soweto Derby and longstanding rugby matches between the Springboks and the All Blacks.

## History

The first Pink ODI was held in 2013 to raise funds and awareness for breast cancer and was inspired by Sydney's Jane McGrath Day, where the Sydney Cricket Ground (SCG) was illuminated in pink to honor Jane McGrath, the wife of Australian fast bowler Glenn McGrath, who died from breast cancer.
The South African team, known as the Proteas, won the first six Pink Day ODIs, during which they wore pink uniforms. One of the notable performances on Pink ODI is by AB de Villiers who scored the fastest ODI century of all time.

## Fund raising

Funds raised from the Pink Day ODI benefit the Breast Care Unit at Charlotte Maxeke Hospital in Johannesburg. Approximately R10 million has been donated to the unit since the event's inception.
# Gaston Ramon

Gaston Ramon (30 September 1886 – 8 June 1963) was a French veterinarian and biologist best known for his role in the treatment of diphtheria and tetanus.
He was born in Bellechaume (Yonne, France) and attended l'École vétérinaire d'Alfort from 1906 to 1910. In 1917 he married Marthe Momont, grandniece of Emile Roux.
During the 1920s, Ramon, along with P. Descombey, made major contributions to the development of effective vaccines for both diphtheria and tetanus. In particular, he developed a method for inactivating the diphtheria toxin and the tetanus toxin using formaldehyde which, in its essentials, is still used in vaccines manufactured today. He also developed a method for determining the potency of the vaccines, an essential element required for the reproducible production of these pharmaceuticals.
He received 155 Nobel Prize in Physiology or Medicine nominations but never received the prize.
A collection of his papers is held at the National Library of Medicine in Bethesda, Maryland.
# Świbie

Świbie is a village in the administrative district of Gmina Wielowieś, within Gliwice County, Silesian Voivodeship, in southern Poland. It lies approximately 6 kilometres (4 mi) west of Wielowieś, 26 km (16 mi) north of Gliwice, and 44 km (27 mi) north-west of the regional capital Katowice.
# Nashville Golf Open

The Simmons Bank Open is a golf tournament on the Korn Ferry Tour. It was first played in June 2016 at the Nashville Golf & Athletic Club in Brentwood, Tennessee. After the event was canceled in 2020 due to COVID-19, it moved to The Grove in May 2021 as a regular season Korn Ferry event. Once it was named the 2022 Korn Ferry Tour Tournament of the year, it was announced that the event would move to September to be a part of the Korn Ferry Tour Finals for the 2023 Korn Ferry Tour season and beyond. Beginning in 2024, the event moved to the Vanderbilt Legends Club's North Course as The Grove will be hosting LIV Golf Nashville's event.

## Winners

| Korn Ferry Tour (Finals event) | 2023–Present |
| Korn Ferry Tour (Regular) | 2016–2022 |
| # | Year | Winner | Score | To par | Margin of victory | Runner(s)-up |
| Simmons Bank Open |||||||
| 9th | 2024 | Paul Peterson | 260 | −20 | 1 stroke | Matt Atkins |
| 8th | 2023 | Grayson Murray | 271 | −17 | 3 strokes | Mason Andersen Carter Jenkins Jamie Lovemark |
| 7th | 2022 | Brent Grant | 272 | −16 | 1 stroke | Kevin Yu |
| 6th | 2021 | Austin Smotherman | 272 | −16 | 3 strokes | Paul Haley II Yuan Yechun |
| 5th | 2020 | Canceled due to the COVID-19 pandemic | Canceled due to the COVID-19 pandemic | Canceled due to the COVID-19 pandemic | Canceled due to the COVID-19 pandemic | Canceled due to the COVID-19 pandemic |
| Nashville Golf Open |||||||
| 4th | 2019 | Robby Shelton | 273 | −15 | Playoff | Scottie Scheffler |
| 3rd | 2018 | Cameron Davis | 270 | −18 | 1 stroke | Kevin Dougherty Lanto Griffin Josh Teater |
| 2nd | 2017 | Lanto Griffin | 272 | −16 | Playoff | Abraham Ancer |
| 1st | 2016 | James Driscoll | 269 | −19 | 3 strokes | Brian Campbell |
Bolded golfers graduated to the PGA Tour via the Korn Ferry Tour regular-season money list.
# Sandie Fitzgibbon

Sandie Fitzgibbon (born 1964 in Cork) is a former camogie player selected on the camogie team of the century in 2004, and winner of six All Ireland medals in 1982, 1983, 1992, 1993, 1995 and 1997.
She played for Glen Rovers Club with whom she won four All Ireland Club Championships. She also holds one Colleges All Ireland, three Minor All Ireland, seven National League and two Gael Linn interprovincial medals. She captained Cork to victory in 1992 when they defeated Wexford.
Her camogie awards include Munster Young Camogie Player for 1983, National Irish Bank Player of the Year in 1992 and 1995, and twice Jury's Hotel Sports Star of the Month. In 2000, she received the Cork Lord Mayor's Millennium Camogie Award.
In 2013, she was given a Northside and District Hall of Fame Award.

## Citation

Her team of the century citation read: "possessing huge natural sporting ability, compact and tidy in her movements, allied to great speed, she was a most influential player who could control a game with ease. Sandie was very polished performer whether at midfield or centre-back."

## Other sports

Her basketball awards include three National Cup and five National League titles, 64 senior basketball caps for Ireland, and the Delta Air Lines Olympic Award.
# Sharad Rao (cricketer)

Sharad Rao (21 March 1957 – 2 September 2017) was an Indian cricketer. He played in ten first-class and three List A matches from 1980/81 to 1985/86, including the final of the 1980–81 Ranji Trophy.
# The Comedy Garage

The Comedy Garage is a documentary by director Logan Leistikow, released in 2011, depicting a day in the life of five rising star comedians who produce a stand up comedy show performed on a self-made stage in their garage in Burbank, California. Shot cinéma vérité style, the film highlights the unique personalities and techniques of comics Cornell Reid, Matthew Sullivan, Sean Green, Paul Danke, and Casey Feigh.
The Comedy Garage had been a staple of the Los Angeles comedy scene before filming began. Leistikow met the comedians while working at Tom Green Live. Once he was invited to a comedy garage show, he got inspired and soon began production on the documentary.
# Tomas Northug

Tomas Northug (born 19 April 1990) is a Norwegian cross-country skier. He was born in Mosvik Municipality, and is the middle brother of Petter Northug and Even Northug.
He won a World Cup victory in Otepää in January 2015. He became Junior World Champion in 2010.
He represented the sports clubs Mosvik IL and Strindheim IL.

## Cross-country skiing results

All results are sourced from the International Ski Federation (FIS).

### World Championships

| Year | Age | 15 km  individual | 30 km  skiathlon | 50 km  mass start | Sprint | 4 × 10 km  relay | Team  sprint |
| 2015 | 24 | — | — | — | 6 | — | — |

### World Cup
#### Season standings

| Season | Age | Discipline standings | Discipline standings | Discipline standings | Ski Tour standings | Ski Tour standings | Ski Tour standings |
| Season | Age | Overall | Distance | Sprint | Nordic Opening | Tour de Ski | World Cup Final |
| 2010 | 19 | 183 | — | 116 | — | — | |
| 2011 | 20 | 104 | — | 58 | — | — | — |
| 2012 | 21 | 101 | — | 50 | — | — | — |
| 2013 | 22 | 64 | NC | 27 | — | — | 42 |
| 2014 | 23 | 110 | NC | 55 | 85 | — | — |
| 2015 | 24 | 32 | — | 7 | — | — | — |

#### Individual podiums

* 1 victory – (1 WC)
* 1 podium – (1 WC)
| No. | Season | Date | Location | Race | Level | Place |
| 1 | 2014–15 | 17 January 2015 | Otepää, Estonia | 1.5 km Sprint C | World Cup | 1st |