title: Ponta Delgada

text: At the beginning of the 20th century, Ponta Delgada's position was relatively high (eighth largest), although the changing importance of rural economies steadily chipped away at its growth. But it remained the central place in the economy and hierarchy of the Azorean archipelago. Consequently, it was at the forefront of political change following the Carnation Revolution. In one such event, property owners and right-leaning farmers challenged the Civil Governor António Borges Coutinho, who was responsible, under the direction of the MFA government, to implement land reforms. The Micalense Farmers' Protest, forced his resignation, and inspired a series of terrorist acts that plunged the Azores into political turmoil. After a clandestine round-up of arrests and detentions by the Military Governor, the Autonomous District of Ponta Delgada was extinguished, along with the other districts (Horta and Angra do Heroísmo) on 22 August 1975, with the establishment of the "Junta Regional dos Açores" ("Regional Junta of the Azores"), the provisional government that assumed the competencies of the administration during the region's transition to constitutional autonomy.


title: Ponta Delgada

text: The municipality of Ponta Delgada is one of the larger administrative divisions in the archipelago, extending from the center of the island to the western coast. Ponta Delgada is bordered on the northeast by the municipality of Ribeira Grande, and southeast by relatively new municipality of Lagoa.


title: Ponta Delgada

text: Geomorphologically, Ponta Delgada covers a volcanic area composed of two structures: the Picos Region and Sete Cidades Massif. The "Picos Region" extends from the shadow of the ancient volcano of the Água de Pau Massif (known locally for the lake that rests within its volcanic crater: "Lagoa do Fogo") until the area around the Sete Cidades caldera. It is a volcanic axial zone oriented generally in a northwest–southeast direction, essentially defined by several spatter cones and lava flows and predominantly covered by dense vegetation and pasture lands. Its relief is relatively planar, especially along the northern and southern coasts, where many of the urban communities are located.


title: Ponta Delgada

text: The "Sete Cidades Massif", the other geomorphological structure that makes up the municipality of Ponta Delgada, consists of a central volcanic caldera and lake-filled cones which surround the crater. It occupies the extreme western part of the island, oriented along a similar northwest–southwest orientation, with many regional radial fractures marked by lava domes and spatter cones. The Sete Cidades Volcano at the center of the Massif consists of a caldera and a polygenetic volcanic field within it, that includes four lakes (two of which Lagoa Azul, the Blue Lake, and "Lagoa Verde", the Green Lake, are linked). The caldera is almost circular and has evolved over the course of three phases. The first occurred 36,000 years ago forming the collapsed principal structure. The second phase conforms to a period approximately 29,000 years ago, when volcanic eruptions collapsed the northwest part of the structure. Finally, the third phase (about 16,000 years ago) caused the collapse of the north and northeastern portions of the caldera. Geologically, within the last 5,000 years, the central cone has been active (17 eruptions) and responsible for causing most of the activity in the archipelago, during that period. These geological eruptions were essentially trachyte eruptions of the sub-Plinian or Plinian type, with hydro-magmatic characteristics. The last eruption, at about 500 years ago, gave rise to the "Caldeira Seca" cone. Although there has been no historical activity today, its active status continues to be debated by the scientific community.


title: Ponta Delgada

text: Most recently, its diverse geography includes various types of basaltic volcanism, both effusive and less explosive (essentially Strombolian and Hawaiian) along its flanks, usually conditioned by local and radial faults. The Mosteiros Graben is also an important feature in this area, representing collapse of lands on the northwestern flank of the caldera. Although there are no active aerial volcanic characteristics (like the fumaroles of Furnas), submarine vents around the region of Ponta da Ferraria and the beach at Mosteiros have been identified.


title: Ponta Delgada

text: Ponta Delgada has a mild maritime climate, which, according to Köppen, straddles a Mediterranean and a humid subtropical climate ("Csa" / "Cfa"). It has warm summers, with moderate precipitation, and mild, wet winters. Much like the rest of the Azores, the city is shaped by the Gulf Stream, and consequently has a narrow temperature variation. Mean temperatures vary between in the winter to around in the summer and daytime highs vary between in the winter to in the summer. The average annual relative humidity is around 80%, which may influence the perceived temperature by a few degrees in the warmer months. Temperatures above , or below have never been registered.


title: Ponta Delgada

text: The Gulf Stream also contributes to an unstable weather that varies greatly during autumn and spring, making weather forecasting on a daily basis difficult. Winters are generally milder and summers are generally humid when compared to those of continental Portugal. Its location is one of the limits for pressure measurement to verify the North Atlantic Oscillation (NAO).


title: Ponta Delgada

text: Much like other communities in the archipelago of the Azores, the municipality is shaped by its geography; most homes are clustered along the regional road network that circles the island, with many ancillary or agricultural access roads bisecting the central portion of the island (primarily in the "Picos Region") along a north–south axis.


title: Ponta Delgada

text: Administratively, the municipality is composed of 24 parishes, that handle development, in the defense of local social, cultural, recreation and environmental concerns:


title: Ponta Delgada

text: Along the southern coast is the urbanized core of the historic village/town of Ponta Delgada, which includes the principal civic infrastructures, high-capacity motorways (), tourist and culture attractions, as well as the businesses and government services. This "city" of Ponta Delgada includes specifically the civil parishes of Santa Clara, São José, São Sebastião and São Pedro, which is divided by the motorways with the urbanized contour of Fajã de Cima and Fajã de Baixo. Not to be confused with a traditional city, the "city" of Ponta Delgada has no legal jurisdiction or mayor, but the "municipality" of Ponta Delgada has an elected official, the "Presidente da Câmara Municipal" who administers and "Assembleia Municipal", which is the representative council, while dispersed parish councils (and elected presidents) govern the localities that circle the western edge of São Miguel.


title: Ponta Delgada

text: The urban core includes the "baixa" or "lower town", referring to the historic centre of buildings, shops and landmarks that gathered over the centuries around the square of São Sebastião and "Praça Gonçalo Velho" (dedicated to the island's discoverer). Immediately around this urban core are the municipal hall, the gates to the city () and old customhouse buildings in front of the main roadway that follows the coast (itself passing the Fort of São Brás and "Campo do São Francisco" in the west). Other important landmarks include the "Portas do Mar" ("Gates of the Sea"), main tower of the SolMar Avenida Center mall and Theatre Micalense.


title: Ponta Delgada

text: With a strong concentration of service activities, the municipality is an important industrial and agricultural centre. The Arrifes-Covoada basin is the main bread-basket on the island of São Miguel, in addition to all the parishes located around the rim of the Sete Cidades Massif.


title: Ponta Delgada

text: In 1999, 1039 companies had their operational seats within the borders of Ponta Delgada, roughly equal to 45.4% of the companies of the Azores. Of these companies, 4.4% were in the primary sector, 13.7% in secondary industries and 81.9% in the tertiary service sector. The volume of sales (in 2000) was equivalent to 1,458 million Euros, associated with the service industry, of which banking, computer programming/services, corporate and commercial services, as well as tourism, dominate.


title: Ponta Delgada

text: Tourist activity in Ponta Delgada accounted for 34% of the hotel occupancy in the region, of which 46% were overnight trips (1997).


title: Ponta Delgada

text: In addition, Ponta Delgada is the centre of administrative services in the region, with many of the governmental secretariats located in this municipal seat (including the Regional Presidency and several directorates).


title: Ponta Delgada

text: Several newspapers are published in Ponta Delgada, including Açoriano Oriental (one of the oldest continuing daily newspapers in the country) and the Diário dos Açores.


title: Ponta Delgada

text: Served by an international airport in the parish of Relva (Ponta Delgada-João Paulo II International Airport), the municipality is the principal port of entry for goods entering and people arriving in the Azores. SATA International and SATA Air Açores have their head offices in Ponta Delgada.


title: Ponta Delgada

text: Near the harbour of Ponta Delgada a broad gauge railway was used several times to build and enlarge the harbor. The track used a seven-foot gauge, but it is unclear if this was Isambard Kingdom Brunel's Brunel gauge.


title: Ponta Delgada

text: Three bus routes operate in the city on weekdays from 07:00 to 19:00. Line A runs in the western part of town, line B in the central/north, and line C in the east. There are bus services between Ponta Delgada and most other towns on the island, but usually only a few times a day. City services and island-wide services are both accessible along "Avenida D. Infante Henriques" and conveniently accessible from major sites in Ponta Delgada. Up to date schedules are available at bus stops and the tourist office. Distances on the island are short with journeys rarely longer than 90 minutes.


title: Ponta Delgada

text: Ponta Delgada is home to the central nucleus of the University of the Azores, a multi-disciplinary institution that ranges from courses in tourism, computer engineering, social sciences and business management. From its principal campus in São Pedro, the rectory manages three poles spread throughout the Azores, including Horta (with courses in Marine Biology, affiliated with the "Department of Oceangraphy and Fishing") and Angra do Heroísmo (with a broad course calendar of courses in teaching, business and agricultural sciences).


title: Ponta Delgada

text: Ponta Delgada is the traditional centre of the annual religious celebrations associated with the Feasts of the Lord Holy Christ of the Miracles (), from the Saint Francis Square (), located opposite the Fort of São Brás. This venerable feast day and week-long celebrations primarily focus on the fifth Sunday of Easter, attracting locals and Micaelense, in addition to peoples from neighbouring islands in the archipelago, the Portuguese diaspora, and tourists on vacation. Associated with the Roman Catholic veneration of an "Ecce Homo" representing Jesus Christ following the Passion (retold in Luke 23:1–25 in the New Testament), a gift to the sisters of the Convent of Caloura in the mid-16th century, the event paralyzes the streets of the city for a day.


title: Ponta Delgada

text: Following the images' move to the Convent of Our Lady of Hope (), under the inspiration of the Venerable Mother Teresa da Anunciada, the figure was used in religious processions that snaked through the streets of the city, stopping at each convent (and former-convent) in the city. The cortege, which includes clergy, politicians, and lay folk, is a popular event, attracting both religious (to the procession, sanctuary and open-air mass) and secular participants (to view and see the procession, imagery and taste traditional foods from the "barracas" located along the main avenue).


title: Ponta Delgada

text: Following Pentecosts, many of the parishes within the municipality participate in feasts dedicated to the Holy Spirit. A tradition across the islands of the Azores, the Cult of the Holy Spirit dates to medieval traditions, involving "promises" made to God (), the processions of faith to and from the Church and feasts of meat-broth soup and bread donated to the poor. In comparison to other islands/parishes of the Azores, most neighbourhoods of São Miguel allow the free participation of visitors, seen as fulfilling the tenets of the tradition, rather than the narrow sub-community of the Brotherhoods of the Holy Spirit.


title: Ponta Delgada

text: One of the more popular non-religious events is the "Noites de Verão" ("Nights of Summer"): a summer event, traditionally held in the square of "Campo do São Francisco", but in recent years dispersed throughout the streets of the city. Attracting families, friends and tourists to the downtown, highlighted by nightly musical events, popular Azorean bands/singers, guest concert bands, folklore groups, and some international stars, in addition to vendor concessions selling food, refreshments or small goods. Starting usually in late June, the "Summer Nights" run until late September (four months), and is sponsored/supported by the municipal government and local/regional businesses.


title: Ponta Delgada

text: In addition to several parks providing green-spaces for multiple recreational activities, the city of Ponta Delgada is home to sporting associations and sites for racket sports, organized team and open-air activities. In addition to multiple water sports, such as swimming, surfing, and canoeing/kayaking, there are cycling routes and spaces for running/walking. Visitors to the region have access to tourist companies providing excursions to island trails, all-terrain paths and sea oriented activities such as diving, sport fishing, and boat tours.


title: Ponta Delgada

text: Home to the Ponta Delgada Football Association, the region has a storied history of football that includes teams that have made it to the 1st and 2nd Divisions of the National Football League. Among them are Club Desportivo Santa Clara (Primeira Liga), Clube União Micaelense, (Portuguese Second Division) and Marítimo da Calheta (São Miguel Regional Championship League).


title: Self/less

text: Self/less is a 2015 American science fiction action thriller film directed by Tarsem Singh, produced by Ram Bergman and James D. Stern and written by Alex and David Pastor. The film tells the story of a business tycoon and billionaire named Damian Hale, who is diagnosed with a terminal illness. However, he manages to save his life with the aid of Professor Albright, who transfers Hale's consciousness into a new, younger body. The film stars Ryan Reynolds, Natalie Martinez, Matthew Goode, Victor Garber, Derek Luke, and Ben Kingsley. Many of the film's elements are similar to the 1966 film "Seconds".


title: Self/less

text: "Self/less" was originally set to release on February 27, 2015, but because of multiple setbacks, it was not released until July 10, 2015. It was produced by Endgame Entertainment and was financed by Filmnation Entertainment. The film grossed $12 million in North America and a total of $30 million worldwide, against a $26 million production budget.


title: Self/less

text: Billionaire New Yorker Damian Hale is diagnosed with terminal cancer. He finds a business card directing him to Professor Albright, who informs him about a medical procedure called "shedding", in which one's consciousness is transferred into a new body. Damian agrees to the procedure and follows Albright's instructions to stage his own public death. Albright then transfers him into a new, younger body, and prescribes medication to alleviate the vivid hallucinations which he claims are side effects of the procedure.


title: Self/less

text: Damian starts a new life in New Orleans under the incognito name of Edward Kidner and is quickly befriended by his neighbor Anton. He later forgets to take his medicine and has hallucinations of a woman and child. Damian (as Edward) questions Albright, who dismisses it, but accidentally mentions details of the hallucinations that Damian had not disclosed.


title: Self/less

text: Albright then arranges for Damian to take a vacation in Hawaii, but Damian, convinced the hallucinations are a real memory, identifies a landmark he saw in his vision and heads to a farmhouse outside of St. Louis. There, he finds the woman, Madeline, who reacts to him as her apparently deceased husband Mark. Damian plays along as Mark, though he is shocked to learn that Mark may have sold himself to Albright, in order to pay for their daughter Anna's life-saving treatment. Damian and Madeline are suddenly attacked by Albright's men, including Anton. Damian fatally wounds Anton and kills his accomplices, then flees with Madeline to collect Anna from school.


title: Self/less

text: At a nearby motel, Damian then uses a laptop to research additional details regarding "shedding", and discovers that a man named Dr. Francis Jensen, now deceased, was the pioneer researcher in the field of transhumanism. In a video, Damian notices a tic Jensen shares with Albright, then sees Albright sitting next to Jensen, deducing that Jensen may have shed his consciousness into Albright's body.


title: Self/less

text: Damian then finds Jensen's wife, Phyllis, in a nursing home, but she is living with Alzheimer's and remembers nothing. Damian lures Jensen (Albright) to the facility, where he reveals that the pills are meant to fully eliminate the original personalities of the bodies used in the shedding procedure, telling Damian that without the pills, Damian's consciousness will die, and Mark's will re-emerge.


title: Self/less

text: Jensen later escapes when more killers arrive. Damian is almost overpowered, but Madeline wounds the attacker, who proves to be Anton in a new body. Anton reveals that he has shed multiple times. While Damian confiscates Anton's pills, Anton taunts Madeline to ask her "husband" why he cannot answer personal questions about their life.


title: Self/less

text: Madeline then confronts "Mark" over his lack of knowledge of their personal details, causing Damian to reveal the entire story. He takes her and Anna to his old friend Martin O'Neill, and convinces Martin to arrange for Madeline and Anna to flee to the Caribbean. When he and Madeline discover Anna playing with Martin's previously deceased child Tony, Martin admits that he allowed Tony to also use shedding, and that Jensen's men are coming. Damian then reveals shedding's secret to Martin, who reacts in shock and disgust. Damian distracts Jensen's men while Martin flees with the others. Damian again fatally injures Anton, but the other thugs realize that Damian is alone and turn to recapture Madeline and Anna.


title: Self/less

text: Damian then purposely stops taking his medicine to experience more of Mark's memories, which reveal that Jensen has a lab in an abandoned warehouse. Jensen captures him and starts to shed Anton into Mark's body. Damian, remembering that metal interferes with the process, hides a bullet casing in his mouth, causing the Shedding Machine to malfunction and destroy Anton's consciousness. Masquerading as Anton, Damian then rescues the others. Although Jensen tries to claim that Damian needs him to survive, Martin was able to reverse-engineer the pills and give Damian the formula, allowing Damian to safely torch Jensen to death with a flamethrower. After killing Jensen, he has Martin complete Madeline and Anna's escape to the Caribbean.


title: Self/less

text: Damian later visits his estranged daughter Claire but does not reveal his presence inside Mark, simply giving her a letter that reconciles Claire with her father. Damian then travels to the Caribbean and fully stops taking his medicine. The real Mark then slowly re-emerges, and finds a video message from Damian thanking him for the time that he gave to him. The story concludes with Mark finally reuniting with his family.


title: Self/less

text: Endgame Entertainment and FilmDistrict financed the film, quickly putting it into development after the success of the two companies' science fiction movie "Looper". FilmNation pre-sold the film at Cannes in 2013. It was the first film to completely sell out at the festival. The strong pre-sales limited the two financiers' exposure to the budget. FilmDistrict was set to distribute the film in the United States, but the company shut down and was absorbed into Universal's subsidiary Focus Features.


title: Self/less

text: Principal photography began in October 2013 in New Orleans. Scenes were filmed at the Commander's Palace and the Howling Wolf. A sequence shortly after the film begins, depicting Hale in his elaborate Manhattan apartment, was shot in the three-story Trump Tower penthouse that served as Donald and Melania Trump's primary residence until 2017.


title: Self/less

text: Antônio Pinto composed the film score. Dudu Aram was credited for additional music, as he had been on other scores by Pinto.


title: Self/less

text: The film was originally set for release on February 27, 2015. On July 2, 2014, the feature's opening was rescheduled to April 17, 2015. On November 8, 2014, the studio once again postponed the release, to July 10, 2015. The first trailer was released on March 4, 2015.


title: Self/less

text: On May 20, 2015, Focus Features relaunched its Gramercy Pictures label for action, horror and science fiction movies. "Self/less" was to be released under the label, but Gramercy branding was absent from the final release. The revival of the Gramercy label would turn out to be short-lived.


title: Self/less

text: "Self/less" was released in North America, Sweden and Turkey on July 10, 2015. In North America, it opened in 2,353 theaters, earning $5.4 million in its opening weekend and ranking number eight at the domestic box office. In Turkey, the film opened in fifth place, making $135,191 from 208 screens, and stayed in the box office for six weeks, finishing with a total of $495,953. It opened in Italy on September 10, 2015, and finished in seventh place with a total of $353,291. "Self/less" would gross $12.3 million in North America and $18.2 million in other territories, for a total of $30.5 million against a production budget of $26.0 million.


title: Self/less

text: The review aggregator website Rotten Tomatoes reports a rating of based on reviews, and an average rating of . The site's consensus reads: ""Self/less" boasts a potential-packed premise, but does frustratingly little with it, settling for lackluster action at the expense of interesting ideas." On Metacritic, the film has a score of 34 out of 100, based on the reviews of 30 critics, indicating "generally unfavorable reviews". In CinemaScore polls, audiences gave "Self/less" an average grade of B+ on an A+ to F scale.


title: Self/less

text: The IGN review by Josh Lasser awarded it a score of 5.0 out of 10, saying, "For someone with great visual command of the medium, Singh's latest is a disappointment."


title: Gillette Stadium

text: Gillette Stadium is a multi-purpose stadium located in the town of Foxborough, Massachusetts, which is southwest of downtown Boston. It serves as the home stadium and administrative offices for both the New England Patriots of the National Football League (NFL) and the New England Revolution of Major League Soccer (MLS). It opened in 2002, replacing the adjacent Foxboro Stadium. It also served as the home venue for the University of Massachusetts (UMass) Minutemen football team in 2012 and 2013, while on-campus Warren McGuirk Alumni Stadium underwent renovations; it continued to serve as a part-time home venue for higher attendance UMass games through 2018. Gillette Stadium's seating capacity is 65,878, including 5,876 club seats and 89 luxury suites.


title: Gillette Stadium

text: The town of Foxborough approved plans for the stadium's construction on December 6, 1999, and work on the stadium began on March 24, 2000. The first official event at the stadium was a New England Revolution soccer game on May 11, 2002. Jeremiah Freed was the opening band at the WBCN River Rave on June 9, making them the first band to play at the stadium. Grand opening ceremonies were held on September 9, when the Patriots unveiled their Super Bowl XXXVI championship banner before a Monday Night Football game against the Pittsburgh Steelers. The stadium was originally known as CMGI Field before the naming rights were bought by Gillette after the "dot-com" bust. Although Gillette was acquired by Procter & Gamble in 2005, the stadium retains the Gillette name. In September 2010, Gillette and the Patriots announced that their partnership, which includes naming rights to the stadium, would extend through the 2031 season. Additionally, uBid (a wholly owned subsidiary of CMGI until 2003) continues to sponsor one of the main entrance gates to the stadium as of 2009.


title: Gillette Stadium

text: Gillette Stadium is accessible by rail via the Providence/Stoughton and Franklin lines at the Foxboro MBTA station, but only during Patriots games and some concerts. The Patriots have sold out every home game since moving to the stadium—preseason, regular season, and playoffs. This streak dates back to the 1994 season at Foxboro Stadium; by September 2016, it had reached 231 games. The stadium is owned and operated by Kraft Sports Group, a subsidiary of the Kraft Group, the company through which businessman Robert Kraft owns the Patriots and Revolution.


title: Gillette Stadium

text: From 1971 to 2001, the Patriots played all of their home games at Foxboro Stadium. The stadium was privately funded on an extremely small budget and featured few amenities. Its aluminum benches would freeze over during cold-weather games and it had an unorganized dirt parking lot.


title: Gillette Stadium

text: Foxboro Stadium did not bring in the profits needed to keep an NFL team in New England; at just over 60,000 seats, it was one of the NFL's smallest stadiums.


title: Gillette Stadium

text: In 1984, team executive Chuck Sullivan funded the Victory Tour of The Jacksons, in an attempt to earn more profit for the team. Tickets sales failed, however, and the team's debt increased even further – to a final total of US$126 million. After two unsuccessful owners bought the team and stadium, it was clear that a new stadium had to be built for the team to stay in New England. This is when other cities in the New England area, including Boston (which was previously home to the Patriots), Hartford, and Providence became interested in building new stadiums to lure the Patriots away from Foxborough.


title: Gillette Stadium

text: The first major stadium proposal from another city came in September 1993. Lowell Weicker, the Governor of Connecticut, proposed to the Connecticut General Assembly that a new stadium should be built in Hartford to attract the Patriots to move there, stating that a stadium had "potentially great benefit" if it were built. The bill passed in the State Assembly on September 27, 1993.


title: Gillette Stadium

text: Back in Massachusetts, there was a proposal to build a "Megaplex" in Boston, which would be the site of the stadium, as well as a new Fenway Park (the home park of the Boston Red Sox) and a convention center. The proposed sites for this hybrid convention center-stadium were along Summer Street in South Boston or at the so-called Crosstown site along Melnea Cass Boulevard in Roxbury, adjacent to Boston's South End. The administration of Massachusetts Governor William Weld pushed for construction of a full "Megaplex" at the crosstown site, with then-new Boston Mayor Thomas Menino favoring construction of a new, stand-alone convention center in South Boston. Ultimately, the residents of neither of these neighborhoods wanted a stadium, and as a result, Menino backed out, fearing that it would affect his chance at re-election. The Fenway Park plan was cancelled after many "Save Fenway Park!" groups popped up to save the historic ballpark.


title: Gillette Stadium

text: Kraft then began a plan to build a new stadium in South Boston. In that plan, Kraft was to pay for the stadium himself, hoping to win the support of Weld and Menino. He began to sketch designs, but the project was leaked to the press in December 1996. The residents of South Boston objected to a stadium being built in that location, causing Menino and Weld to become angry at Kraft. Kraft abandoned all plans for a Boston Stadium after the affair. In January 1997, Kraft began talks with Providence mayor Vincent Cianci to relocate the team to Providence and build a new stadium there. The proposed 68,000-seat domed stadium would have cost $250 million, and would have been paid through income taxes, public bonds, surcharges on tickets, and private funds. Residents of the neighborhood of the proposed project were extremely opposed to the project because the surrounding area would have needed massive infrastructure improvements. The proposal fell through after a few weeks.


title: Gillette Stadium

text: During a news conference in September 1998, the team revealed plans to build a new stadium in Foxborough, keeping the team in Massachusetts. It was to be funded by the state as well as Kraft himself. This plan brought more competition from Connecticut, as a $1 billion plan to renovate an area of Hartford, including building a stadium. Kraft then signed an agreement to move the team to Hartford on November 18, 1998. The proposed stadium included 68,000 seats, 60 luxury boxes, and had a projected cost of $375 million. As before in Boston and Providence, construction of the stadium was challenged by the residents. Problems with the site were discovered, and an agreement could not be reached regarding the details of the stadium. The entire plan eventually fell through, enraging then Connecticut governor John G. Rowland, who lobbied hard for the stadium and spent weeks deliberating with Robert Kraft. Rowland announced at a press conference that he was officially "a New York Jets fan, now and probably forever". In 1999, the team officially announced that it would remain in Foxborough, which led to Gillette Stadium's construction. After the Hartford proposal fell through, Robert Kraft paid for 100% of the construction costs, a rare instance of an NFL owner privately financing the construction of a stadium.


title: Gillette Stadium

text: On April 18, 2000, the team revealed plans for the new stadium in Foxborough. It was announced as a 68,000-seat stadium at a cost of $325 million, with the entire cost privately funded. Boston is thus the only city in professional sports in which all facilities are privately owned and operated. The Kraft Group (owner of the NFL team the Patriots and the MLS team the Revolution) owns Gillette Stadium, the Red Sox own Fenway Park, and TD Garden is owned by Delaware North (the owner of the Bruins) (the Celtics rent the TD Garden from Delaware North).


title: Gillette Stadium

text: Concurrently announced was a new road to access the stadium from U.S. Route 1, and an additional 3,000 parking spaces to accommodate the increased number of fans.


title: Gillette Stadium

text: The stadium was designed by HOK Sport (now Populous). Kraft wanted it modeled on M&T Bank Stadium which had opened in Baltimore in 1998. Kraft insisted on it having a "front door" with a Disneyland-like entrance. Populous went through 200 designs before coming up with one that Kraft liked. The entrance includes a lighthouse (which was originally designed to shoot a light high) and a bridge modeled on Boston's Longfellow Bridge. The lighthouse and bridge are now featured on the stadium's logo.


title: Gillette Stadium

text: For the first eight years of its existence the stadium used a video display, with a smaller LED scoreboard just beneath it, at each end of the field. The south side also had a large LED scoreboard in addition to the smaller one. In 2010, the stadium installed two new HD Daktronics video displays to replace the entire previous setup at both ends. At the time of their construction, the larger screen, at 41.5 feet tall and 164 feet wide (12.6 m x 50.0 m), was the second-largest video monitor in any NFL stadium; only AT&T Stadium had a larger one.


title: Gillette Stadium

text: Gillette Stadium ranks first among all NFL venues in stadium food safety with a 0% critical violations. The Gillette Stadium food service, instead of being outsourced like most NFL teams, is run in-house and is led by the Patriots executive director of foods and beverage David Wheeler.


title: Gillette Stadium

text: Marking the 20th anniversary of the September 11 attacks, a memorial garden was installed outside Gillette Stadium. It has a semicircle of six flowering trees, a commemorative plaque, a mural and tribute stones with the names of the victims.


title: Gillette Stadium

text: On December 10, 2021, a $225 million renovation project was announced. Construction began in January 2022 and is set to be completed prior to the 2023 NFL season. The renovations include a new 22,000 square-foot outdoor video board to be installed at the north end, the largest video board of its kind in the United States. A new lighthouse, which will tower 218 feet into the sky, will provide 360-degree views of the stadium, Patriot Place, the town of Foxborough, and beyond. 75,000 square feet of hospitality and function spaces will be constructed to connect the East and West Putnam Clubs, the Dell Technology Suite Levels, and the upper concourse. The construction of these new spaces will connect all levels 360 degrees. A new plaza and fan entrance will also be built on the north end.


title: Gillette Stadium

text: The venue has hosted the NFL's nationally–televised primetime season–opening games in 2002, 2004, 2005, 2015, 2017, and 2019 (when the Patriots unveiled their championship banners from Super Bowls XXXVI, XXXVIII, XXXIX, XLIX, LI, and LIII. The first ever NFL game at the stadium was held on September 9, 2002 against the Pittsburgh Steelers, a 30-14 Patriots victory. The stadium's first playoff game was held the next year following the 2003 regular season. Playing in the Divisional Round against the Tennessee Titans, the Patriots hosted the coldest game (, wind chill) in New England Patriots history. The Patriots won 17–14. The stadium also played host to the 2003 AFC Championship Game, in which the Patriots defeated the Indianapolis Colts 24–14.


title: Gillette Stadium

text: The Patriots won the first seven playoff games held at the stadium between the 2003 and 2007 seasons, including the 2007 AFC Championship Game, where they beat the San Diego Chargers to improve to 18-0 and advance to Super Bowl XLII. On January 10, 2010, the Baltimore Ravens beat the Patriots 33–14, giving the Patriots their first home loss in the playoffs in Gillette Stadium. The Patriots suffered their second consecutive home playoff loss on January 16, 2011 in a 28–21 New York Jets victory. During the 2011-12 NFL playoffs, the Patriots defeated the Denver Broncos, 45–10, and the stadium hosted its third AFC Championship, where they won against the Baltimore Ravens, 23–20. However, the New York Giants ruined the Patriots' season by beating them in the Super Bowl for the second time. The following year, they again hosted the AFC Championship game, where they lost 28–13 to the Baltimore Ravens in the final game for long term Patriots radio announcer Gil Santos. During the Divisional Round of the 2014-15 NFL playoffs, the Patriots avenged their 2012 defeat by the Baltimore Ravens by beating them 35–31. The following week, they defeated the Indianapolis Colts 45–7 in the 2014 AFC Championship. The stadium hosted its sixth AFC Championship game during the 2016 playoffs, as the Patriots defeated the Pittsburgh Steelers 36–17. The seventh AFC Championship hosted at Gillette Stadium came the next year, when the Patriots knocked off the Jacksonville Jaguars by a score of 24–20. In the 2018 season, Gillette Stadium hosted a Divisional Round game, as the Patriots knocked off the Los Angeles Chargers by a score of 41–28 on the way to winning Super Bowl LIII. In Tom Brady's final game as a Patriot, were upset by the Tennessee Titans in the First Round of the 2019 playoffs with a loss of 20–13. Entering the 2021 season, the Patriots had an all time playoff record of 19-4 at the stadium.


title: Gillette Stadium

text: As part of the UMass football program's move to Division I FBS, the Minutemen played all of their home games at Gillette Stadium for the 2012 and 2013 seasons. The stadium is 95 miles away from the UMass campus in Amherst—the longest trip of any FBS member. The Minutemen's on-campus stadium, Warren McGuirk Alumni Stadium, was not suitable for FBS football in its previous configuration. Its small size (17,000 seats) would have made it prohibitively difficult to meet FBS average attendance requirements, and its press box and replay facilities were well below Mid-American Conference standards. Additionally, several nonconference teams would not even consider playing games in Amherst. McGuirk Stadium was renovated to FBS standards for the 2014 season, but the Minutemen's current deal with the Kraft Group calls for the Minutemen to play four of their home games in Foxborough from 2014 to 2016 in exchange for keeping part of the revenue from ticket sales. Moving forward, Gillette will continue to host UMass football with those games of anticipated larger attendance.


title: Gillette Stadium

text: Gillette Stadium also hosted the eighth edition of the NHL Winter Classic, between the Boston Bruins and Montreal Canadiens, on January 1, 2016.


title: Gillette Stadium

text: Memorable Major League Soccer playoff victories include wins over the Chicago Fire in the 2005 and 2007 Eastern Conference Final, sending the Revs to the MLS Cup. Additionally, the venue hosted MLS Cup 2002, four games of the 2003 FIFA Women's World Cup, and some Copa America Centenario matches in 2016.


title: Gillette Stadium

text: The crowd of 61,316 drawn to the 2002 MLS Cup Final was the largest stand-alone MLS post-season crowd on record until the 2018 MLS Cup in Atlanta at Mercedes-Benz Stadium.


title: Gillette Stadium

text: Gillette Stadium hosted the NCAA Men's Lacrosse Championships in 2008, 2009, 2012, 2017, and 2018 and was the home of the Boston Cannons for the 2015 season.


title: Gillette Stadium

text: On February 15, 2019, the Premier Lacrosse League announced that Boston would be the first city on the schedule for the 2019 season. It was also announced that Gillette Stadium would be the venue to host the league on June 1 and 2. The PLL was planning on returning to Gillette for the 2020 season, but the COVID-19 pandemic put the season on pause and the league scrapped their 2020 schedule.


title: Gillette Stadium

text: On June 2, 2019, Gillette will host a handful of games for the Women's Professional Lacrosse League to start their 2019 season.


title: Gillette Stadium

text: On November 14, 2006, two days after a rainstorm contributed to the deterioration of the grass surface in a Patriots game against the Jets, team management decided to replace the natural grass surface with a synthetic surface, FieldTurf. Normally, NFL rules insist that such work could only be done during the off-season; however, the grass field was in such poor condition, the league agreed to waive the rule. The entire job was done during a two-week road trip, with three shifts working around the clock. The Patriots' first game on the surface was a victory over the previously 9–1 Chicago Bears on November 26. Brady and his teammates commended the much-improved surface. At the conclusion of the 2007 season, Patriots quarterback Tom Brady had a career record of 31–3 on artificial turf. The team lost a preseason matchup in August 2007 to the Tennessee Titans on the new FieldTurf but otherwise won its first eleven regular-season and playoff games on the surface covering the period of November 2006 until September 2008, when the Patriots lost to the Miami Dolphins.


title: Gillette Stadium

text: In February 2010, the surface was pulled and upgraded to FieldTurf "Duraspine Pro", which was expected to meet FIFA standards that the previous turf did not, preventing the team from having to place sod on top of their turf to host international soccer matches.


title: Gillette Stadium

text: The surface was upgraded again in April 2014 to FieldTurf "Revolution" with "VersaTile" drainage system. The FieldTurf Revolution product is currently used at many venues across North America, including Lumen Field (home to the NFL's Seattle Seahawks and MLS's Seattle Sounders) and Providence Park, home of the MLS's Portland Timbers, where its installation was recently completed.


title: Gillette Stadium

text: When the field is configured for American football, the Patriots have their "Flying Elvis" logo (or "Pat Patriot" if they are wearing throwback uniforms) painted on the field at dead center of the 50-yard line. Off to both sides along the 50-yard line, the Gillette Stadium logo is also painted on the field. This is a gray-and-blue stylized representation of the bridge and tower at the north entrance of the stadium.


title: Gillette Stadium

text: In 2006, the Patriots and Kraft announced plans to build a "super regional lifestyle and entertainment center" in the area around Gillette Stadium named Patriot Place. The cost of the project was $350 million, more than the cost to build Gillette Stadium itself; Kraft had purchased much of the surrounding land, about , when he bought Foxboro Stadium in the late 1980s.


title: Gillette Stadium

text: The first phase of the project opened in fall of 2007, and featured the first Bass Pro Shops in New England, as well as Circuit City (now closed), Bed Bath & Beyond, Five Guys Burgers, Christmas Tree Shops, and Staples. In December 2007, the Patriots and CBS announced plans to build a themed restaurant and nightclub, named "CBS Scene", at the site, which would also include studios for CBS-owned WBZ-TV. The restaurant was part of the second phase of the project, which included an open mall, a health center, a Cinema de Lux movie theater, a four-star Renaissance hotel, and "The Hall at Patriot Place." Attached to Gillette Stadium, the Hall includes a two-level interactive museum honoring the Patriots accomplishments and Super Bowl championships, plus the Patriots Pro Shop. The first restaurants and stores in phase two began opening in July 2008, and were followed by the openings of the Hall at Patriot Place and the CBS Scene in time for the beginning of the 2008 New England Patriots season. More locations, including the health center and hotel, opened in 2009, along with additional sites in phase one.


title: Gillette Stadium

text: From January 18, 2021 to June 14, 2021, Gillette Stadium was used as a mass distribution site for the COVID-19 vaccine, with a total of 610,283 shots being administered.


title: Hyperbola

text: In mathematics, a hyperbola (; pl. hyperbolas or hyperbolae ; adj. hyperbolic ) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows. The hyperbola is one of the three kinds of conic section, formed by the intersection of a plane and a double cone. (The other conic sections are the parabola and the ellipse. A circle is a special case of an ellipse.) If the plane intersects both halves of the double cone but does not pass through the apex of the cones, then the conic is a hyperbola.


title: Hyperbola

text: Each branch of the hyperbola has two arms which become straighter (lower curvature) further out from the center of the hyperbola. Diagonally opposite arms, one from each branch, tend in the limit to a common line, called the asymptote of those two arms. So there are two asymptotes, whose intersection is at the center of symmetry of the hyperbola, which can be thought of as the mirror point about which each branch reflects to form the other branch. In the case of the curve formula_1 the asymptotes are the two coordinate axes.


title: Hyperbola

text: Hyperbolas share many of the ellipses' analytical properties such as eccentricity, focus, and directrix. Typically the correspondence can be made with nothing more than a change of sign in some term. Many other mathematical objects have their origin in the hyperbola, such as hyperbolic paraboloids (saddle surfaces), hyperboloids ("wastebaskets"), hyperbolic geometry (Lobachevsky's celebrated non-Euclidean geometry), hyperbolic functions (sinh, cosh, tanh, etc.), and gyrovector spaces (a geometry proposed for use in both relativity and quantum mechanics which is not Euclidean).


title: Hyperbola

text: The word "hyperbola" derives from the Greek , meaning "over-thrown" or "excessive", from which the English term hyperbole also derives. Hyperbolae were discovered by Menaechmus in his investigations of the problem of doubling the cube, but were then called sections of obtuse cones. The term hyperbola is believed to have been coined by Apollonius of Perga (c. 262–c. 190 BC) in his definitive work on the conic sections, the "Conics".


title: Hyperbola

text: The names of the other two general conic sections, the ellipse and the parabola, derive from the corresponding Greek words for "deficient" and "applied"; all three names are borrowed from earlier Pythagorean terminology which referred to a comparison of the side of rectangles of fixed area with a given line segment. The rectangle could be "applied" to the segment (meaning, have an equal length), be shorter than the segment or exceed the segment.


title: Hyperbola

text: A hyperbola can be defined geometrically as a set of points (locus of points) in the Euclidean plane:


title: Hyperbola

text: The midpoint formula_8 of the line segment joining the foci is called the "center" of the hyperbola. The line through the foci is called the "major axis". It contains the "vertices" formula_9, which have distance formula_10 to the center. The distance formula_11 of the foci to the center is called the "focal distance" or "linear eccentricity". The quotient formula_12 is the "eccentricity" formula_13.


title: Hyperbola

text: If formula_15 is the circle with midpoint formula_16 and radius formula_17, then the distance of a point formula_3 of the right branch to the circle formula_15 equals the distance to the focus formula_20:


title: Hyperbola

text: formula_15 is called the "circular directrix" (related to focus formula_16) of the hyperbola. In order to get the left branch of the hyperbola, one has to use the circular directrix related to formula_20. This property should not be confused with the definition of a hyperbola with help of a directrix (line) below.


title: Hyperbola

text: If the "xy"-coordinate system is rotated about the origin by the angle formula_25 and new coordinates formula_26 are assigned, then formula_27.


title: Hyperbola

text: A rotation of the original hyperbola by formula_43 results in a rectangular hyperbola entirely in the second and fourth quadrants, with the same asymptotes, center, semi-latus rectum, radius of curvature at the vertices, linear eccentricity, and eccentricity as for the case of formula_25 rotation, with equation


title: Hyperbola

text: Shifting the hyperbola with equation formula_49 so that the new center is formula_50, yields the new equation


title: Hyperbola

text: The two lines at distance formula_55 from the center and parallel to the minor axis are called directrices of the hyperbola (see diagram).


title: Hyperbola

text: For an arbitrary point formula_3 of the hyperbola the quotient of the distance to one focus and to the corresponding directrix (see diagram) is equal to the eccentricity:


title: Hyperbola

text: The proof for the pair formula_58 follows from the fact that formula_59 and formula_60 satisfy the equation


title: Hyperbola

text: The "inverse statement" is also true and can be used to define a hyperbola (in a manner similar to the definition of a parabola):


title: Hyperbola

text: For any point formula_62 (focus), any line formula_63 (directrix) not through formula_62 and any real number formula_13 with formula_66 the set of points (locus of points), for which the quotient of the distances to the point and to the line is formula_13


title: Hyperbola

text: The directrix formula_63 has equation formula_74. With formula_75, the relation formula_76 produces the equations


title: Hyperbola

text: This is the equation of an "ellipse" (formula_81) or a "parabola" (formula_82) or a "hyperbola" (formula_83). All of these non-degenerate conics have, in common, the origin as a vertex (see diagram).


title: Hyperbola

text: Because of formula_90 point formula_91 of directrix formula_92 (see diagram) and focus formula_20 are inverse with respect to the circle inversion at circle formula_94 (in diagram green). Hence point formula_95 can be constructed using the theorem of Thales (not shown in the diagram). The directrix formula_92 is the perpendicular to line formula_97 through point formula_95. <br>


title: Hyperbola

text: "Alternative construction of formula_95": Calculation shows, that point formula_95 is the intersection of the asymptote with its perpendicular through formula_20 (see diagram).


title: Hyperbola

text: The intersection of an upright double cone by a plane not through the vertex with slope greater than the slope of the lines on the cone is a hyperbola (see diagram: red curve). In order to prove the defining property of a hyperbola (see above) one uses two Dandelin spheres formula_102, which are spheres that touch the cone along circles formula_103 , formula_104 and the intersecting (hyperbola) plane at points formula_20 and formula_16. It turns out: formula_5 are the "foci" of the hyperbola.


title: Hyperbola

text: The definition of a hyperbola by its foci and its circular directrices (see above) can be used for drawing an arc of it with help of pins, a string and a ruler:


title: Hyperbola

text: The following method to construct single points of a hyperbola relies on the Steiner generation of a non degenerate conic section:


title: Hyperbola

text: For the generation of points of the hyperbola formula_145 one uses the pencils at the vertices formula_9. Let formula_147 be a point of the hyperbola and formula_148. The line segment formula_149 is divided into n equally-spaced segments and this division is projected parallel with the diagonal formula_126 as direction onto the line segment formula_151 (see diagram). The parallel projection is part of the projective mapping between the pencils at formula_152 and formula_153 needed. The intersection points of any two related lines formula_154 and formula_155 are points of the uniquely defined hyperbola.


title: Hyperbola

text: "Remark:" The subdivision could be extended beyond the points formula_111 and formula_113 in order to get more points, but the determination of the intersection points would become more inaccurate. A better idea is extending the points already constructed by symmetry (see animation).


title: Hyperbola

text: A hyperbola with equation formula_158 is uniquely determined by three points formula_159 with different "x"- and "y"-coordinates. A simple way to determine the shape parameters formula_160 uses the "inscribed angle theorem" for hyperbolas:


title: Hyperbola

text: An affine transformation of the Euclidean plane has the form formula_173, where formula_111 is a regular matrix (its determinant is not 0) and formula_175 is an arbitrary vector. If formula_176 are the column vectors of the matrix formula_111, the unit hyperbola formula_178 is mapped onto the hyperbola


title: Hyperbola

text: formula_175 is the center, formula_181 a point of the hyperbola and formula_182 a tangent vector at this point.


title: Hyperbola

text: In general the vectors formula_176 are not perpendicular. That means, in general formula_184 are "not" the vertices of the hyperbola. But formula_185 point into the directions of the asymptotes. The tangent vector at point formula_186 is


title: Hyperbola

text: Because at a vertex the tangent is perpendicular to the major axis of the hyperbola one gets the parameter formula_188 of a vertex from the equation


title: Hyperbola

text: Solving the parametric representation for formula_194 by Cramer's rule and using formula_195, one gets the implicit representation


title: Hyperbola

text: The definition of a hyperbola in this section gives a parametric representation of an arbitrary hyperbola, even in space, if one allows formula_197 to be vectors in space.


title: Hyperbola

text: Because the unit hyperbola formula_172 is affinely equivalent to the hyperbola formula_199, an arbitrary hyperbola can be considered as the affine image (see previous section) of the hyperbola formula_200


title: Hyperbola

text: formula_202 is the center of the hyperbola, the vectors formula_203 have the directions of the asymptotes and formula_204 is a point of the hyperbola. The tangent vector is


title: Hyperbola

text: The following properties of a hyperbola are easily proven using the representation of a hyperbola introduced in this section.


title: Hyperbola

text: and hence independent of point formula_3. The last equation follows from a calculation for the case, where formula_3 is a vertex and the hyperbola in its canonical form formula_219


title: Hyperbola

text: For a hyperbola with parametric representation formula_220 (for simplicity the center is the origin) the following is true:


title: Hyperbola

text: This property provides a possibility to construct points of a hyperbola if the asymptotes and one point are given.


title: Hyperbola

text: For simplicity the center of the hyperbola may be the origin and the vectors formula_224 have equal length. If the last assumption is not fulfilled one can first apply a parameter transformation (see above) in order to make the assumption true. Hence formula_225 are the vertices, formula_226 span the minor axis and one gets formula_227 and formula_228.


title: Hyperbola

text: For the intersection points of the tangent at point formula_229 with the asymptotes one gets the points


title: Hyperbola

text: formula_233 is the area of the rhombus generated by formula_224. The area of a rhombus is equal to one half of the product of its diagonals. The diagonals are the semi-axes formula_85 of the hyperbola. Hence:


title: Hyperbola

text: The reciprocation of a circle "B" in a circle "C" always yields a conic section such as a hyperbola. The process of "reciprocation in a circle "C"" consists of replacing every line and point in a geometrical figure with their corresponding pole and polar, respectively. The "pole" of a line is the inversion of its closest point to the circle "C", whereas the polar of a point is the converse, namely, a line whose closest point to "C" is the inversion of the point.


title: Hyperbola

text: The eccentricity of the conic section obtained by reciprocation is the ratio of the distances between the two circles' centers to the radius "r" of reciprocation circle "C". If B and C represent the points at the centers of the corresponding circles, then


title: Hyperbola

text: Since the eccentricity of a hyperbola is always greater than one, the center B must lie outside of the reciprocating circle "C".


title: Hyperbola

text: This definition implies that the hyperbola is both the locus of the poles of the tangent lines to the circle "B", as well as the envelope of the polar lines of the points on "B". Conversely, the circle "B" is the envelope of polars of points on the hyperbola, and the locus of poles of tangent lines to the hyperbola. Two tangent lines to "B" have no (finite) poles because they pass through the center C of the reciprocation circle "C"; the polars of the corresponding tangent points on "B" are the asymptotes of the hyperbola. The two branches of the hyperbola correspond to the two parts of the circle "B" that are separated by these tangent points.


title: Hyperbola

text: A hyperbola can also be defined as a second-degree equation in the Cartesian coordinates ("x", "y") in the plane,


title: Hyperbola

text: A special case of a hyperbola—the "degenerate hyperbola" consisting of two intersecting lines—occurs when another determinant is zero:


title: Hyperbola

text: Given the above general parametrization of the hyperbola in Cartesian coordinates, the eccentricity can be found using the formula in Conic section#Eccentricity in terms of coefficients.


title: Hyperbola

text: Rotating the coordinate axes so that the "x"-axis is aligned with the transverse axis brings the equation into its canonical form


title: Hyperbola

text: For comparison, the corresponding equation for a degenerate hyperbola (consisting of two intersecting lines) is


title: Hyperbola

text: The normal line is perpendicular to the tangent line, and both pass through the same point ("x", "y").


title: Hyperbola

text: the left focus is formula_257 and the right focus is formula_258 where is the eccentricity. Denote the distances from a point ("x, y") to the left and right foci as formula_259 and formula_260 For a point on the right branch,


title: Hyperbola

text: If Cartesian coordinates are introduced such that the origin is the center of the hyperbola and the "x"-axis is the major axis, then the hyperbola is called "east-west-opening" and


title: Hyperbola

text: formula_277 and to the second focus formula_278. Hence the point formula_275 is on the hyperbola if the following condition is fulfilled


title: Hyperbola

text: Remove the square roots by suitable squarings and use the relation formula_281 to obtain the equation of the hyperbola:


title: Hyperbola

text: This equation is called the canonical form of a hyperbola, because any hyperbola, regardless of its orientation relative to the Cartesian axes and regardless of the location of its center, can be transformed to this form by a change of variables, giving a hyperbola that is congruent to the original (see below).


title: Hyperbola

text: The axes of symmetry or "principal axes" are the "transverse axis" (containing the segment of length 2"a" with endpoints at the vertices) and the "conjugate axis" (containing the segment of length 2"b" perpendicular to the transverse axis and with midpoint at the hyperbola's center). As opposed to an ellipse, a hyperbola has only two vertices: formula_283. The two points formula_284 on the conjugate axes are "not" on the hyperbola.


title: Hyperbola

text: It follows from the equation that the hyperbola is "symmetric" with respect to both of the coordinate axes and hence symmetric with respect to the origin.


title: Hyperbola

text: Two hyperbolas are geometrically similar to each other – meaning that they have the same shape, so that one can be transformed into the other by rigid left and right movements, rotation, taking a mirror image, and scaling (magnification) – if and only if they have the same eccentricity.


title: Hyperbola

text: for large values of formula_289. These two lines intersect at the center (origin) and are called "asymptotes" of the hyperbola formula_290


title: Hyperbola

text: The length of the chord through one of the foci, perpendicular to the major axis of the hyperbola, is called the "latus rectum". One half of it is the "semi-latus rectum" formula_302. A calculation shows


title: Hyperbola

text: The simplest way to determine the equation of the tangent at a point formula_305 is to implicitly differentiate the equation formula_306 of the hyperbola. Denoting "dy/dx" as "y′", this produces


title: Hyperbola

text: A particular tangent line distinguishes the hyperbola from the other conic sections. Let "f" be the distance from the vertex "V" (on both the hyperbola and its axis through the two foci) to the nearer focus. Then the distance, along a line perpendicular to that axis, from that focus to a point P on the hyperbola is greater than 2"f". The tangent to the hyperbola at P intersects that axis at point Q at an angle ∠PQV of greater than 45°.


title: Hyperbola

text: In the case formula_311 the hyperbola is called "rectangular" (or "equilateral"), because its asymptotes intersect at right angles. For this case, the linear eccentricity is formula_312, the eccentricity formula_313 and the semi-latus rectum formula_314. The graph of the equation formula_199 is a rectangular hyperbola.


title: Hyperbola

text: Using the hyperbolic sine and cosine functions formula_316, a parametric representation of the hyperbola formula_306 can be obtained, which is similar to the parametric representation of an ellipse:


title: Hyperbola

text: Exchange formula_320 and formula_321 to obtain the equation of the conjugate hyperbola (see diagram):


title: Hyperbola

text: The polar coordinates used most commonly for the hyperbola are defined relative to the Cartesian coordinate system that has its "origin in a focus" and its x-axis pointing towards the origin of the "canonical coordinate system" as illustrated in the first diagram.


title: Hyperbola

text: Just as the trigonometric functions are defined in terms of the unit circle, so also the hyperbolic functions are defined in terms of the unit hyperbola, as shown in this diagram. In a unit circle, the angle (in radians) is equal to twice the area of the circular sector which that angle subtends. The analogous hyperbolic angle is likewise defined as twice the area of a hyperbolic sector.


title: Hyperbola

text: Let formula_10 be twice the area between the formula_344 axis and a ray through the origin intersecting the unit hyperbola, and define formula_345 as the coordinates of the intersection point.


title: Hyperbola

text: Then the area of the hyperbolic sector is the area of the triangle minus the curved region past the vertex at formula_346:


title: Hyperbola

text: Other hyperbolic functions are defined according to the hyperbolic cosine and hyperbolic sine, so for example


title: Hyperbola

text: Let formula_357 be the point on the line formula_117 with the distance formula_17 to the focus formula_16 (see diagram, formula_10 is the semi major axis of the hyperbola). Line formula_362 is the bisector of the angle between the lines formula_356. In order to prove that formula_362 is the tangent line at point formula_3, one checks that any point formula_366 on line formula_362 which is different from formula_3 cannot be on the hyperbola. Hence formula_362 has only point formula_3 in common with the hyperbola and is, therefore, the tangent at point formula_3.


title: Hyperbola

text: From the diagram and the triangle inequality one recognizes that formula_372 holds, which means: formula_373. But if formula_366 is a point of the hyperbola, the difference should be formula_17.


title: Hyperbola

text: The proof of the property on midpoints is best done for the hyperbola formula_199. Because any hyperbola is an affine image of the hyperbola formula_199 (see section below) and an affine transformation preserves parallelism and midpoints of line segments, the property is true for all hyperbolas:


title: Hyperbola

text: For parallel chords the slope is constant and the midpoints of the parallel chords lie on the line formula_382


title: Hyperbola

text: Consequence: for any pair of points formula_383 of a chord there exists a "skew reflection" with an axis (set of fixed points) passing through the center of the hyperbola, which exchanges the points formula_383 and leaves the hyperbola (as a whole) fixed. A skew reflection is a generalization of an ordinary reflection across a line formula_334, where all point-image pairs are on a line perpendicular to formula_334.


title: Hyperbola

text: Because a skew reflection leaves the hyperbola fixed, the pair of asymptotes is fixed, too. Hence the midpoint formula_8 of a chord formula_388 divides the related line segment formula_389 between the asymptotes into halves, too. This means that formula_390. This property can be used for the construction of further points formula_366 of the hyperbola if a point formula_3 and the asymptotes are given.


title: Hyperbola

text: If the chord degenerates into a "tangent", then the touching point divides the line segment between the asymptotes in two halves.


title: Hyperbola

text: For a hyperbola formula_393 the intersection points of "orthogonal" tangents lie on the circle formula_394.


title: Hyperbola

text: Any hyperbola can be described in a suitable coordinate system by an equation formula_306. The equation of the tangent at a point formula_397 of the hyperbola is formula_398 If one allows point formula_397 to be an arbitrary point different from the origin, then


title: Hyperbola

text: Such a relation between points and lines generated by a conic is called pole-polar relation or just "polarity". The pole is the point, the polar the line. See Pole and polar.


title: Hyperbola

text: The arc length of a hyperbola does not have an elementary expression. The upper half of a hyperbola can be parameterized as


title: Hyperbola

text: Then the integral giving the arc length formula_418 from formula_419 to formula_420 can be computed as:


title: Hyperbola

text: After using the substitution formula_422, this can also be represented using the incomplete elliptic integral of the second kind formula_423 with parameter formula_424:


title: Hyperbola

text: where formula_62 is the incomplete elliptic integral of the first kind with parameter formula_428 and formula_429 is the Gudermannian function.


title: Hyperbola

text: Several other curves can be derived from the hyperbola by inversion, the so-called inverse curves of the hyperbola. If the center of inversion is chosen as the hyperbola's own center, the inverse curve is the lemniscate of Bernoulli; the lemniscate is also the envelope of circles centered on a rectangular hyperbola and passing through the origin. If the center of inversion is chosen at a focus or a vertex of the hyperbola, the resulting inverse curves are a limaçon or a strophoid, respectively.


title: Hyperbola

text: A family of confocal hyperbolas is the basis of the system of elliptic coordinates in two dimensions. These hyperbolas are described by the equation


title: Hyperbola

text: where the foci are located at a distance "c" from the origin on the "x"-axis, and where θ is the angle of the asymptotes with the "x"-axis. Every hyperbola in this family is orthogonal to every ellipse that shares the same foci. This orthogonality may be shown by a conformal map of the Cartesian coordinate system "w" = "z" + 1/"z", where "z"= "x" + "iy" are the original Cartesian coordinates, and "w"="u" + "iv" are those after the transformation.


title: Hyperbola

text: Other orthogonal two-dimensional coordinate systems involving hyperbolas may be obtained by other conformal mappings. For example, the mapping "w" = "z" transforms the Cartesian coordinate system into two families of orthogonal hyperbolas.


title: Hyperbola

text: Besides providing a uniform description of circles, ellipses, parabolas, and hyperbolas, conic sections can also be understood as a natural model of the geometry of perspective in the case where the scene being viewed consists of circles, or more generally an ellipse. The viewer is typically a camera or the human eye and the image of the scene a central projection onto an image plane, that is, all projection rays pass a fixed point "O", the center. The lens plane is a plane parallel to the image plane at the lens "O".


title: Hyperbola

text: These results can be understood if one recognizes that the projection process can be seen in two steps: 1) circle c and point "O" generate a cone which is 2) cut by the image plane, in order to generate the image.


title: Hyperbola

text: One sees a hyperbola whenever catching sight of a portion of a circle cut by one's lens plane. The inability to see very much of the arms of the visible branch, combined with the complete absence of the second branch, makes it virtually impossible for the human visual system to recognize the connection with hyperbolas.


title: Hyperbola

text: Hyperbolas may be seen in many sundials. On any given day, the sun revolves in a circle on the celestial sphere, and its rays striking the point on a sundial traces out a cone of light. The intersection of this cone with the horizontal plane of the ground forms a conic section. At most populated latitudes and at most times of the year, this conic section is a hyperbola. In practical terms, the shadow of the tip of a pole traces out a hyperbola on the ground over the course of a day (this path is called the "declination line"). The shape of this hyperbola varies with the geographical latitude and with the time of the year, since those factors affect the cone of the sun's rays relative to the horizon. The collection of such hyperbolas for a whole year at a given location was called a "pelekinon" by the Greeks, since it resembles a double-bladed axe.


title: Hyperbola

text: A hyperbola is the basis for solving multilateration problems, the task of locating a point from the differences in its distances to given points — or, equivalently, the difference in arrival times of synchronized signals between the point and the given points. Such problems are important in navigation, particularly on water; a ship can locate its position from the difference in arrival times of signals from a LORAN or GPS transmitters. Conversely, a homing beacon or any transmitter can be located by comparing the arrival times of its signals at two separate receiving stations; such techniques may be used to track objects and people. In particular, the set of possible positions of a point that has a distance difference of 2"a" from two given points is a hyperbola of vertex separation 2"a" whose foci are the two given points.


title: Hyperbola

text: The path followed by any particle in the classical Kepler problem is a conic section. In particular, if the total energy "E" of the particle is greater than zero (that is, if the particle is unbound), the path of such a particle is a hyperbola. This property is useful in studying atomic and sub-atomic forces by scattering high-energy particles; for example, the Rutherford experiment demonstrated the existence of an atomic nucleus by examining the scattering of alpha particles from gold atoms. If the short-range nuclear interactions are ignored, the atomic nucleus and the alpha particle interact only by a repulsive Coulomb force, which satisfies the inverse square law requirement for a Kepler problem.


title: Hyperbola

text: The hyperbolic trig function formula_431 appears as one solution to the Korteweg–de Vries equation which describes the motion of a soliton wave in a canal.


title: Hyperbola

text: As shown first by Apollonius of Perga, a hyperbola can be used to trisect any angle, a well studied problem of geometry. Given an angle, first draw a circle centered at its vertex O, which intersects the sides of the angle at points A and B. Next draw the line segment with endpoints A and B and its perpendicular bisector formula_432. Construct a hyperbola of eccentricity "e"=2 with formula_432 as directrix and B as a focus. Let P be the intersection (upper) of the hyperbola with the circle. Angle POB trisects angle AOB.


title: Hyperbola

text: To prove this, reflect the line segment OP about the line formula_432 obtaining the point P' as the image of P. Segment AP' has the same length as segment BP due to the reflection, while segment PP' has the same length as segment BP due to the eccentricity of the hyperbola. As OA, OP', OP and OB are all radii of the same circle (and so, have the same length), the triangles OAP', OPP' and OPB are all congruent. Therefore, the angle has been trisected, since 3×POB = AOB.


title: Hyperbola

text: In portfolio theory, the locus of mean-variance efficient portfolios (called the efficient frontier) is the upper half of the east-opening branch of a hyperbola drawn with the portfolio return's standard deviation plotted horizontally and its expected value plotted vertically; according to this theory, all rational investors would choose a portfolio characterized by some point on this locus.


title: Hyperbola

text: In biochemistry and pharmacology, the Hill equation and Hill-Langmuir equation respectively describe biological responses and the formation of protein–ligand complexes as functions of ligand concentration. They are both rectangular hyperbolae.


title: Olga Tokarczuk

text: Olga Nawoja Tokarczuk (; born 29 January 1962) is a Polish writer, activist, and public intellectual. She is one of the most critically acclaimed and successful authors of her generation in Poland; in 2019, she was awarded the 2018 Nobel Prize in Literature as the first Polish female prose writer for "a narrative imagination that with encyclopedic passion represents the crossing of boundaries as a form of life". For her novel "Flights", Tokarczuk has been awarded the 2018 Man Booker International Prize (translated by Jennifer Croft). Her works include "Primeval and Other Times", "Drive Your Plow Over the Bones of the Dead", and "The Books of Jacob".


title: Olga Tokarczuk

text: Tokarczuk is noted for the mythical tone of her writing. A clinical psychologist from the University of Warsaw, she has published a collection of poems, several novels, as well as other books with shorter prose works. For "Flights" and "The Books of Jacob", she won the Nike Awards, Poland's top literary prize, among other accolades; she also won five times Nike audience award. In 2015, she received the German-Polish Bridge Prize for contribution in mutual understanding between European nations. Tokarczuk faced some backlash from nationalist groups in her homeland after the publication of "The Books of Jacob", which is set in 18th-century Poland, because the novel celebrates the country’s cultural diversity.


title: Olga Tokarczuk

text: Her works have been translated into almost 40 languages, making her one of the most translated contemporary Polish writers. "The Books of Jacob", regarded as her magnum opus, was released in the UK in November 2021 after seven years of translation work, followed by release in the US in February 2022. In March, the novel was nominated for the 2022 Man Booker International Prize.


title: Olga Tokarczuk

text: Olga Tokarczuk was born in Sulechów near Zielona Góra, in western Poland. She is a daughter of two teachers, Wanda Słabowska and Józef Tokarczuk, and has a sister. Her parents were resettled from former Polish eastern regions after the Second World War; one of her grandmothers was of Ukrainian origin. The family lived in the countryside in Klenica, some 11 mi away from Zielona Góra, where her parents taught at the People's University and her father also ran a school library in which she found her love of literature. Her father was a member of the Polish United Workers' Party. Tokarczuk liked popular Henryk Sienkiewicz's novel "In Desert and Wilderness" and fairy tales, among others. They later moved south-east to Kietrz in Opolian Silesia, where she graduated from the C.K. Norwid High school. In 1979, she debuted with two short stories in prose published in youth scouting magazine "Na Przełaj" (No. 39, under the pseudonym Natasza Borodin).


title: Olga Tokarczuk

text: Tokarczuk went on to study clinical psychology at the University of Warsaw in 1980, and during her studies she volunteered in an asylum for adolescents with behavioural problems. After graduation in 1985, she moved to Wrocław and later to Wałbrzych, where she worked as a psychotherapist in 1986–89 and teachers' trainer in 1989–96. In the meantime, she published poems and reviews in the press, and published a book of poetry in 1989. Her works were awarded at Walbrzych Literary Paths (1988, 1990). Tokarczuk quit to concentrate on literature, she also said she felt "more neurotic than [her] clients." She worked doing odd jobs in London for a while, improving her English, and went for literary scholarships in the United States (1996) and in Berlin (2001/02).


title: Olga Tokarczuk

text: Tokarczuk considers herself a disciple of Carl Jung and cites his psychology as an inspiration for her literary work.


title: Olga Tokarczuk

text: Since 1998, she has lived between Krajanów and Wrocław, in Lower Silesia. Her home in Krajanów near Nowa Ruda is located in the Sudetes mountains at the multi-cultural Polish-Czech borderland. The locale has influenced her literary work; the novel "House of Day, House of Night" (1998) touches on life in the adopted home, and the action of "Drive Your Plow Over the Bones of the Dead" (2009) takes place in the picturesque Kłodzko Valley. In 1998, together with her first husband, Tokarczuk founded the Ruta publishing house, which operated until 2004. She was an organizer of the International Short Story Festival, which inaugurated in Wrocław in 2004. As a guest lecturer, she conducted prose workshops at universities in Kraków and Opole. Tokarczuk joined the editorial team of "Krytyka Polityczna" (Eng. ed. "Political Critique"), a magazine as well as large pan-regional network of institutions and activists, and currently serves on the Board of trustees of its academic and research unit – Institute for Advance Study in Warsaw. She also travelled around the world.


title: Olga Tokarczuk

text: In 2009, Tokarczuk received a literary scholarship from the Netherlands Academy of Arts and Sciences, and during her stay at the NIAS campus in Wassenaar, she wrote her novel "Drive Your Plow Over the Bones of the Dead", which was published the same year.


title: Olga Tokarczuk

text: Roman Fingas, fellow psychologist, was Tokarczuk's first husband. They married when she was 23 and later divorced; their son Zbigniew was born in 1986. Grzegorz Zygadło is her second husband. She is a vegetarian.


title: Olga Tokarczuk

text: Olga Tokarczuk's first book was published in 1989, a collection of poems entitled "Miasta w lustrach" (Cities in Mirrors). Her debut novel, "Podróż ludzi księgi" (The Journey of the Book-People), was published in 1993. A parable on two lovers' quest for the "secret of the Book" – a metaphor for the meaning of life – is set in 17th century, and portrays an expedition to a monastery in the Pyrenees on the trail of a book which reveals the mystery of life, ending with an ironic twist. It was well received by critics, and won Polish Publisher’s Prize for best debut. Ever since then, Tokarczuk’s novels and short stories have ranked her amongst the top of Polish contemporary writers of prose.


title: Olga Tokarczuk

text: The follow-up novel "E.E." (1995) plays with the conventions of the modernist psychological novel, and took its title from the initials of its protagonist, the adolescent Erna Eltzner, who develops psychic abilities. Growing up in a wealthy German-Polish family in the 1920s in Wrocław, which was at that time a German city named Breslau, she allegedly becomes a medium, a fact her mother begins to take advantage of by organizing spiritual sessions. Tokarczuk introduces the characters of scientists, the psychiatrist-patient relationship, and despite elements of spiritualism, occultism as well as gnosticism, she represents psychological realism and cognitive scepticism. Katarzyna Kantner, a literary scholar who defended her PhD thesis on the works of Olga Tokarczuk, points to C. G. Jung’s doctoral dissertation "On the Psychology and Pathology of So-Called Occult Phenomena" as an inspiration.


title: Olga Tokarczuk

text: Her third novel, "Primeval and Other Times" ("Prawiek i inne czasy", Eng. 2010), was published in 1996 and became highly successful. It is set in the fictitious village of Primeval at the very heart of Poland, which is populated by some eccentric, archetypical characters. The village, a microcosm of Europe, is guarded by four archangels, from whose perspective the book chronicles the lives of its inhabitants over a period of eight decades, beginning in the year that World War I broke out. The book presents the creation of a myth emerging before the reader’s eyes. "This is Primeval: an enclosed snow globe, a world in itself, which it may or may not be possible to ever leave. [...] And yet, as much as the town of Primeval is devastated, over and over, by history, there is also a counter dream, full of creaturely magic and wonder." Translated into many languages, with English version by Antonia Lloyd-Jones, "Primeval and Other Times" established Tokarczuk's international reputation as one of the most important representatives of Polish literature in her generation.


title: Olga Tokarczuk

text: After "Primeval and Other Times", her work began drifting away from the novel genre towards shorter prose texts and essays. Tokarczuk's next book "Szafa" (The Wardrobe, 1997) was a collection of three novella-type stories.


title: Olga Tokarczuk

text: "House of Day, House of Night" ("Dom dzienny, dom nocny", 1998, Eng. 2003), is what Tokarczuk terms the ’constellation novel’, a patchwork of loosely connected disparate stories, sketches, and essays about life past and present in the author's adopted home in Krajanów, which allow various interpretations and enable communication at a deeper, psychological level. Her goal is to make those images, fragments of narrative and motif, merge together only on entering the reader’s consciousness. While some, at least those unfamiliar with Central European history, have labeled it Tokarczuk's most "difficult" piece, it was her first book to be published in English, and was shortlisted for the International Dublin Literary Award in 2004.


title: Olga Tokarczuk

text: "House of Day, House of Night" was followed by a collection of short stories "Gra na wielu bębenkach" (Playing on Many Drums, 2001) as well as a book-length non-fiction essay "Lalka i perła" (The Doll and the Pearl, 2000), on the subject of Bolesław Prus' classic novel "The Doll". She also published a volume with three modern Christmas tales, together with her fellow writers Jerzy Pilch and Andrzej Stasiuk ("Opowieści wigilijne", 2000). "Ostatnie historie" (The Last Stories) of 2004 is an exploration of death from the perspectives of three generations, while the novel "Anna in the Tombs of the World" (2006) was a contribution to the Canongate Myth Series by Polish publisher Znak.


title: Olga Tokarczuk

text: Tokarczuk's novel "Flights" ("Bieguni", 2007, Eng. 2018) returns to the patchwork approach of essay and fiction, the major theme of which is modern day nomads. The book explores how a person moves through time and space as well as psychology of travelling. For "Flights" she has been awarded both the jury and the readers prize of Polish Nike Awards in 2008, and then the 2018 Man Booker International Prize (translation by Jennifer Croft). The novel landed on the short list for the U.S. prestigious National Book Award in the "Translated Literature" category; a panel of judges stated:


title: Olga Tokarczuk

text: In 2009 she published an existential, noir thriller novel "Drive Your Plow Over the Bones of the Dead" ("Prowadź swój pług przez kości umarłych", Eng. 2019), which is not a conventional crime story, transforming into an acid social satire. The main character and narrator is Janina Duszejko, a woman in her 60s living in a rural area at the Polish Kłodzko Valley, eccentric in perception of other humans through astrology and fond of the poetry of William Blake, from whose work the title of the book is taken. She decides to investigate the murders of members of the local hunting club, and initially explains these deaths as having been caused by wild animals taking revenge on hunters. The novel became a bestseller in Poland. It was the basis of the crime film "Spoor" (2017) directed by Agnieszka Holland, which won the Alfred Bauer Prize (Silver Bear) at the 67th Berlin International Film Festival. The English translation by Antonia Lloyd-Jones earned Tokarczuk a second nomination for the Man Booker International Prize.


title: Olga Tokarczuk

text: An epic novel "The Books of Jacob" (2014, English translation 2021 by Jennifer Croft) is a journey over seven borders, five languages, and three major religions. Beginning in 1752 at the historical eastern Galicia region, now western Ukraine, it revolves around a controversial 18th-century Polish-Jewish religious leader and mystic Jacob Frank among other historical figures, and winds up near mid-20th-century Korolówka, Poland, where a family of local Jews had hidden from the Holocaust. Frank, who founded the Frankist sect fighting for the rights and emancipation of the Jews, encouraged his followers to transgress moral boundaries, even promoting orgiastic rites. The Frankists were persecuted in the Jewish community, especially after Frank led his followers to be baptised by the Roman Catholic church. The church later imprisoned him for heresy for more than a decade, only for Frank to declare that he was the messiah. Through third-person accounts, the action takes place also in present-day Turkey, Greece, Austria and Germany, capturing regional spirit, climate as well as interesting customs. Jan Michalski Prize jury praised:


title: Olga Tokarczuk

text: In regard to the historical and ideological divides of Polish literature, the book has been characterized as anti-Sienkiewicz. It was soon acclaimed by critics and readers alike, but its reception has been hostile in some Polish nationalist circles and Olga Tokarczuk became a target of some internet hate and harassment campaign.


title: Olga Tokarczuk

text: Since its foundation in 2015, Olga Tokarczuk has become co-host of the annual Literary Heights Festival, which has included events in her village. The festival has a rich programme of cultural events such as educational sessions and workshops, debates, concerts, film screenings as well as various exhibitions.


title: Olga Tokarczuk

text: In November 2019, Tokarczuk has established a foundation with a planned wide range of activities related to literature to create progressive intellectual and artistic centre. It was declared that Polish poet Tymoteusz Karpowicz's villa in Wrocław would become its future seat. The writer allocated 10% of her Nobel financial prize to the body and, aside from her, Agnieszka Holland and Ireneusz Grin have joined the Foundation Council. The foundation has started its operations in October 2020 implementing educational programs, organizing writing contests and public debates, funding scholarships for young aspiring writers as well as, also international, residencies.


title: Olga Tokarczuk

text: Tokarczuk is a leftist, an atheist, and a feminist. She has been criticized by some nationalist groups in Poland as unpatriotic, anti-Christian and a promoter of eco-terrorism. She has denied the allegations, has described herself as a "true patriot" and said that groups criticizing her are xenophobic and damage Poland's international reputation.


title: Olga Tokarczuk

text: In 2015, after the publication of "The Books of Jacob", Tokarczuk was criticized by the Nowa Ruda Patriots association, who demanded that the town's council revoke the writer's honorary citizenship of Nowa Ruda because, as the association claimed, she had tarnished the good name of the Polish nation. Those people's postulate was supported by Senator Waldemar Bonkowski of the Law and Justice Party, according to whom Tokarczuk's literary output and public statements are in "absolute contradiction to the assumptions of the Polish historical politics". Tokarczuk asserted that she is the true patriot, not the people and groups who criticize her, and whose alleged xenophobic and racist attitudes and actions are harmful to Poland and its image abroad.


title: Olga Tokarczuk

text: In 2020, she was one of the signatories alongside other prominent writers such as Margaret Atwood, John Banville and John Maxwell Coetzee of an open letter addressed to the President of the European Commission, Ursula von der Leyen, urging the European Union "to take immediate steps to defend core European values – equality, non-discrimination, respect for minorities – which are being blatantly violated in Poland" and appealing to the Polish government to stop targeting sexual minorities and to withdraw support from organizations promoting homophobia.


title: Olga Tokarczuk

text: Olga Tokarczuk is the laureate of numerous literary awards both in and outside Poland. Her works have become the subject of several dozen academic papers and theses.


title: Olga Tokarczuk

text: Her first recognition, in 2004, was for the English translation (by Antonia Lloyd-Jones) of her 1998 novel "House of Day, House of Night", which was shortlisted for the International Dublin Literary Award.


title: Olga Tokarczuk

text: Tokarczuk has been twice awarded Nike Award, the most important Polish literary accolade – for "Flights" in 2008, and "The Books of Jacob" in 2015. She won the Nike Readers' Choice Award five times, "Primeval & Other Times" being the award's first recipient ever.


title: Olga Tokarczuk

text: In 2010, Tokarczuk received the Silver Medal for Merit to Culture – Gloria Artis. In 2013, she was awarded the Slovene Vilenica Prize.


title: Olga Tokarczuk

text: She is the recipient of the 2015 Brückepreis, the 20th edition of the award granted by the "Europa-City Zgorzelec/Görlitz". The prize is a joint undertaking of the German and Polish border twin cities aimed at advancing mutual, regional and European peace, understanding and cooperation among people of different nationalities, cultures and viewpoints. Particularly appreciated by the jury was Tokarczuk's creation of literary bridges connecting people, generations and cultures, especially residents of the border territories of Poland, Germany and the Czech Republic, who have had often different existential and historical experiences. Also stressed was Tokarczuk's "rediscovery" and elucidation of the complex multinational and multicultural past of the Lower Silesia region, an area of great political conflicts. Attending the award ceremony in Görlitz, Tokarczuk was impressed by the positive and pragmatic attitude demonstrated by the mayor of the German town in regard to the current refugee and migrant crisis, which she contrasted with the ideological uproar surrounding the issue in Poland.


title: Olga Tokarczuk

text: For "The Books of Jacob", Tokarczuk was awarded the 2016 Kulturhuset Stadsteatern International Literary Prize in Stockholm. The French translation of the novel was recognized as the 2018 "Best European novel" by France's cultural magazine "Transfuge". It also won the 2018 Swiss Jan Michalski Prize, and the 2019 French Prix Laure Bataillon for the best foreign-language book translated in the previous year.


title: Olga Tokarczuk

text: In 2018, "Flights" (English translation by Jennifer Croft) was awarded the Man Booker International Prize.


title: Olga Tokarczuk

text: A year later, "Drive Your Plow Over the Bones of the Dead" (translation by Antonia Lloyd-Jones) was shortlisted for the 2019 Man Booker International Prize.


title: Olga Tokarczuk

text: Olga Tokarczuk was awarded the 2018 Nobel Prize for Literature in 2019 for "a narrative imagination that with encyclopedic passion represents the crossing of boundaries as a form of life" and delivered the Nobel Lecture, "The Tender Narrator", on 7 December of that year. The 2018 award had been postponed due to controversy within the Nobel committee.


title: Olga Tokarczuk

text: In 2020, she received the title of an Honorary Citizen of Warsaw as a recognition of her literary achievements.


title: Olga Tokarczuk

text: In 2021, Tokarczuk received the titles of a Doctor Honoris Causa from the University of Warsaw, University of Wrocław, and then from the Kraków's Jagiellonian University. She also became Honorary Citizen of Kraków, which was the second, or maybe even the first, Poland's official capital.


title: Olga Tokarczuk

text: In March 2022, "The Books of Jacob" (translated by Jennifer Croft) was longlisted for the 2022 Man Booker International Prize, subsequently being shortlisted in April.


title: Physiognomy

text: Physiognomy (from the Greek , , meaning "nature", and , meaning "judge" or "interpreter") is the practice of assessing a person's character or personality from their outer appearance—especially the face. The term can also refer to the general appearance of a person, object, or terrain without reference to its implied characteristics—as in the physiognomy of an individual plant (see plant life-form) or of a plant community (see vegetation).


title: Physiognomy

text: Physiognomy as a practice meets the contemporary definition of pseudoscience and it is so regarded among academic circles because of its unsupported claims; popular belief in the practice of physiognomy is nonetheless still widespread. The practice was well-accepted by ancient Greek philosophers, but fell into disrepute in the Middle Ages while practised by vagabonds and mountebanks. It revived and was popularised by Johann Kaspar Lavater, before falling from favor in the late 19th century. Physiognomy in the 19th century is particularly noted as a basis for scientific racism.


title: Physiognomy

text: Notions of the relationship between an individual's outward appearance and inner character are historically ancient, and occasionally appear in early Greek poetry. Siddhars from ancient India defined as identifying personal characteristics with body features. Chinese physiognomy or Chinese face reading () reaches back at least to the Spring and Autumn period.


title: Physiognomy

text: Early indications of a developed physiognomic theory appear in 5th century BC Athens, with the works of Zopyrus (who was featured in a dialogue by Phaedo of Elis), an expert in the art. By the 4th century BC, the philosopher Aristotle frequently referred to theory and literature concerning the relationship of appearance to character. Aristotle was receptive to such an idea, evidenced by a passage in his "Prior Analytics":


title: Physiognomy

text: The first systematic physiognomic treatise is a slim volume, ("Physiognomonics"), ascribed to Aristotle, but probably of his "school", rather than created by the philosopher. The volume is divided into two parts, conjectured as originally two separate works. The first section discusses arguments drawn from nature or other races, and concentrates on the concept of human behavior. The second section focuses on animal behavior, dividing the animal kingdom into male and female types. From these are deduced correspondences between human form and character.


title: Physiognomy

text: Ancient Greek mathematician, astronomer, and scientist Pythagoras—who some believe originated physiognomics—once rejected a prospective follower named Cylon because, to Pythagoras, his appearance indicated bad character.


title: Physiognomy

text: After inspecting Socrates, a physiognomist announced he was given to intemperance, sensuality, and violent bursts of passion—which was so contrary to Socrates's image, his students accused the physiognomist of lying. Socrates put the issue to rest by saying, originally, he was given to all these vices, but had particularly strong self-discipline.


title: Physiognomy

text: The term 'physiognomy' was common in Middle English, often written as or , as in the "Tale of Beryn", a spurious addition to "The Canterbury Tales": .


title: Physiognomy

text: Physiognomy's validity was once widely accepted. Michael Scot, a court scholar for Frederick II, Holy Roman Emperor, wrote in the early 13th century concerning the subject. English universities taught physiognomy until Henry VIII of England outlawed "beggars and vagabonds playing 'subtile, crafty and unlawful games such as physnomye or 'palmestrye'" in 1530 or 1531. Around this time, scholastic leaders settled on the more erudite Greek form 'physiognomy' and began to discourage the entire concept of 'fisnamy'.


title: Physiognomy

text: Leonardo da Vinci dismissed physiognomy in the early 16th century as "false", a chimera with "no scientific foundation". Nevertheless, Leonardo believed that lines caused by facial expressions could indicate personality traits. For example, he wrote that "those who have deep and noticeable lines between the eyebrows are irascible".


title: Physiognomy

text: The principal promoter of physiognomy in modern times was the Swiss pastor Johann Kaspar Lavater (1741–1801) who was briefly a friend of Goethe. Lavater's essays on physiognomy were first published in German in 1772 and gained great popularity. These influential essays were translated into French and English.


title: Physiognomy

text: Lavater found confirmation of his ideas from the English physician-philosopher Sir Thomas Browne (1605–1682), and the Italian Giambattista Della Porta (1535–1615). Browne in his "Religio Medici" (1643) discusses the possibility of the discernment of inner qualities from the outer appearance of the face, thus:


title: Physiognomy

text: Browne also introduced the word caricature into the English language, whence much of physiognomical belief attempted to entrench itself by illustrative means, in particular through visual political satire.


title: Physiognomy

text: Della Porta's works are well represented in the Library of Sir Thomas Browne including "Of Celestial Physiognomy", in which Porta argued that it was not the stars but a person's temperament that influences their facial appearance and character. In "De humana physiognomia "(1586), Porta used woodcuts of animals to illustrate human characteristics. Both Della Porta and Browne adhered to the 'doctrine of signatures'—that is, the belief that the physical structures of nature such as a plant's roots, stem, and flower, were indicative keys (or 'signatures') to their medicinal potentials.


title: Physiognomy

text: Lavater received mixed reactions from scientists, with some accepting his research and others criticizing it. For example, the harshest critic was scientist Georg Christoph Lichtenberg, who said pathognomy, discovering the character by observing the behaviour, was more effective. Writer Hannah More complained to Horace Walpole, "In vain do we boast ... that philosophy had broken down all the strongholds of prejudice, ignorance, and superstition; and yet, at this very time ... Lavater's physiognomy books sell at fifteen guineas a set."


title: Physiognomy

text: The popularity of physiognomy grew throughout the first quarter of the 18th century and into the 19th century. It was discussed seriously by academics, who believed in its potential.