title: North American T-28 Trojan

text: The North American Aviation T-28 Trojan is a radial-engine military trainer aircraft manufactured by North American Aviation and used by the United States Air Force and United States Navy beginning in the 1950s. Besides its use as a trainer, the T-28 was successfully employed as a counter-insurgency aircraft, primarily during the Vietnam War. It has continued in civilian use as an aerobatics and warbird performer.


title: North American T-28 Trojan

text: On September 24, 1949, the XT-28 (company designation NA-159) was flown for the first time, designed to replace the T-6 Texan. The T-28A arrived at the Air Proving Ground, Eglin Air Force Base, Florida, in mid-June 1950, for suitability tests as an advanced trainer by the 3200th Fighter Test Squadron, with consideration given to its transition, instrument, and gunnery capabilities. Found satisfactory, a contract was issued and between 1950 and 1957, a total of 1,948 were built.


title: North American T-28 Trojan

text: Following the T-28's withdrawal from U.S. military service, a number were remanufactured by Hamilton Aircraft into two versions called the Nomair. The first refurbished machines, designated T-28R-1 were similar to the standard T-28s they were adapted from, and were supplied to the Brazilian Navy. Later, a more ambitious conversion was undertaken as the T-28R-2, which transformed the two-seat tandem aircraft into a five-seat cabin monoplane for general aviation use. Other civil conversions of ex-military T-28As were undertaken by PacAero as the Nomad Mark I and Nomad Mark II


title: North American T-28 Trojan

text: After becoming adopted as a primary trainer by the USAF, the United States Navy and Marine Corps adopted it as well. Although the Air Force phased out the aircraft from primary pilot training by the early 1960s, continuing use only for limited training of special operations aircrews and for primary training of select foreign military personnel, the aircraft continued to be used as a primary trainer by the Navy (and by default, the Marine Corps and Coast Guard) well into the early 1980s.


title: North American T-28 Trojan

text: The largest single concentration of this aircraft was employed by the U.S. Navy at Naval Air Station Whiting Field in Milton, Florida, in the training of student naval aviators. The T-28's service career in the U.S. military ended with the completion of the phase-in of the T-34C turboprop trainer. The last U.S. Navy training squadron to fly the T-28 was VT-27 "Boomers", based at Naval Air Station Corpus Christi, Texas, flying the last T-28 training flight in early 1984. The last T-28 in the Training Command, BuNo 137796, departed for Naval District Washington on 14 March 1984 to be displayed permanently at Naval Support Facility Anacostia, D.C.


title: North American T-28 Trojan

text: In 1963, a Royal Lao Air Force T-28 piloted by Lieutenant Chert Saibory, a Thai national, defected to North Vietnam. Saibory was immediately imprisoned and his aircraft was impounded. Within six months the T-28 was refurbished and commissioned into the North Vietnamese Air Force as its first fighter aircraft.


title: North American T-28 Trojan

text: T-28s were supplied to the Republic of Vietnam Air Force (RVNAF) in support of ARVN ground operations, seeing extensive service during the Vietnam War in RVNAF hands, as well as the Secret War in Laos. A T-28 Trojan was the first US fixed wing attack aircraft (non-transport type) lost in South Vietnam, during the Vietnam War. Capt. Robert L. Simpson, USAF, Detachment 2A, 1st Air Commando Group, and Lt. Hoa, RVNAF, were shot down by ground fire on August 28, 1962 while flying close air support. Neither crewman survived. The USAF lost 23 T-28s to all causes during the war, with the last two losses occurring in 1968.


title: North American T-28 Trojan

text: The T-28B and D were the primary ground attack aircraft of Khmer Air Force in Cambodia during the war there, largely provided from the U.S. Military Equipment Delivery Team and maintained by Air America. On the night of 21 January 1971, PAVN sappers managed to get close enough to destroy the majority at Pochentong airbase. Replacements were quickly shipped in. On 17 March 1973 a pilot of a T-28, said to be Capt. So Petra, a common-law husband of one of the daughters of the overthrown Prince Norodom Sihanouk, machine gunned and bombed the palace of Lon Nol in an attempt to assassinate him, killing at least 20 and wounding 35, before defecting to Khmer Rouge held lands.


title: North American T-28 Trojan

text: France's Armée de l'Air used locally re-manufactured Trojans, "T-28S Fennec", for close support missions in Algeria.


title: North American T-28 Trojan

text: Nicaragua replaced its fleet of 30+ ex-Swedish P-51s with T-28s in the early 1960s, with more aircraft acquired in the 1970s and 1980s.


title: North American T-28 Trojan

text: The Philippines utilized T-28s (colloquially known as "Tora-toras") during the 1989 Philippine coup attempt. The aircraft were often deployed as dive bombers by rebel forces.


title: North American T-28 Trojan

text: AeroVironment modified and armored a T-28A to fly weather research for South Dakota School of Mines & Technology, funded by the National Science Foundation, and operated in this capacity from 1969 to 2005. SDSM&T was planning to replace it with another modified, but more modern, former military aircraft, specifically a Fairchild Republic A-10 Thunderbolt II. This plan was found to carry too many risks associated with the costly modifications required and the program was cancelled in 2018.


title: North American T-28 Trojan

text: Many retired T-28s were subsequently sold to private civil operators, and due to their reasonable operating costs are often found flying or displayed as warbirds today.


title: North American T-28 Trojan

text: Many T-28s are on display throughout the world. In addition, a considerable number of flyable examples exist in private ownership, as the aircraft is a popular sport plane and warbird.


title: Kawasaki Ninja 300

text: The Kawasaki Ninja 300, or EX300, is a Ninja series sport bike introduced by Kawasaki in 2012 for the 2013 model year. It is sold in Asia, Australia, Europe, and North America. When introduced, the Ninja 300R replaced the Ninja 250R in some markets, and in others they were sold alongside each other. When the 2018 model year Ninja 400 was introduced, it replaced the 300 in some markets.


title: Kawasaki Ninja 300

text: The Ninja 300 is based on the Ninja 250R, a lightweight and inexpensive sport bike in production for over three decades. Like the Ninja 250R, it has a full fairing, but a wider rear tire, 140/70, instead of the 130/70 on the 250R. The Ninja 300 also has 5 spoke wheels, neutral finder, and optional antilock braking system (ABS). By comparison with the 250R, the Ninja 300 also has a slightly smaller fuel tank, taller gearing, and a back-torque-limiting slipper clutch with an assist mechanism that decreases clutch lever effort. Despite being a sport bike, it has comfortable ergonomics (such as windscreen effectively protecting from wind blast) which promotes commuting.


title: Kawasaki Ninja 300

text: The Ninja 300 has a straight-twin engine. Dynamometer tests showed that the Ninja 300 produces more power with compared with the 250's , and higher torque across the rev range at .


title: Kawasaki Ninja 300

text: Its top speed has been recorded at and acceleration at 5.6 seconds from , and around 14.5 seconds at in the quarter mile. The stopping distance from of the ABS model was .


title: Kawasaki Ninja 300

text: The Ninja 300's fuel economy was measured at around , while other sources reported it at , though regardless of the methodology, the 300 showed improved gas mileage over the Ninja 250R.


title: Kawasaki Ninja 300

text: The Ninja 300 competes with (and is commonly compared with) other entry-level (300/250 cc) bikes such as Yamaha R3, KTM RC390, Suzuki GSXR-250 and Honda CBR300R.


title: Kawasaki Ninja 300

text: In an effort to increase its compliance with Euro IV, Kawasaki released the Ninja 400 which replaced the Ninja 300 in most markets.


title: Kawasaki Ninja 300

text: In 2022, the bike was released with new decals. In August 2022, it is offered at an ex-showroom price of in India.


title: Tyger Drew-Honey

text: Lindzi James Tyger Drew-Honey (born 26 January 1996) is an English actor and television presenter. He is best known for his role as Jake Brockman in the British sitcom "Outnumbered", Citizen Khan as Richard Scab before later appearing in "" and the television series "Cuckoo".


title: Tyger Drew-Honey

text: Tyger Drew-Honey is the son of pornographic film stars Ben Dover and Linzi Drew. He was educated at Danes Hill School, in Oxshott, followed by Epsom College.


title: Tyger Drew-Honey

text: Between 2007 and 2016, Drew-Honey played Jake Brockman in the British sitcom "Outnumbered". Other appearances have included "The Armstrong & Miller Show" and "Doctors". He co-presented the CBBC series "Friday Download" from 2011 until 2012. He played Mr. Lovett in "The Ministry of Curious Stuff" for CBBC and the role of Dylan in the BBC Three sitcom "Cuckoo" (2012–2019).


title: Tyger Drew-Honey

text: He has done more than 200 voiceovers for television and radio, including for Red Bull and Dell, and was the voice of Lester Large in the children's animated series "The Large Family". He was a presenter on the CBBC show "Friday Download".


title: Tyger Drew-Honey

text: In 2014, Drew-Honey started presenting his own documentary series on BBC Three called "Tyger Takes On...", presenting on pornography, the "perfect body", love, sexuality, and sexism. In this series he stated that he might be bisexual, clarifying his belief in a sexuality spectrum where he is not entirely straight.


title: Tyger Drew-Honey

text: In 2015, Drew-Honey appeared in the four-part series "24 Hours in the Past", along with five other celebrities, to experience what life was like in Victorian Britain. He also had guest roles in "Citizen Khan", "Midsomer Murders", and "Death in Paradise". In 2016, he took part in the E4 dating series "Celebs Go Dating". In 2018, he co-presented Episode 33 of "The Calum McSwiggan Show" on FUBAR Radio.


title: Tyger Drew-Honey

text: In October 2011, Drew-Honey and his co-stars from "Outnumbered", Daniel Roche and Ramona Marquez, covered "(Theme From) The Monkees" to raise funds for the BBC charity campaign Children in Need. A music video featuring them performing the song on the set of "Outnumbered" appeared on the "Children in Need" programme and was released on YouTube in November 2011.


title: Tyger Drew-Honey

text: Drew-Honey was nominated for Best Male Newcomer at the 2009 British Comedy Awards for his role in "Outnumbered" but lost to Charlie Brooker.


title: Tyger Drew-Honey

text: "Outnumbered" was nominated, without success, for a number of awards including a National Television Award and a Royal Television Society Award.


title: University of Cape Town

text: The University of Cape Town (UCT) (, ) is a public research university in Cape Town, South Africa. Established in 1829 as the South African College, it was granted full university status in 1918, making it the oldest university in South Africa and the oldest university in Sub-Saharan Africa in continuous operation.


title: University of Cape Town

text: UCT is organised in 57 departments across six faculties offering bachelor's (NQF 7) to doctoral degrees (NQF 10) solely in the English language. Home to 30 000 students, it encompasses six campuses in the Capetonian suburbs of Rondebosch, Hiddingh, Observatory, Mowbray, and the Waterfront.


title: University of Cape Town

text: Although UCT was founded by a private act of Parliament in 1918, the Statute of the University of Cape Town (issued in 2002 in terms of the Higher Education Act) sets out its structure and roles and places the Chancellor - currently, Dr Precious Moloi Motsepe - as the ceremonial figurehead and invests real leadership authority in the Vice Chancellor, currently Prof Mamokgethi Phakeng, who is accountable to the University Council.


title: University of Cape Town

text: A vibrant student community consisting of over 100 societies and clubs caters to diverse interests such as religion, politics, culture, community outreach and sport. UCT prominently appears in national leagues such as, but not limited to, the Varsity Cup. The historic academic, sporting, and political rivalry between UCT and Stellenbosch University brought about the nickname 'Ikeys', originally an anti-Semitic epithet for students of the university.


title: University of Cape Town

text: UCT is consistently the highest-ranked African university in the QS World University Rankings, the Times Higher Education World University Rankings, and the Academic Ranking of World Universities. Its Commerce, Law, and Medicine Faculties are consistently placed among the hundred best internationally. It is the only African member of the Global University Leaders Forum (GULF) within the World Economic Forum, which is made up of 26 of the world's top universities.


title: University of Cape Town

text: Five alumni, staff members, and researchers associated with UCT have won the Nobel Prize. As of March 2020, 35 UCT staff members are A-rated researchers according to the National Research Foundation of South Africa (almost 30% of the national total), which is the most prestigious ranking possible in the NRF rating classification scheme, a recognition of researchers who are unequivocally recognised by their peers as leading international scholars in their field for the high quality and impact of their recent research outputs. 88 staff members are part of the Academy of Sciences of South Africa.


title: University of Cape Town

text: The University of Cape Town was founded at a meeting in the Groote Kerk in 1829 as the South African College, a high school for young men. The college had a small tertiary-education facility, introduced in 1874 that grew substantially after 1880, when the discovery of gold and diamonds in the north - and the resulting demand for skills in mining - gave it the financial boost it needed to grow. The college developed into a fully fledged university during the period 1880 to 1900, thanks to increased funding from private sources and the government.


title: University of Cape Town

text: During these years, the college built its first dedicated science laboratories, and started the departments of mineralogy and geology to meet the need for skilled personnel in the country's emerging diamond and gold-mining industries. The UCT crest was designed in 1859 by Charles Davidson Bell, Surveyor-General of the Cape Colony at the time. Bell was an accomplished artist who also designed medals and the triangular Cape stamp. Another key development during this period was the admission of women. In 1886 the Professor of Chemistry, Paul Daniel Hahn, convinced the council to admit four women into his chemistry class on a trial basis. Owing to the exceptional standard of work by the women students, the college decided to admit women students permanently in honour of Queen Victoria's Diamond Jubilee in 1887.


title: University of Cape Town

text: The years 1902 to 1918 saw the establishment of the Medical School, the introduction of engineering courses and a Department of Education. UCT was formally established as a university in 1918, on the basis of the Alfred Beit bequest and additional substantial gifts from mining magnates Julius Wernher and Otto Beit. The new university also attracted substantial support from well-wishers in the Cape Town area and, for the first time, a significant state grant.


title: University of Cape Town

text: In 1928, the university was able to move the bulk of its facilities to Groote Schuur on the slopes of Devil's Peak, on land bequeathed to the nation by Cecil John Rhodes as the site for a national university. UCT celebrated its centenary the following year.


title: University of Cape Town

text: Apart from establishing itself as a leading research and teaching university in the decades that followed, UCT earned itself the nickname "Moscow on the Hill" during the period 1960 to 1990 for its sustained opposition to apartheid, particularly in higher education.


title: University of Cape Town

text: The university admitted its first small group of black students in the 1920s. The number of black students remained relatively low until the 1980s and 90s, when the institution, reading and welcoming the signs of change in the country, committed itself to a deliberate and planned process of internal transformation. From the 1980s to the early 1990s, the number of black students admitted to the university rose by 35 percent. By 2004, nearly half of UCT's 20,000 students were black and just under half of the student body was female. Today the university boasts having one of the most diverse campuses in South Africa.


title: University of Cape Town

text: Rhodes Must Fall (stylised as #RhodesMustFall) was a protest movement that began on 9 March 2015, originally directed against a statue at the University of Cape Town (UCT) that commemorates Cecil Rhodes. The campaign for the statue's removal received global attention and led to a wider movement to "decolonise" education across South Africa. On 9 April 2015, following a UCT Council vote the previous night, the statue was removed.


title: University of Cape Town

text: <nowiki>#</nowiki>FeesMustFall was a student protest movement which was arguably indirectly inspired by the RhodesMustFall. It formally began at the University of the Witwatersrand and spread to UCT and Rhodes University and then the rest of the South African universities. It called for the abolition of tuition fee increases for the 2016 academic year. Diverse demands arose such as the abolition of fees and decolonisation of higher education which led to substantial changes at South African public universities. At UCT, the Senate began a widespread curriculum reform process and the university began the process of the renaming of buildings on campus (the most notable example was when Jameson Hall was renamed to Sarah Baartman Hall in 2019).


title: University of Cape Town

text: In September 2019, Film and Media studies student Uyinene Mrwetyana went missing. After the community and police began searching, her body was discovered in the Cape Flats area of Cape Town and Luyanda Botha was arrested and convicted for her rape and murder. Her death and the rape and death of other women precipitated widespread public outcry that led to a campus shutdown and protests on campus, at the Parliament precinct in Cape Town CBD and at campuses around South Africa. Subsequently, President Ramaphosa announced reforms such as harsher punishments for sex offenders and the public disclosure of the National Register for Sex Offenders to stem sexual and physical violence against women and children. Moreover, the Uyinene Mrwetyana Foundation was established and a special fund in her name was created to provide scholarships to female students in the Humanities Faculty.


title: University of Cape Town

text: In March 2020, UCT opened the Neuroscience Institute at the Groote Schuur Hospital in collaboration with the Western Cape Provincial Government, the first dedicated cross- and interdisciplinary centre for the study of and development of treatments for neurological and mental disorders in Africa.


title: University of Cape Town

text: The main teaching campus, known as Upper Campus, is located on the Rhodes Estate on the slopes of Devil's Peak. This campus contains, in a relatively compact site, the faculties of Science, Engineering, Commerce, and Humanities (except for the arts departments), as well as Smuts Hall and Fuller Hall residences. Upper Campus is centered on Sarah Baartman Hall, the location for graduation and other ceremonial events, as well as many examinations. The original buildings and layout of Upper Campus were designed by JM Solomon and built between 1928 and 1930. Since that time, many more buildings have been added as the university has grown. Upper Campus is also home to the main library, The Chancellor Oppenheimer Library, which holds the majority of the university's 1.3 million volume collection.


title: University of Cape Town

text: Contiguous with Upper Campus, but separated from it by university sports fields and the M3 expressway, are the Middle and Lower Campuses. These campuses, which are spread through the suburbs of Rondebosch, Rosebank and Mowbray, contain the Law faculty, the South African College of Music, the School of Economics, most of the student residences, most of the university administrative offices, and various sporting facilities. The state of the art artificial grass soccer field has been approved by FIFA for training for World Cup teams. The Upper, Middle and Lower Campuses together are often referred to as the "main campus".


title: University of Cape Town

text: The Faculty of Health Sciences is located on the Medical School campus next to the Groote Schuur Hospital in Observatory. The Fine Arts and Drama departments are located on the Hiddingh Campus in central Cape Town. The university's original building, now known as the "Egyptian Building", on the Hiddingh campus, was built in the Egyptian Revival style. The only other campus built in this style was the Medical College of Virginia in Richmond, Virginia in the United States. The UCT Graduate School of Business is located on the Breakwater Lodge Campus at the Victoria & Alfred Waterfront.


title: University of Cape Town

text: The Baxter Theatre Centre, located on the Lower Campus, is part of the University of Cape Town; it is also the second largest performing arts complex in Cape Town, after the Artscape Theatre Centre. It has three venues:


title: University of Cape Town

text: For his contribution of the tract of land which the campus was founded on, a bronze statue of Cecil Rhodes was erected in 1934 on the Upper Campus, overlooking the university's rugby fields. The statue was removed in April 2015 following pressure from student groups due to its representation of South Africa's colonialist apartheid past and the university's inadequate representation of black students, faculty, and staff.


title: University of Cape Town

text: The upper campus was affected by the Table Mountain fire in April 2021; the Jagger Library building, which housed rare books and documents including a large African Studies collection, was gutted.


title: University of Cape Town

text: The university has 19 student residences (or "res" as known colloquially), offering both single-gender and mixed-gender housing. The Department of Student Housing oversees the residence system College House is the oldest university residence in Africa, being established in 1887. UCT's residence system is composed of three tiers. Students living in residence are placed in a tier according to the length of time that they have been in the residence system, studying in the university and service or part-time employment in a residence. As a student progresses through their academic journey they are moved into a higher tier. Postgraduate students are usually housed in the third-tier residences unless employed in lower-tier residences.


title: University of Cape Town

text: The University of Cape Town was originally incorporated as a public university by a private act of Parliament in 1918. At present it is incorporated and structured by an institutional statute issued under the provisions of the Higher Education Act, 1997.


title: University of Cape Town

text: The titular head of the university is the Chancellor; this is a ceremonial position without executive power. The primary role of the Chancellor is to confer degrees on behalf of the university, and to represent the university to the rest of the world. The current Chancellor is fashion entrepreneur and philanthropist Dr Precious Moloi-Motsepe who was elected in November 2019 and assumed the role on 1 January 2020 after the expiration of Ms Graça Machel's second consecutive 10-year term.


title: University of Cape Town

text: The University Council is the highest ranked decision-making and appointative structure in the university. With wide-ranging powers of governance over areas such as the strategy, well-being and mission of the university, it is directly accountable to the Government of the Republic through the Minister of Higher Education, currently Dr Blade Nzimande for matters relating to the university. It is composed of 30 broad stakeholder representatives such as students, academics, staff and appointees of the City of Cape Town, Convocation, Premier of the Western Cape and the Minister of Higher Education among others, and the presiding officer of the council, the chair, is currently Sipho Pityana. The Registrar, who acts as the secretary of the Council and Senate, oversees academic registration and legal matters, and administers the Convocation, is currently Royston Pillay.


title: University of Cape Town

text: The Convocation, composed of alumni, the Vice Chancellor, Deputy Vice Chancellors, academic staff, emeritus professors and emeritus associate professors, is a statutory body administered by the Office of the Registrar, which provides a platform for former members of the university to participate and engage with matters affecting the university. Helmed by the President of the Convocation, currently Prof Eddy Maloka, it can make recommendations and pass non-binding resolutions in its Annual General Meetings.


title: University of Cape Town

text: The Leadership Lekgotla is a coordinating and decision-making structure composed of senior executives of the university who oversee the day-to-day running of the university. It contrasts with the University Council which arises from the University Statute and exercises supreme governance over the university. The Leadership Lekgotla's members are senior executives who oversee different areas of the university's operations and policies.  The most senior executive is the Vice Chancellor (ranked below the Chancellor in the ceremonial protocol and order of precedence of the university) is the de facto head and chief executive of the university, currently Prof Mamokgethi Phakeng appointed in July 2018, who is accountable to the council. Below her are the Deputy Vice Chancellors of Transformation (currently Prof Loretta Feris), of Research and Internationalisation (currently Prof Susanne Harris) and of Teaching and Learning (currently Prof Lis Lange). The Chief Operations Officer, currently Dr Reno Morar, brings together and oversees the functional, support and technical areas of the university's operations.


title: University of Cape Town

text: The university is composed of six Faculties (Commerce, Engineering and the Built Environment, Health Sciences, Law, Sciences and Humanities) which together comprise 57 departments. Faculties are helmed by a Dean and their administrative and operational matters are administered by a Director. The Senate has delegated substantial powers to the faculties in academic matters over their internal protocol and management such as on matters concerning class timetables, admission requirements, academic exclusion, examinations, research projects and so on. Faculties vary substantially in student size and in buildings occupied, with the Commerce faculty having the highest student population and the Law faculty having the lowest while the Humanities faculty spans the most buildings followed by the Faculty of Health Sciences with the Commerce and Law faculties having (by far) the lowest physical footprint.


title: University of Cape Town

text: Notwithstanding interdisciplinary research units and centers, additional academic structures exist that eschew the faculty-based organisational structure. The multidisciplinary Center for Higher Education Development ranks on an equal level as the faculties and the UCT Graduate School of Business maintains substantial latitude over its internal affairs despite being nominally part of the Faculty of Commerce. The interdisciplinary School of Information Technology, comprising the Departments of Information Systems and of Computer Science in the Commerce and Science faculties is neither a faculty nor a department but a coordinating mechanism to promote IT education and research.


title: University of Cape Town

text: The university's endowment (the financial capital and investment funds on which it can draw to carry out its work) is deposited with the UCT Foundation (a legally independent nonprofit organisation) and it is managed by the Investment Office. Through the Distinguishing UCT fundraising campaign, the university is trying to raise its endowment. As of 2019, its designated endowment stands at R2.5 billion and its undesignated endowment stands at R676 million with R133 million raised for infrastructure projects (bringing the total undesignated endowment to R809 million which the university aims to increase to R1 billion).


title: University of Cape Town

text: There have been several campaigns at the university to divest its endowment. Fossil Free UCT was formally established in 2015 as a campaign by environmental activism lobbying groups and student organisations, most notably the Green Campus Initiative compel UCT to divest from fossil fuel companies which resulted in a non-binding resolution passed by UCT's Convocation in 2017 to support the divestment. Student lobby groups, most notably the Palestinian Solidarity Front and the SRC called on the university's management to divest from Israeli companies and organisations working in the Palestinian Occupied Territories (among other demands), which, in the end, the university refused to do.


title: University of Cape Town

text: The university's income comes from a combination of government grants, tuition fees, donations, investment and research income. In the 2017–2018 financial year, the university received R1.415 billion in state subsidies, R1.428 billion in tuition fees and R539 million in other income. R1.2 billion was committed to student financial aid for both undergraduate and postgraduate students from the university, the government through the NSFAS scheme and the university's partners and donors.


title: University of Cape Town

text: , there were 27,907 students; 25% of whom were black South African, 22% were white South African, 18% identified as another race, 15% were international students. In 2016 there were 29,074 students enrolled (18,421 undergraduates and 10,653 postgraduates) and 4,542 staff were employed (1,179 academic and 3,363 professional, administrative, support and service staff).


title: University of Cape Town

text: The UCT Employment Equity Plan April (2010 to 2015) indicated moderate but consistent changes in the demographic makeup of the staff body. The five-year plan specified specific targets ranging from between about 5% to 10% adjustments in the representation of SA black staff. According to the plan the staff makeup would have changed by 2015 by achieving either parity or more SA black staff than SA white in all categories other than senior lecturer and professor positions.


title: University of Cape Town

text: UCT spokesperson Elijah Moholola noted that, in 2017, UCT employed 45 white professors, 38 black African, Cape Coloured or Indian South African professors, 67 foreign national professors and 7 who did not disclose their race.


title: University of Cape Town

text: UCT had 36 different sports clubs in 2003, including team sports, individual sports, extreme sports and martial arts.


title: University of Cape Town

text: The university's sports teams, in particular the rugby union team, are known as the "Ikey Tigers" or the "Ikeys". The "Ikey" nickname originated in the 1910s as an anti-semitic epithet applied to UCT students by the students of Stellenbosch University, because of the supposed large number of Jewish students at UCT. Stellenbosch is UCT's traditional rugby opponent; an annual "Intervarsity" match is played between the two universities. The University of Cape Town Football Club also known as the "Ikeys Warriors" is the main team for association football (soccer), representing the university at tournaments such as Varsity Football.


title: University of Cape Town

text: In addition to the plethora of student societies, there are several student organisations dedicated to the development of communities surrounding the university in the Cape Metropolitan Area. Some of the biggest include: SHAWCO, Ubunye and RAG. Recently, several students movements have developed, such as the Green Campus Initiative.


title: University of Cape Town

text: The University of Cape Town is the most prestigious African university according to several rankings. It achieved a rank of 198 in the 2019 QS World University Rankings, a rank of 156 in the 2019 Times Higher Education World University Rankings, and a rank of 201–300 in the Shanghai Academic Ranking of World Universities, making it the highest-ranked African university in these rankings.


title: University of Cape Town

text: The faculty of Commerce as well as the faculty of Law and Medicine have appeared in the top 100 faculties internationally. The Law Faculty achieved a global rank of 40 in the 2014 QS World University Rankings by Subject. Although the university remains the highest ranking in Africa as of 2022 its ranking has been declining since 2015.


title: University of Cape Town

text: UCT is a member of the Worldwide Universities Network (WUN), the Association of African Universities, the Association of Commonwealth Universities, the Cape Higher Education Consortium, Higher Education South Africa, the International Alliance of Research Universities (IARU), the African Research Universities Alliance (ARUA) and the International Association of Universities.


title: University of Cape Town

text: Five alumni of the University of Cape Town have been awarded Nobel Prizes: Ralph Bunche, American political scientist and diplomat awarded the Nobel Peace Prize in 1950 for his role in the 1949 Armistice Agreements, Professor Allan McLeod Cormack, physicist awarded the Nobel Prize in Medicine (1979) for his work on X-ray computed tomography, Max Theiler, virologist awarded the Nobel Prize in Physiology or Medicine in 1951 for developing a vaccine against yellow fever, Sir Aaron Klug, chemist and biophysicist awarded the Nobel Prize in Chemistry (1982) for his development of crystallographic electron microscopy and his structural elucidation of biologically important nucleic acid-protein complexes and Professor Emeritus J. M. Coetzee (Literature, 2003).


title: University of Cape Town

text: UCT alumni have gone on to achieve positions in academica, politics and other fields as follows. According to a non-peer reviewed study conducted by the Mail & Guardian in 2018, 6% of members of the Parliament of South Africa obtained a degree from UCT (the study had a sample of 247 out of 449 MPs). Ministers of the Cabinet of South Africa, Naledi Pandor and Ebrahim Patel, former Vice President of the World Bank and former Vice Chancellor of UCT, Mamphela Ramphele, South African surgeon Christiaan Barnard, South African writer Breyten Breytenbach, South African entrepreneur and inventor behind Ubuntu, Mark Shuttleworth, South African activist and judge Albie Sachs, former member of the South African music band Freshlyground, Zolani Mahola, South African cartoonist Zapiro and former Speaker of the National Assembly of South Africa, Baleka Mbete are among the alumni of the university. Kindly refer to List of Notable Alumni of the University of Cape Town for further information on notable UCT alumni.


title: University of Cape Town

text: The National Research Foundation of South Africa rates researchers and academics according to the quality of their research output in four categories. , 35 staff are A-rated, that being they are internationally recognised leaders in their fields. These are 30% of the A-rated researchers recognised by the NRF, making UCT, by far, the university with the highest number of such researchers. 6 researchers are recognised as P-rated, that being they have potential to become leaders in their fields. , 15% of South Africa's total NRF-rated researchers (about 524) are employed or associated with UCT. For a comprehensive and up-to-date list of B, Y and C-rated researchers, see this site.


title: University of Cape Town

text: , 19% of South African Research Chairs Initiative (SARChI) research chairs (about 42 academics) are held by UCT employed or associated researchers. 88 members of faculty are members of the Academy of Sciences of South Africa. Notable staff members include Minister of Trade and Industry, Ebrahim Patel, Minister of International Relations and Cooperation, Naledi Pandor, former Premier of the Western Cape, Helen Zille and George Ellis, collaborator with Stephen Hawking and winner of the 2004 Templeton Prize, was a professor of applied mathematics in the Faculty of Sciences. For a larger albeit inexhaustive list of former and current notable UCT faculty and staff, see the List of University of Cape Town faculty.


title: University of Cape Town

text: A debate at UCT over the removal of a statue of Cecil Rhodes spawned Rhodes Must Fall movement. The FeesMustFall movement, which began at Wits and spread to UCT, was inspired by the Rhodes Must Fall protests.


title: University of Cape Town

text: Since the removal of the Rhodes statue, other art has been removed or destroyed. FeesMustFall students burned 23 of the university's historical paintings in February 2016.


title: University of Cape Town

text: According to GroundUp, art experts connected to the university are concerned about intolerance towards art at the institution, as UCT has removed and censored 75 further "vulnerable" art which it claims are offensive to students.


title: University of Cape Town

text: An Artworks Task Team was set up in September 2015 to assess art at the university "with a view to transformation and inclusivity", and went about finding "artworks on campus that may be seen to recognize or celebrate colonial oppressors and/or which may be offensive or controversial", and specifically artworks deemed to be "offensive" in their depiction of black people. Both Stanley Pinker’s "Decline and Fall", which makes ironic use of colonial iconology, and Breyten Breytenbach's "Hovering Dog", which shows a black person wearing a white mask and a white person wearing a black mask, were removed; and Diane Victor’s "Pasiphaë", which depicts black farmers with allusions to Greek mythology, was covered by a wooden panel. In response, Breyten Breytenbach remarked that UCT were making fools of themselves, while Diane Victor thought UCT's actions were "slightly comical" and her artwork was being understood on a "simplistic level".


title: University of Cape Town

text: Jacques Rousseau, then chair of the Academic Freedom Committee, told GroundUp: "There are a number of artworks in UCT's collection that could legitimately be regarded as problematic. Even so, any piece of art is potentially offensive to someone, and the very point of art is to provoke reflection and sometimes discomfort." The Academic Freedom Committee noted with "grave concern recent instances of threats to academic freedom".


title: University of Cape Town

text: The South African Human Rights Commission was investigating the matter as of May 2017, in order to determine whether the university was infringing on the constitutional right to freedom of expression, in particular the right to artistic creativity.


title: University of Cape Town

text: The university was the shooting location of the 2019 film "Critters Attack!" where it was called Leroy College and the 2008 film "Disgrace".


title: University of Cape Town

text: The university was the shooting location of Netflix movies "The Kissing Booth" and "The Kissing Booth 2" and the 2020 Netflix series "Blood & Water". The Upper Campus residence served as the grounds and building for the show's fictional Parkhurst College.


title: Kikimora

text: Kikimora () is a legendary creature, a female house spirit in Slavic mythology. Her role in the house is usually juxtaposed with that of the domovoy. The kikimora can either be a "bad" or a "good" spirit, which will depend on the behavior of the homeowner. When the kikimora inhabits a house, she lives behind the stove or in the cellar, and usually produces noises similar to those made by mice in order to obtain food. Kikimory (in plural) were the first traditional explanation for sleep paralysis in Russian folklore.


title: Kikimora

text: Most sources link the suffix -"mora" with the Proto-Slavic *"morà" ('nightly spirit, bad dream') and the Proto-Germanic *"marōn" ("id."), as in the modern English nightmare.


title: Kikimora

text: In Polish folklore, mora are the souls of living people that leave the body during the night, and are seen as wisps of straw or hair or as moths. Accordingly, Polish "mora", Czech "můra" denote both a kind of elf or spirit as well as a "sphinx moth" or "night butterfly". Other Slavic languages with cognates that have the double meaning of moth are: Kashubian "mòra", and Slovak "mora".


title: Kikimora

text: In Slovene, Croatian and Serbian, "mora" refers to a "nightmare". "Mora" or "Mara" is one of the spirits from ancient Slav mythology. Mara was a dark spirit that takes a form of a beautiful woman and then visits men in their dreams, torturing them with desire, and dragging life out of them. In Serbia, a mare is called "mora", or "noćnik/noćnica" ("night creature", masculine and feminine respectively). In Romania they were known as "Moroi".


title: Kikimora

text: The word "kikimora" may have derived from the Udmurt (Finno-Ugric) word "kikka-murt", meaning "scarecrow" (literally "bag-made person").


title: Kikimora

text: The origin of the kikimora comes from the 8th to 13th century when Slavic paganism was slowly subsumed by Christianity. However, even after Christianity took hold in the Slavic regions, the belief of the kikimora was still strong. Belief in the entity still continues today where it is imbued with old Slavic folk religion and Christianity's concept of demonic forces.


title: Kikimora

text: The kikimora might have the snout of a dog, a chicken beak or can even resemble a goat-like entity with glowing eyes and horns. In fact, it can take any part of an animal's face or body. It is always feminine and can appear as an old woman or a beautiful girl. She might even appear as a deceased family member.


title: Kikimora

text: The swamp kikimora is usually described as a small, ugly, hunchbacked, thin, and scruffy old woman with a pointed nose and disheveled hair. She was said to use moss and grass as clothes. It was believed that she frightens people, knocks travelers off the road or even drowns them. She also kidnaps children.


title: Kikimora

text: It is a common belief that "mora" enters the room through the keyhole, sits on the chest of the sleepers and tries to strangle them (hence "moriti", "to torture", "to bother", "to strangle"). To repel "moras", children are advised to look at the window or to turn the pillow and make a sign of cross on it ("prekrstiti jastuk"); in the early 19th century, Vuk Karadžić mentions that people would repel "moras" by leaving a broom upside down behind the door, or putting their belt on top of their sheets, or saying an elaborate prayer poem before they go to sleep.


title: Kikimora

text: There are two different kinds of kikimoras. The one that comes from the forest is married to the Domovoi. The other one comes from the swamp () and is married to Leshy. It is said that she can be identified by her wet footprints. When home builders wanted to cause harm to someone buying a house, they would bring in kikimora. Once she is inside, it is difficult to get her to leave.


title: Kikimora

text: There is a Russian bylichka about one swamp kikimora, who loved to brew beer. Her name was Baba Bolotnitsa (). When she was brewing beer, fog rose over the river (or swamp).


title: Kikimora

text: When the house is in order, kikimora looks after the chickens and housework. If not, she whistles, breaks dishes, and makes noises at night. She also comes out at night to spin thread.


title: Kikimora

text: The legend is the basis of "Kikimora" (op. 63), a tone poem for orchestra by Anatoly Lyadov. Lyadov wrote that she "grows up with a magician in the mountains. From dawn to sunset the magician’s cat regales kikimora with fantastic tales of ancient times and faraway places, as kikimora rocks in a cradle made of crystal. It takes her seven years to reach maturity, by which time her head is no larger than a thimble and her body no wider than a strand of straw. Kikimora spins flax from dusk and to dawn, with evil intentions for the world."


title: Kikimora

text: The kikimora is mentioned by Russian "New Age" writer Vladimir Megre in "The Space of Love", Book 3 of his "Ringing Cedars" series. Megre likens a man who marries unwisely based on looks and fashion to one who marries a kikimora. A footnote in the English version describes the kikimora as a malevolent female ghost said to attach itself to a particular house and disturb the inhabitants, males in particular. By extension, the term may also suggest an ugly woman in shabby clothing, ill-tempered and grumbling, striving to make the life of her husband (and men in general) unbearable.


title: Kikimora

text: In 1988, Kirill Eskov discovered and described a new genus and species of sheetweaver spider, "kikimora palustris" after this spirit.


title: Kikimora

text: The concept of the kikimora is thought to serve basic functions and duties of the household. A kikimora would haunt a household if a woman did not keep a clean house; if a husband was lazy or abusive; or if children were poorly disciplined. Reversing one's behaviour is believed to remove her presence from the house. Besides that, the kikimora entity is thought to console or explain tragic events like the death of a family member or the loss of household items.


title: Korapat Kirdpan

text: Korapat Kirdpan (, ; born 18 December 2000), nicknamed Nanon (), is a Thai television actor. He is best known for his leading roles in "Senior Secret Love" (2016), "My Dear Loser" (2017), "The Gifted" (2018), "Blacklist" (2019), " (2020)", "Bad Buddy Series" (2021) and most recently in " Vice Versa" (2022).


title: Korapat Kirdpan

text: Born in Bangkok, Thailand, Korapat is the son of Thai actor Khunakorn Kirdpan and Poonsuk Kirdpan. He has one younger sister named Pitchaporn Kirdpan. He completed his secondary education at Amatyakul School and is currently studying in acting and directing for cinema from the College of Social Communication Innovation at Srinakharinwirot University.


title: Korapat Kirdpan

text: Korapat started his acting career at the age of three by appearing in several TV commercials. He made his acting debut in 2014 with the television drama series "" where he had a guest role as M. In 2015, he had supporting roles in "Ugly Duckling Series: Don't" and "Love Flight" - television programs produced by GMM 25. He also reprised his role as M in "".


title: Korapat Kirdpan

text: In 2016, he played a supporting role in "Little Big Dream". He would later become known for leading roles in "Senior Secret Love: My Lil Boy & My Lil Boy 2" (2016) alongside Kanyawee Songmuang, "My Dear Loser: Edge of 17" (2017), "The Gifted" (2018), and "" (2020). In 2021, Nanon starred with Pawat Chittsawangdee (Ohm) in the BL series "Bad Buddy". He and Pawat will have a fan meeting event in the Philippines on January 2023.


title: Divya Agarwal

text: Divya Agarwal is an Indian actress, model and dancer known for participating in several reality shows. She is the runner-up of "MTV Splitsvilla 10" and winner of "Ace of Space 1" and "Bigg Boss OTT". She made her acting debut with the horror web series "".


title: Divya Agarwal

text: Agarwal got her master's degree in journalism. She trained in dance from Terence Lewis Dance Academy, and then opened her own dance academy called Elevate Dance Institute. She has choreographed several actresses like Ileana D'Cruz, Sunny Leone and Shilpa Shetty. In 2010, she and a Pakistani choreographer worked on choreography for the IPL 2010.


title: Divya Agarwal

text: She had also participated in several beauty pageants. In 2015, she won the title of "Miss Navi Mumbai". In 2016, she was crowned the winner of the Indian Princess pageant She also won title of Miss India Tourism International 2017 and Miss Tourism International 2017.


title: Divya Agarwal

text: Agarwal rose to fame in 2017 when she participated in MTV India's "Splitsvilla 10" wherein she finished as the runner-up with Priyank Sharma.


title: Divya Agarwal

text: In 2018, she would act as a mentor in MTV India's "Date To Remember" show. In March 2018, Agarwal and "Splitsvilla 10" contestant Baseer Ali guest co-hosted an episode of "On Road With Roadies". In October, she participated in MTV India's "Ace of Space 1" where she emerged as the winner.


title: Divya Agarwal

text: In January 2019, Agarwal starred in her first international project by participating in "Travel With A Goat", broadcast on Insight TV, where she and television celebrity chef Dean Edwards travel across Bulgaria with a sheep and must decide whether to have it slaughtered or save its life. In February 2019, she made a cameo appearance in Alt Balaji's web drama "Puncch Beat". In March, Agarwal and Varun Sood participated as Roadies Insiders for "", broadcast on Voot. Next, she hosted Voot's "Voot Night Live" with RJ Anmol. In December, she starred opposite Sood to play Ragini/Savitri Devi in season 2 of Alt Balaji's horror web series "". In 2020, Agarwal and Sood co-hosted the "Ace of Space" spinoff "MTV Ace the Quarantine".


title: Divya Agarwal

text: In 2021, Agarwal participated in Voot's "Bigg Boss OTT" and emerged as the winner. She also portrayed a mysterious make-up artist character named Grissy in the action-drama web series "Cartel".


title: Divya Agarwal

text: In 2017, She met actor and model Priyank Sharma on "MTV Splitsvilla 10" where they were both runners-up. They were dating post "Splitsvilla" and Agarwal entered "Bigg Boss 11" to part ways with Sharma.


title: Divya Agarwal

text: In 2018, she met actor and former "MTV Roadies" contestant Varun Sood. They worked together on "" and "MTV Ace of Space". Following "Ace of Space", she and Sood confirmed they are dating. On 6 March 2022, she announced on social media that they had split.


title: Divya Agarwal

text: Agarwal was listed sixth among "Times of India"s Top 20 Most Desirable Women On Indian Television List in 2019, and nineteenth in 2020.


title: Adam Darski

text: Adam Nergal Darski (born Adam Michał Darski, 10 June 1977), often referred to by his stage name Nergal, is a Polish musician and television personality. He is best known as the frontman of extreme metal band Behemoth.


title: Adam Darski

text: Nergal was born Adam Michał Darski in Gdynia, raised Catholic, and started playing guitar at age eight. He goes by the stage name Nergal (naming himself after a Babylonian deity), and he is the founder, lyricist, main composer, frontman and manager of the band Behemoth, which he started when he was still a teenager. He also plays lead, rhythm and acoustic guitar. For a brief time, he used the alias Holocausto, inspired by Beherit leader Nuclear Holocausto. In the late 1990s, he was a vocalist and guitarist of the Danzig-influenced band, Wolverine, which was showcasing Nergal's capability of clean singing. He is also known for his contributions with the following bands: Hermh, Nile, Damnation, Vader, Sweet Noise, Mastiphal, December's Fire, Mess Age, Corruption, Hangover, Ex Deo, and Hefeystos.


title: Adam Darski

text: Inspired by Norway's Black Circle, Nergal formed together with Blasphemous (from the band Veles) and Venom (from Xantotol) the Temple of Infernal Fire. Later other bands joined and far-right politics were introduced, and the group renamed the Temple of Fullmoon. Nergal then distanced himself from the group, mainly because he had no interest in politics. This led to remaining members of the Temple of Fullmoon to accuse Behemoth of betrayal and caused tensions between Nergal and Rob Darken, frontman of the Polish NSBM band Graveland, leading to death threats. Several years later, the tensions are gone and Nergal and Darken are in good terms nowadays, or as Nergal said in an interview: "We don't share the same interests but we share a mutual respect."


title: Adam Darski

text: Nergal has completed six years of history, including one year of Latin at University of Gdańsk, and is qualified to be a museum curator.


title: Adam Darski

text: In 2009, ESP guitars released the first Nergal's signature guitar. It is a 7-string guitar with a V-style body, which is called the "Hex-7".


title: Adam Darski

text: In March 2010, Nergal was held on trial in Poland on blasphemy charges for publicly denouncing religion by ripping up a Bible on stage in 2007. Nergal made the argument that he has artistic license to enhance his live performances by doing such an action, and suggested that it was not meant to be offensive. He also supported that freedom of speech should come before religion in Poland. He faced up to two years in prison due to the Bible-tearing, but Darski's charges were dropped on 28 June 2010.


title: Adam Darski

text: In July 2012, Nergal became the newest spokesman for Demon Energy drinks that would be distributed throughout Poland. Nergal appeared in full Behemoth attire on the front of four different flavors of the Demon Energy brand alongside the brand's slogan of "No Limits, No Laws". Darski reportedly donated the majority of funds for this limited edition placement to one of the world's most renowned bone marrow donor centers.


title: Adam Darski

text: In October 2012, Nergal returned to the Polish Supreme Court regarding the 2007 incident where he tore up a bible and denounced the Catholic Church. The Supreme Court ruled that Darski could be guilty of the


title: Adam Darski

text: crime of "offending religious feelings" even though he did not act with the "direct intention" of doing so. The case was returned to a lower court which found him guilty of "intentionally insulting the Holy Bible" but the following appeal dismissed the case due to the statute of limitations.


title: Adam Darski

text: From mid-2009 through early 2011, he was in a highly publicized relationship with Dorota Rabczewska, a Polish pop singer professionally known as Doda. On 17 March 2011, News.pl reported the couple had called off the engagement and broken up.


title: Adam Darski

text: Since 2014, Nergal has been the co-owner of three barbershops in Poland—two in Warsaw and one in his hometown, Gdańsk. In 2015 he opened a nightclub in Sopot named Libation.


title: Adam Darski

text: On 8 August 2010, Nergal was rushed to the hematology ward of the Gdańsk Medical University Hospital for treatment of a then-undisclosed illness. All Behemoth shows through November 2010, including a Russian and North American tours, were cancelled. On 24 August 2010, Darski was diagnosed with leukemia. The illness was thought to have advanced far enough to make chemotherapy ineffective, but such reports have since been proven false. His then-fiancée Dorota Rabczewska-Stępień offered to donate her marrow, but her marrow didn't match. On 8 November 2010, following his then-girlfriend's appeal to the wider public, which has been met with a great response, Darski underwent treatment to receive a bone marrow transplant.


title: Adam Darski

text: Nergal was discharged from the Uniwersyteckie Centrum Kliniczne (UCK) hospital in Gdańsk on 16 January 2011, three weeks after undergoing bone marrow transplantation. "Adam feels good and is resting comfortably but cannot see any visitors as he can’t risk viral infections", said his ex-fiancée, Doda. However, Nergal was readmitted to the hematology division of Uniwersyteckie Centrum Kliniczne (UCK) in Gdańsk after he developed an infection six weeks later. At the time, it was not immediately clear if the infection would affect Nergal's adoption of the bone marrow transplant and how long he would have to remain in hospital. On 30 March 2011, MetalSucks published an interview with Nergal where he said that his health was improving. As of the interview, he had been out of the hospital for several weeks, and, according to Darski, "everything is going according to plan".


title: Adam Darski

text: Nergal started a solo project alongside John Porter called Me and that Man, which focuses on country, blues and folk. The project's debut album titled "Songs of Love and Death" was released on 24 March 2017. The project's follow-up album, "New Man, New Songs, Same Shit, Vol. 1" was released on 27 March 2020, and features guest vocals from Corey Taylor, Niklas Kvarforth, Matt Heafy, Ihsahn, and others.


title: Chancellor

text: Chancellor () is a title of various official positions in the governments of many nations. The original chancellors were the of Roman courts of justice—ushers, who sat at the or lattice work screens of a basilica or law court, which separated the judge and counsel from the audience. A chancellor's office is called a chancellery or chancery. The word is now used in the titles of many various officers in various settings (government, education, religion). Nowadays the term is most often used to describe:


title: Chancellor

text: The Chancellor of Austria, denominated ' for males and ' for females, is the title of the head of the Government of Austria. Since 2021, the Chancellor of Austria is Karl Nehammer.


title: Chancellor

text: The Chancellor of Germany, denominated ' for males and ' for females, is the title for the head of government in Germany. In German politics, the ' position is equivalent to that of a prime minister and is elected by the ' ("Federal Diet", the directly elected federal parliament) every four years on the beginning of the electoral period after general elections. Between general elections, the Chancellor (together with the whole cabinet) can only be removed from office by a ' (constructive vote of no confidence), which consists in the candidacy of an opposition candidate for the office of Chancellor in the '. Candidates receiving a majority of the entire membership of the " will be sworn in immediately as new Chancellor.


title: Chancellor

text: The former German Empire, the Weimar Republic and Great Nazi Germany had the equivalent position of ' ("Reich Chancellor") as the head of the executive. Between 1871 and 1918, the Chancellor was appointed by the German Emperor. During the Weimar Republic (1919-1933), the Chancellor was chosen by the "Reichspräsident" ("Reich President") and stood under his authority. This continued (formally) during the first two years of the Nazi regime until the death of President Paul von Hindenburg in 1934. Between 1934 and 1945, Adolf Hitler was dictatorial head of state "and" government of Nazi Germany, being officially titled "'" (literally "Leader and Reich Chancellor").


title: Chancellor

text: In Switzerland, the Chancellor (, , ) is not the political head of government, but rather its administrative head as the Chief of Staff of the Swiss Federal Government. They are elected by the Swiss Federal Assembly (, , ) to head the Federal Chancellery () — the general staff of the seven-member executive Federal Council, the Swiss federal government. The Chancellor participates in the meetings of the seven Federal Councilors with a consultative vote and prepares the reports on policy and activities of the council to parliament (assembly). The chancellery is responsible for the publication of all federal laws.


title: Chancellor

text: In most Swiss cantons there is a State Chancellor who heads the central administrative unit of the cantonal government. In the Canton of Geneva, the first documents attesting to the existence of a Chancellor go back to the 12th century. In the 16th century the Chancery is officially described as the permanent secretariat of the executive and legislature. The first of these functions still constitutes an important part of its activities in Geneva and other cantons. In the Canton of Berne, the Chancellor is elected by the Grand Council (i.e. Parliament) and has the task of supporting the Grand Council and the Executive Council in carrying out their tasks. The Chancellor directs the staff of the Executive Council, supports the President of the Government and the Executive Council in the performance of their duties, and usually participates as an advisor to the President of the Grand Council in Grand Council sessions.


title: Chancellor

text: In most countries of Latin America, the equivalents to "chancellor" ("Canciller" in Spanish and "Chanceler" in Portuguese) are commonly used to refer to the post of foreign minister. It is often used as a synonym to the full titles of the ministers of foreign affairs. Likewise, the ministry of foreign affairs in Spanish-speaking countries in the Americas is referred to as the "Cancillería" or in Portuguese-speaking Brazil as "Chancelaria". However, in Spain the term "canciller" refers to a civil servant in the Spanish diplomatic service responsible for technical issues relating to foreign affairs. As to the German foreign service, the term "Kanzler" (chancellor) refers to the administrative head of a diplomatic mission.


title: Chancellor

text: In Finland the Chancellor of Justice (', ') supervises the legality of actions taken by the government and monitors the implementation of basic civil liberties. In this special function the chancellor also sits in the Finnish Cabinet, the Finnish Council of State.


title: Chancellor

text: In Sweden the Chancellor of Justice or ' acts as the Solicitor General for the Swedish Government. The office was introduced by Charles XII of Sweden in 1713. Historically there was also a Lord High Chancellor or ' as the most senior member of the Privy Council of Sweden. There is in addition to this a University Chancellor or "", who leads the National Agency for Higher Education.


title: Chancellor

text: Some U.S. states, like Delaware, Tennessee, and Mississippi, still maintain a separate Court of Chancery with jurisdiction over equity cases. Judges who sit on those courts are called chancellors.


title: Chancellor

text: In Denmark, the office of chancellor (or royal chancellor) seems to have appeared in the 12th century, and until 1660 it was the title of the leader of the state administration (a kind of a "Home Office" but often with foreign political duties). Often he appeared to be the real leader of the government. From 1660 until 1848, the title continued as "Grand Chancellor" or "President of the Danish Chancellery", and was replaced in 1730 by the title "Minister of Domestic Affairs".


title: Chancellor

text: In Estonia, a Chancellor (') directs the work of a ministry and coordinates institutions subject to the ministry. A ministry can also have one or several Vice-Chancellors ("Asekantsler"), who fulfill the duties of the Chancellor, when they are absent. The Chancellor of Justice (', currently Ülle Madise) supervises the legality of actions taken by the government and monitors the implementation of basic civil liberties.


title: Chancellor

text: In the United States, the only "chancellor" established by the federal government is the Chancellor of the Smithsonian Institution, a largely ceremonial office held by the Chief Justice of the United States. As the Smithsonian is a research and museum system, its use of the title is perhaps best thought of as akin to a university's chancellor.


title: Chancellor

text: The chancellor is the principal record-keeper of a diocese or eparchy, or their equivalent. The chancellor is a notary, so that he may certify official documents, and often has other duties at the discretion of the bishop of the diocese: he may be in charge of some aspect of finances or of managing the personnel connected with diocesan offices, although his delegated authority cannot extend to vicars of the diocesan bishop, such as vicars general, episcopal vicars or judicial vicars. His office is within the "chancery". Vice-chancellors may be appointed to assist the chancellor in busy chanceries. Normally, the chancellor is a priest or deacon, although in some circumstances a layperson may be appointed to the post. In the eparchial curia a chancellor is to be appointed who is to be a presbyter (priest) or deacon and whose principal obligation, unless otherwise established by the particular law, is to see that the acts of the curia are gathered and arranged as well as preserved in the archives of the eparchial curia.


title: Chancellor

text: In England, the Consistory courts of the Church of England are each presided over by a Chancellor of the Diocese.


title: Chancellor

text: In the United Methodist Church, each Annual Conference has a Conference Chancellor, who is the Annual Conference's legal adviser and representative. While the Annual Conference usually hires outside professional counsel in matters that require legal representation, that hiring and representation is done under the supervision, and with the consent, of the Conference Chancellor.


title: Chancellor

text: A chancellor is the leader, either ceremonial or executive, of many public and private universities and related institutions.


title: Chancellor

text: The heads of the New York City Department of Education and the District of Columbia Public Schools, who run the municipally-operated public schools in those jurisdictions, carry the title of Chancellor. New York State also has a Chancellor of the University of the State of New York, the body that licenses and regulates all educational and research institutions in the state and many professions (not to be confused with the State University of New York, an actual institution of higher learning).


title: Chancellor

text: In a few instances, the term chancellor applies to a student or faculty member in a high school or an institution of higher learning who is either appointed or elected as chancellor to preside on the highest ranking judicial board or tribunal. They handle non-academic matters such as violations of behavior.


title: Chancellor

text: In Germany many heads of university administration carry the title ' (Chancellor) while the academical heads carry the title ' (Rector). In order to avoid any misunderstanding, the head of the German Federal Government is therefore usually called by the official title ' (Federal Chancellor).


title: Difference in differences

text: Difference in differences (DID or DD) is a statistical technique used in econometrics and quantitative research in the social sciences that attempts to mimic an experimental research design using observational study data, by studying the differential effect of a treatment on a 'treatment group' versus a 'control group' in a natural experiment. It calculates the effect of a treatment (i.e., an explanatory variable or an independent variable) on an outcome (i.e., a response variable or dependent variable) by comparing the average change over time in the outcome variable for the treatment group to the average change over time for the control group. Although it is intended to mitigate the effects of extraneous factors and selection bias, depending on how the treatment group is chosen, this method may still be subject to certain biases (e.g., mean regression, reverse causality and omitted variable bias).


title: Difference in differences

text: In contrast to a time-series estimate of the treatment effect on subjects (which analyzes differences over time) or a cross-section estimate of the treatment effect (which measures the difference between treatment and control groups), difference in differences uses panel data to measure the differences, between the treatment and control group, of the changes in the outcome variable that occur over time.


title: Difference in differences

text: Difference in differences requires data measured from a treatment group and a control group at two or more different time periods, specifically at least one time period before "treatment" and at least one time period after "treatment." In the example pictured, the outcome in the treatment group is represented by the line P and the outcome in the control group is represented by the line S. The outcome (dependent) variable in both groups is measured at time 1, before either group has received the treatment (i.e., the independent or explanatory variable), represented by the points "P" and "S". The treatment group then receives or experiences the treatment and both groups are again measured at time 2. Not all of the difference between the treatment and control groups at time 2 (that is, the difference between "P" and "S") can be explained as being an effect of the treatment, because the treatment group and control group did not start out at the same point at time 1. DID therefore calculates the "normal" difference in the outcome variable between the two groups (the difference that would still exist if neither group experienced the treatment), represented by the dotted line "Q". (Notice that the slope from "P" to "Q" is the same as the slope from "S" to "S".) The treatment effect is the difference between the observed outcome (P) and the "normal" outcome (the difference between P and Q).


title: Difference in differences

text: where formula_2 is the dependent variable for individual formula_3 and time formula_4, formula_5 is the group to which formula_3 belongs (i.e. the treatment or the control group), and formula_7 is short-hand for the dummy variable equal to 1 when the event described in formula_8 is true, and 0 otherwise. In the plot of time versus formula_9 by group, formula_10 is the vertical intercept for the graph for formula_11, and formula_12 is the time trend shared by both groups according to the parallel trend assumption (see Assumptions below). formula_13 is the treatment effect, and formula_14 is the residual term.


title: Difference in differences

text: and suppose for simplicity that formula_16 and formula_17. Note that formula_18 is not random; it just encodes how the groups and the periods are labeled. Then


title: Difference in differences

text: Without loss of generality, assume that formula_21 is the treatment group, and formula_22 is the after period, then formula_23 and formula_24, giving the DID estimator


title: Difference in differences

text: which can be interpreted as the treatment effect of the treatment indicated by formula_18. Below it is shown how this estimator can be read as a coefficient in an ordinary least squares regression. The model described in this section is over-parametrized; to remedy that, one of the coefficients for the dummy variables can be set to 0, for example, we may set formula_27.


title: Difference in differences

text: All the assumptions of the OLS model apply equally to DID. In addition, DID requires a parallel trend assumption. The parallel trend assumption says that formula_28 are the same in both formula_29 and formula_30. Given that the formal definition above accurately represents reality, this assumption automatically holds. However, a model with formula_31 may well be more realistic. In order to increase the likelihood of the parallel trend assumption holding, a difference-in-differences approach is often combined with matching. This involves 'Matching' known 'treatment' units with simulated counterfactual 'control' units: characteristically equivalent units which did not receive treatment. By defining the Outcome Variable as a temporal difference (change in observed outcome between pre- and posttreatment periods), and Matching multiple units in a large sample on the basis of similar pre-treatment histories, the resulting ATE (i.e. the ATT: Average Treatment Effect for the Treated) provides a robust difference-in-differences estimate of treatment effects. This serves two statistical purposes: firstly, conditional on pre-treatment covariates, the parallel trends assumption is likely to hold; and secondly, this approach reduces dependence on associated ignorability assumptions necessary for valid inference.


title: Difference in differences

text: As illustrated to the right, the treatment effect is the difference between the observed value of "y" and what the value of "y" would have been with parallel trends, had there been no treatment. The Achilles' heel of DID is when something other than the treatment changes in one group but not the other at the same time as the treatment, implying a violation of the parallel trend assumption.


title: Difference in differences

text: To guarantee the accuracy of the DID estimate, the composition of individuals of the two groups is assumed to remain unchanged over time. When using a DID model, various issues that may compromise the results, such as autocorrelation and Ashenfelter dips, must be considered and dealt with.


title: Difference in differences

text: The DID method can be implemented according to the table below, where the lower right cell is the DID estimator.


title: Difference in differences

text: where formula_33 is a dummy variable for the period, equal to formula_34 when formula_35, and formula_36 is a dummy variable for group membership, equal to formula_34 when formula_30. The composite variable formula_39 is a dummy variable indicating when formula_40. Although it is not shown rigorously here, this is a proper parametrization of the model formal definition, furthermore, it turns out that the group and period averages in that section relate to the model parameter estimates as follows


title: Difference in differences

text: where formula_42 stands for conditional averages computed on the sample, for example, formula_43 is the indicator for the after period, formula_44 is an indicator for the control group. Note that formula_45 is an estimate of the counterfactual rather than the impact of the control group. The control group is often used as a proxy for the counterfactual (see, Synthetic control method for a deeper understanding of this point). Thereby, formula_45 can be interpreted as the impact of both the control group and the intervention's (treatment's) counterfactual. Similarly, formula_47, due to the parallel trend assumption, is also the same differential between the treatment and control group in formula_48. The above descriptions should not be construed to imply the (average) effect of only the control group, for formula_45, or only the difference of the treatment and control groups in the pre-period, for formula_47. As in Card and Krueger, below, a first (time) difference of the outcome variable formula_51 eliminates the need for time-trend (i.e., formula_45) to form an unbiased estimate of formula_53, implying that formula_45 is not actually conditional on the treatment or control group. Consistently, a difference among the treatment and control groups would eliminate the need for treatment differentials (i.e., formula_47) to form an unbiased estimate of formula_53. This nuance is important to understand when the user believes (weak) violations of parallel pre-trend exist or in the case of violations of the appropriate counterfactual approximation assumptions given the existence of non-common shocks or confounding events. To see the relation between this notation and the previous section, consider as above only one observation per time period for each group, then


title: Difference in differences

text: But this is the expression for the treatment effect that was given in the formal definition and in the above table.


title: Difference in differences

text: The Card and Krueger article on minimum wage in New Jersey, published in 1994, is considered one of the most famous DID studies; Card was later awarded the 2021 Nobel Memorial Prize in Economic Sciences in part for this and related work. Card and Krueger compared employment in the fast food sector in New Jersey and in Pennsylvania, in February 1992 and in November 1992, after New Jersey's minimum wage rose from $4.25 to $5.05 in April 1992. Observing a change in employment in New Jersey only, before and after the treatment, would fail to control for omitted variables such as weather and macroeconomic conditions of the region. By including Pennsylvania as a control in a difference-in-differences model, any bias caused by variables common to New Jersey and Pennsylvania is implicitly controlled for, even when these variables are unobserved. Assuming that New Jersey and Pennsylvania have parallel trends over time, Pennsylvania's change in employment can be interpreted as the change New Jersey would have experienced, had they not increased the minimum wage, and vice versa. The evidence suggested that the increased minimum wage did not induce a decrease in employment in New Jersey, contrary to what some economic theory would suggest. The table below shows Card & Krueger's estimates of the treatment effect on employment, measured as FTEs (or full-time equivalents). Card and Krueger estimate that the $0.80 minimum wage increase in New Jersey led to a 2.75 FTE increase in employment.


title: Stereographic projection

text: In mathematics, a stereographic projection is a perspective projection of the sphere, through a specific point on the sphere (the "pole" or "center of projection"), onto a plane (the "projection plane") perpendicular to the diameter through the point. It is a smooth, bijective function from the entire sphere except the center of projection to the entire plane. It maps circles on the sphere to circles or lines on the plane, and is conformal, meaning that it preserves angles at which curves meet and thus locally approximately preserves shapes. It is neither isometric (distance preserving) nor equiareal (area preserving).


title: Stereographic projection

text: The stereographic projection gives a way to represent a sphere by a plane. The metric induced by the inverse stereographic projection from the plane to the sphere defines a geodesic distance between points in the plane equal to the spherical distance between the spherical points they represent. A two-dimensional coordinate system on the stereographic plane is an alternative setting for spherical analytic geometry instead of spherical polar coordinates or three-dimensional cartesian coordinates. This is the spherical analog of the Poincaré disk model of the hyperbolic plane.


title: Stereographic projection

text: Intuitively, the stereographic projection is a way of picturing the sphere as the plane, with some inevitable compromises. Because the sphere and the plane appear in many areas of mathematics and its applications, so does the stereographic projection; it finds use in diverse fields including complex analysis, cartography, geology, and photography. Sometimes stereographic computations are done graphically using a special kind of graph paper called a stereographic net, shortened to stereonet, or Wulff net.


title: Stereographic projection

text: The stereographic projection was known to Hipparchus, Ptolemy and probably earlier to the Egyptians. It was originally known as the planisphere projection. "Planisphaerium" by Ptolemy is the oldest surviving document that describes it. One of its most important uses was the representation of celestial charts. The term "planisphere" is still used to refer to such charts.


title: Stereographic projection

text: In the 16th and 17th century, the equatorial aspect of the stereographic projection was commonly used for maps of the Eastern and Western Hemispheres. It is believed that already the map created in 1507 by Gualterius Lud was in stereographic projection, as were later the maps of Jean Roze (1542), Rumold Mercator (1595), and many others. In star charts, even this equatorial aspect had been utilised already by the ancient astronomers like Ptolemy.


title: Stereographic projection

text: François d'Aguilon gave the stereographic projection its current name in his 1613 work "Opticorum libri sex philosophis juxta ac mathematicis utiles" (Six Books of Optics, useful for philosophers and mathematicians alike).


title: Stereographic projection

text: In the late 16th century, Thomas Harriot proved that the stereographic projection is conformal; however, this proof was never published and sat among his papers in a box for more than three centuries. In 1695, Edmond Halley, motivated by his interest in star charts, was the first to publish a proof. He used the recently established tools of calculus, invented by his friend Isaac Newton.


title: Stereographic projection

text: The unit sphere in three-dimensional space is the set of points such that . Let be the "north pole", and let be the rest of the sphere. The plane runs through the center of the sphere; the "equator" is the intersection of the sphere with this plane.


title: Stereographic projection

text: For any point on , there is a unique line through and , and this line intersects the plane in exactly one point , known as the stereographic projection of onto the plane.


title: Stereographic projection

text: In Cartesian coordinates on the sphere and on the plane, the projection and its inverse are given by the formulas


title: Stereographic projection

text: In spherical coordinates on the sphere (with the zenith angle, , and the azimuth, ) and polar coordinates on the plane, the projection and its inverse are


title: Stereographic projection

text: Here, is understood to have value when = 0. Also, there are many ways to rewrite these formulas using trigonometric identities. In cylindrical coordinates on the sphere and polar coordinates on the plane, the projection and its inverse are


title: Stereographic projection

text: Some authors define stereographic projection from the north pole (0, 0, 1) onto the plane , which is tangent to the unit sphere at the south pole (0, 0, −1). The values and produced by this projection are exactly twice those produced by the equatorial projection described in the preceding section. For example, this projection sends the equator to the circle of radius 2 centered at the origin. While the equatorial projection produces no infinitesimal area distortion along the equator, this pole-tangent projection instead produces no infinitesimal area distortion at the south pole.


title: Stereographic projection

text: In general, one can define a stereographic projection from any point on the sphere onto any plane such that


title: Stereographic projection

text: As long as meets these conditions, then for any point other than the line through and meets in exactly one point , which is defined to be the stereographic projection of "P" onto "E".


title: Stereographic projection

text: More generally, stereographic projection may be applied to the unit -sphere in ()-dimensional Euclidean space . If is a point of and a hyperplane in , then the stereographic projection of a point is the point of intersection of the line with . In Cartesian coordinates (, from 0 to ) on and (, from 1 to "n") on , the projection from is given by


title: Stereographic projection

text: Still more generally, suppose that is a (nonsingular) quadric hypersurface in the projective space . In other words, is the locus of zeros of a non-singular quadratic form in the homogeneous coordinates . Fix any point on and a hyperplane in not containing . Then the stereographic projection of a point in is the unique point of intersection of with . As before, the stereographic projection is conformal and invertible outside of a "small" set. The stereographic projection presents the quadric hypersurface as a rational hypersurface. This construction plays a role in algebraic geometry and conformal geometry.


title: Stereographic projection

text: The first stereographic projection defined in the preceding section sends the "south pole" (0, 0, −1) of the unit sphere to (0, 0), the equator to the unit circle, the southern hemisphere to the region inside the circle, and the northern hemisphere to the region outside the circle.


title: Stereographic projection

text: The projection is not defined at the projection point = (0, 0, 1). Small neighborhoods of this point are sent to subsets of the plane far away from (0, 0). The closer is to (0, 0, 1), the more distant its image is from (0, 0) in the plane. For this reason it is common to speak of (0, 0, 1) as mapping to "infinity" in the plane, and of the sphere as completing the plane by adding a point at infinity. This notion finds utility in projective geometry and complex analysis. On a merely topological level, it illustrates how the sphere is homeomorphic to the one-point compactification of the plane.


title: Stereographic projection

text: In Cartesian coordinates a point on the sphere and its image on the plane either both are rational points or none of them:


title: Stereographic projection

text: Stereographic projection is conformal, meaning that it preserves the angles at which curves cross each other (see figures). On the other hand, stereographic projection does not preserve area; in general, the area of a region of the sphere does not equal the area of its projection onto the plane. The area element is given in coordinates by


title: Stereographic projection

text: Along the unit circle, where , there is no inflation of area in the limit, giving a scale factor of 1. Near (0, 0) areas are inflated by a factor of 4, and near infinity areas are inflated by arbitrarily small factors.


title: Stereographic projection

text: and is the unique formula found in Bernhard Riemann's "Habilitationsschrift" on the foundations of geometry, delivered at Göttingen in 1854, and entitled "Über die Hypothesen welche der Geometrie zu Grunde liegen".


title: Stereographic projection

text: No map from the sphere to the plane can be both conformal and area-preserving. If it were, then it would be a local isometry and would preserve Gaussian curvature. The sphere and the plane have different Gaussian curvatures, so this is impossible.


title: Stereographic projection

text: Circles on the sphere that do "not" pass through the point of projection are projected to circles on the plane. Circles on the sphere that "do" pass through the point of projection are projected to straight lines on the plane. These lines are sometimes thought of as circles through the point at infinity, or circles of infinite radius. These properties can be verified by using the expressions of formula_11 in terms of formula_12 given in : using these expressions for a substitution in the equation formula_13 of the plane containing a circle on the sphere, and clearing denominators, one gets the equation of a circle, that is, a second-degree equation with formula_14 as its quadratic part. The equation becomes linear if formula_15 that is, if the plane passes through the point of projection.


title: Stereographic projection

text: All lines in the plane, when transformed to circles on the sphere by the inverse of stereographic projection, meet at the projection point. Parallel lines, which do not intersect in the plane, are transformed to circles tangent at projection point. Intersecting lines are transformed to circles that intersect transversally at two points in the sphere, one of which is the projection point. (Similar remarks hold about the real projective plane, but the intersection relationships are different there.)


title: Stereographic projection

text: where the parameter measures the "tightness" of the loxodrome. Thus loxodromes correspond to logarithmic spirals. These spirals intersect radial lines in the plane at equal angles, just as the loxodromes intersect meridians on the sphere at equal angles.


title: Stereographic projection

text: The stereographic projection relates to the plane inversion in a simple way. Let and be two points on the sphere with projections and on the plane. Then and are inversive images of each other in the image of the equatorial circle if and only if and are reflections of each other in the equatorial plane.


title: Stereographic projection

text: Stereographic projection plots can be carried out by a computer using the explicit formulas given above. However, for graphing by hand these formulas are unwieldy. Instead, it is common to use graph paper designed specifically for the task. This special graph paper is called a stereonet or Wulff net, after the Russian mineralogist George (Yuri Viktorovich) Wulff.


title: Stereographic projection

text: The Wulff net shown here is the stereographic projection of the grid of parallels and meridians of a hemisphere centred at a point on the equator (such as the Eastern or Western hemisphere of a planet).


title: Stereographic projection

text: In the figure, the area-distorting property of the stereographic projection can be seen by comparing a grid sector near the center of the net with one at the far right or left. The two sectors have equal areas on the sphere. On the disk, the latter has nearly four times the area of the former. If the grid is made finer, this ratio approaches exactly 4.


title: Stereographic projection

text: On the Wulff net, the images of the parallels and meridians intersect at right angles. This orthogonality property is a consequence of the angle-preserving property of the stereographic projection. (However, the angle-preserving property is stronger than this property. Not all projections that preserve the orthogonality of parallels and meridians are angle-preserving.)


title: Stereographic projection

text: For an example of the use of the Wulff net, imagine two copies of it on thin paper, one atop the other, aligned and tacked at their mutual center. Let be the point on the lower unit hemisphere whose spherical coordinates are (140°, 60°) and whose Cartesian coordinates are (0.321, 0.557, −0.766). This point lies on a line oriented 60° counterclockwise from the positive -axis (or 30° clockwise from the positive -axis) and 50° below the horizontal plane . Once these angles are known, there are four steps to plotting :


title: Stereographic projection

text: To plot other points, whose angles are not such round numbers as 60° and 50°, one must visually interpolate between the nearest grid lines. It is helpful to have a net with finer spacing than 10°. Spacings of 2° are common.


title: Stereographic projection

text: To find the central angle between two points on the sphere based on their stereographic plot, overlay the plot on a Wulff net and rotate the plot about the center until the two points lie on or near a meridian. Then measure the angle between them by counting grid lines along that meridian.


title: Stereographic projection

text: Although any stereographic projection misses one point on the sphere (the projection point), the entire sphere can be mapped using two projections from distinct projection points. In other words, the sphere can be covered by two stereographic parametrizations (the inverses of the projections) from the plane. The parametrizations can be chosen to induce the same orientation on the sphere. Together, they describe the sphere as an oriented surface (or two-dimensional manifold).


title: Stereographic projection

text: This construction has special significance in complex analysis. The point in the real plane can be identified with the complex number . The stereographic projection from the north pole onto the equatorial plane is then


title: Stereographic projection

text: define a stereographic projection from the south pole onto the equatorial plane. The transition maps between the - and -coordinates are then and , with approaching 0 as goes to infinity, and "vice versa". This facilitates an elegant and useful notion of infinity for the complex numbers and indeed an entire theory of meromorphic functions mapping to the Riemann sphere. The standard metric on the unit sphere agrees with the Fubini–Study metric on the Riemann sphere.


title: Stereographic projection

text: The set of all lines through the origin in three-dimensional space forms a space called the real projective plane. This plane is difficult to visualize, because it cannot be embedded in three-dimensional space.


title: Stereographic projection

text: However, one can visualize it as a disk, as follows. Any line through the origin intersects the southern hemisphere  ≤ 0 in a point, which can then be stereographically projected to a point on a disk in the XY plane. Horizontal lines through the origin intersect the southern hemisphere in two antipodal points along the equator, which project to the boundary of the disk. Either of the two projected points can be considered part of the disk; it is understood that antipodal points on the equator represent a single line in 3 space and a single point on the boundary of the projected disk (see quotient topology). So any set of lines through the origin can be pictured as a set of points in the projected disk. But the boundary points behave differently from the boundary points of an ordinary 2-dimensional disk, in that any one of them is simultaneously close to interior points on opposite sides of the disk (just as two nearly horizontal lines through the origin can project to points on opposite sides of the disk).


title: Stereographic projection

text: Also, every plane through the origin intersects the unit sphere in a great circle, called the "trace" of the plane. This circle maps to a circle under stereographic projection. So the projection lets us visualize planes as circular arcs in the disk. Prior to the availability of computers, stereographic projections with great circles often involved drawing large-radius arcs that required use of a beam compass. Computers now make this task much easier.


title: Stereographic projection

text: Further associated with each plane is a unique line, called the plane's "pole", that passes through the origin and is perpendicular to the plane. This line can be plotted as a point on the disk just as any line through the origin can. So the stereographic projection also lets us visualize planes as points in the disk. For plots involving many planes, plotting their poles produces a less-cluttered picture than plotting their traces.


title: Stereographic projection

text: This construction is used to visualize directional data in crystallography and geology, as described below.


title: Stereographic projection

text: Stereographic projection is also applied to the visualization of polytopes. In a Schlegel diagram, an -dimensional polytope in is projected onto an -dimensional sphere, which is then stereographically projected onto . The reduction from to can make the polytope easier to visualize and understand.


title: Stereographic projection

text: In elementary arithmetic geometry, stereographic projection from the unit circle provides a means to describe all primitive Pythagorean triples. Specifically, stereographic projection from the north pole (0,1) onto the -axis gives a one-to-one correspondence between the rational number points on the unit circle (with ) and the rational points of the -axis. If is a rational point on the -axis, then its inverse stereographic projection is the point


title: Stereographic projection

text: The pair of trigonometric functions can be thought of as parametrizing the unit circle. The stereographic projection gives an alternative parametrization of the unit circle:


title: Stereographic projection

text: The fundamental problem of cartography is that no map from the sphere to the plane can accurately represent both angles and areas. In general, area-preserving map projections are preferred for statistical applications, while angle-preserving (conformal) map projections are preferred for navigation.


title: Stereographic projection

text: Stereographic projection falls into the second category. When the projection is centered at the Earth's north or south pole, it has additional desirable properties: It sends meridians to rays emanating from the origin and parallels to circles centered at the origin.


title: Stereographic projection

text: The stereographic is the only projection that maps all circles on a sphere to circles on a plane. This property is valuable in planetary mapping where craters are typical features. The set of circles passing through the point of projection have unbounded radius, and therefore degenerate into lines.


title: Stereographic projection

text: In crystallography, the orientations of crystal axes and faces in three-dimensional space are a central geometric concern, for example in the interpretation of X-ray and electron diffraction patterns. These orientations can be visualized as in the section Visualization of lines and planes above. That is, crystal axes and poles to crystal planes are intersected with the northern hemisphere and then plotted using stereographic projection. A plot of poles is called a pole figure.


title: Stereographic projection

text: In electron diffraction, Kikuchi line pairs appear as bands decorating the intersection between lattice plane traces and the Ewald sphere thus providing "experimental access" to a crystal's stereographic projection. Model Kikuchi maps in reciprocal space, and fringe visibility maps for use with bend contours in direct space, thus act as road maps for exploring orientation space with crystals in the transmission electron microscope.


title: Stereographic projection

text: Researchers in structural geology are concerned with the orientations of planes and lines for a number of reasons. The foliation of a rock is a planar feature that often contains a linear feature called lineation. Similarly, a fault plane is a planar feature that may contain linear features such as slickensides.


title: Stereographic projection

text: These orientations of lines and planes at various scales can be plotted using the methods of the Visualization of lines and planes section above. As in crystallography, planes are typically plotted by their poles. Unlike crystallography, the southern hemisphere is used instead of the northern one (because the geological features in question lie below the Earth's surface). In this context the stereographic projection is often referred to as the equal-angle lower-hemisphere projection. The equal-area lower-hemisphere projection defined by the Lambert azimuthal equal-area projection is also used, especially when the plot is to be subjected to subsequent statistical analysis such as density contouring.