the-french-artist/wikipedia_20220301.simple_sentence_embeddings huggingface dataset:
Hyperbolic geometry 
 The hyperbolic distance between two points on the hyperboloid can then be identified with the relative rapidity between the two corresponding observers.
Hyperbolic geometry 
 It is also possible to see quite plainly the negative curvature of the hyperbolic plane, through its effect on the sum of angles in triangles and squares.
Hyperbolic geometry 
 From this we see that the sum of angles of a triangle in the hyperbolic plane must be smaller than 180°.
Hyperbolic geometry 
 In Circle Limit IV, for example, one can see that the number of angels and demons  within a distance of n from the center rises exponentially.
Hyperbolic geometry 
 The demons have equal hyperbolic area, so the area of a ball of radius n must rise exponentially in n.
Hyperbolic geometry 
 The art of crochet has been used to demonstrate hyperbolic planes with the first being made by Daina Taimina.
Hyperbolic geometry 
 In 2000, Keith Henderson demonstrated a quick-to-make paper model dubbed the "hyperbolic soccerball".
Hyperbolic geometry 
 Visions of Infinity: Tiling a hyperbolic floor inspires both mathematics and art Science News: Dec. 23, 2000; Vol.
Hyperbolic geometry 
 Java freeware for creating sketches in both the Poincaré Disk and the Upper Half-Plane Models of Hyperbolic Geometry University of New Mexico
Hyperbolic geometry 
 "The Hyperbolic Geometry Song" A short music video about the basics of Hyperbolic Geometry available at YouTube.
Hyperbolic geometry 
 More on hyperbolic geometry, including movies and equations for conversion between the different models  University of Illinois at Urbana-Champaign
Hyperbolic geometry 
 Nikolai I. Lobachevsky, Pangeometry, Translator and Editor: A. Papadopoulos,  Heritage of European Mathematics Series, Vol.
Hyperbolic geometry 
 Reynolds, William F. (1993) Hyperbolic Geometry on a Hyperboloid, American Mathematical Monthly 100:442-455.
Parallel postulate 
 Sometimes it is also called Euclid's fifth postulate, because it is the fifth postulate in Euclid's Elements.
Parallel postulate 
 If you cut a line segment with two lines, and the two interior angles the lines form add up to less than 180°, then the two lines will eventually meet if you extend them long enough.
Parallel postulate 
 Some mathematicians thought that Euclid's fifth postulate was much longer and more complicated than the other four postulates.
Parallel postulate 
 Those who tried to do it included Omar Khayyám, and later Giovanni Gerolamo Saccheri, John Wallis, Lambert, and Legendre.
Parallel postulate 
 Some mathematicians announced that they had proven the proposition from the simpler propositions, but they all turned out to be mistaken.
Parallel postulate 
 Given a straight line and a point not on this line, you can only draw one straight line through this point that will not meet the other straight line.
Parallel postulate 
 In fact, mathematicians found out that this axiom is not only similar to Euclid's fifth postulate, but has exactly the same implications.
Parallel postulate 
 Today Playfair's axiom is used more often by mathematicians than Euclid's original parallel postulate.
Parallel postulate 
 Given a straight line and a point not on this line, you cannot draw a straight line through this point that will not eventually cross the other straight line.
Parallel postulate 
 Mathematicians found that when they replaced Euclid's fifth postulate with this axiom, they were still able to prove many of Euclid's other theorems.
Parallel postulate 
 On a globe, lines of longitude appear to be parallel at the equator, but they all meet at the poles.
Parallel postulate 
 After this, mathematicians mostly stopped trying to prove the fifth postulate from the other four postulates.
Parallel postulate 
 Instead, many mathematicians began studying other geometries that do not follow Euclid's fifth postulate.
Parallel postulate 
 Given a straight line and a point not on this line, you can draw at least two straight lines through this point that will not eventually cross the other straight line.
City of London School 
 The City of London School (CLS) is a private school for boys, aged 10 to 18, next to the River Thames in the City of London.
City of London School 
 It is the brother school of the City of London School for Girls (a girls' school within the City) and of the City of London Freemen's School (a day and boarding school in Surrey).
Pedro Antonio de Alarcón 
 He gained his first literary recognition with A Witness' Diary of the African War (1859-1860), a patriotic account of the campaign.
Bobby Moore 
 Robert Frederick Chelsea "Bobby" Moore (12 April 1941 - 24 February 1993) was an English former footballer.
Wat Tyler 
 First, he was hit by William Walworth, mayor of London, and then one of the king's squires stabbed him in the stomach, killing him.
San Juan Province (Dominican Republic) 
 Since colonial times, the territory was part of Azua province until the dictator, Rafael Trujillo, made this province in 1938 with the name Benefactor with the municipalities of Las Matas de Farfán y El Cercado.
San Juan Province (Dominican Republic) 
 In 1998, Matayaya became a municipal district; Pedro Corto in 2000; Sabaneta, Arroyo Cano and Yaque in 2004; Carrera de Yeguas, Sabana Alta, El Rosario, Hato del Padre, Guanito, La Jagua, Derrumbadero and Batista in 2005; Las Maguanas-Hato Nuevo, Las Charcas de María Nova, Jinova and Jorjillo in 2006; and Las Zanjas in 2007.
San Juan Province (Dominican Republic) 
 The San Juan province has Santiago Rodríguez and Santiago provinces to the north, Azua province (and a short part of La Vega) to the east, Baoruco province to the south and Elías Piña province to the west.
San Juan Province (Dominican Republic) 
 In  (last national census), there were  people living in the San Juan province, and 139,620 () living in towns and cities.
San Juan Province (Dominican Republic) 
 Its population represents  of the total population of the country and the province is ranked as the 11th (out of 31 plus the National District) more populated province.
San Juan Province (Dominican Republic) 
 The largest city of the province is San Juan de la Maguana, its head municipality or capital, with an urban population (in ) of 71,494 inhabitants.
San Juan Province (Dominican Republic) 
 It has  of the area of the Dominican Republic and it is ranked as the 1st (out of 31 plus the National District) largest province.
San Juan Province (Dominican Republic) 
 The Cordillera Central ("Central mountain chain") is in the northern part of the province, and the Sierra de Neiba runs across the southern half.
San Juan Province (Dominican Republic) 
 The area between those two mountain ranges is the San Juan valley, which the Taínos call Maguana, meaning "small valley".
San Juan Province (Dominican Republic) 
 The highest mountain in the province is Pico Duarte, with 3,087 m. It is the highest mountain in the West Indies and is on the border with Santiago province.
San Juan Province (Dominican Republic) 
 The climate of the province is a tropical climate, hot most of the year, but it is cooler in the mountains.
San Juan Province (Dominican Republic) 
 The main economic activity of the province is farming; the main products are rice, maize, peanut, sorghum and beans.
San Luis Rey River 
 It begins in the Cleveland National Forest, near a mountain called Palomar Mountain, in several forks.
San Luis Rey River 
 The lower part of the river is polluted, but the water in the upper part of the river can be used for drinking water.
Forth Rail Bridge 
 The Forth Rail Bridge is more correctly called the Forth Bridge, but the title is to distinguish it from the nearby Forth Road Bridge).
Forth Rail Bridge 
 Built in 1890, it is a cantilever bridge design, with three major sections, each about  long, connecting to each other.
Forth Rail Bridge 
 More than 55,000 tons of steel were used, as well as 18,122 m³ of granite and over eight million rivets.
Forth Rail Bridge 
 The bridge has a speed limit of 50 mph (80 km/h) for passenger trains and 20 mph (32 km/h) for freight trains.
New River 
 The New River flows north 15 miles (25 km) through Mexico and another 66 miles (100 km) through California into the Salton Sea, the largest lake in California.
Gravitational wave 
 To make gravity waves strong enough to be detected, something very massive must accelerate very fast.
Gravitational wave 
 Sources of detectable gravitational waves include binary star systems composed of white dwarfs, neutron stars, or black holes.
Gravitational wave 
 In physics, gravitational waves are ripples in the curvature of spacetime that travel outward from the source.
Gravitational wave 
 They do not exist in the Newtonian theory of gravitation, in which physical interactions propagate at infinite speed.
Gravitational wave 
 However, the detection of gravitational waves proves the last prediction of Einstein’s general theory of relativity.
Gravitational wave 
 In 1993, the Nobel Prize in Physics was awarded for measurements of the Hulse-Taylor binary star system that suggests gravitational waves are more than mathematical anomalies.
Gravitational wave 
 This is about 40 mega parsecs or 130 mega light years away in the direction of the Constellation Hydra.
Rock pigeon 
 The rock pigeon (otherwise known as a rock dove or common pigeon) (Columba livia) is a member of the bird family Columbidae, commonly referred to as simply pigeons.
Rock pigeon 
 They can be seen scrounging around dumpsters, picking up French fries dropped near the door to a fast food restaurant, and begging from picnickers in the park.
Twelfth Night 
 A man named Antonio has rescued him from the surf; at some risk to himself, because Antonio fought against the Duke at one time.
Twelfth Night 
 Meanwhile, in Olivia's house, Sir Toby Belch (her cousin) has tricked Sir Andrew Aguecheek into supporting him, by convincing him that he could be a suitor for Olivia.
Twelfth Night 
 So with the help of Maria, Olivia's maid, and Feste, a clown, Belch plots to make a fool of the steward.
Twelfth Night 
 Belch tries to get Sir Andrew to fight a duel with Viola's "Cesario" character as she leaves but Olivia has a crush on Cesario.
Twelfth Night 
 Antonio intervenes to defend Cesario, because he thinks he is his friend Sebastian, and is arrested for piracy against Orsino.
Twelfth Night 
 Later, Belch and Sir Andrew talk to Sebastian, who does not back down from Aguecheek when challenged and beats him in the duel.
Twelfth Night 
 Adding to this confusion, Belch and Aguecheek enter claiming that Viola/Cesario has violently assaulted them.
Twelfth Night 
 Olivia and Sebastian are happily wed, and Olivia fusses at Belch and Maria for their abuse of Malvolio, who vows to get even.
Quokka 
 Like other animals in the macropod family, such as kangaroos and wallabies, the quokka  eats grass and small plants, and is mainly nocturnal.
Quokka 
 It lives on some small islands off the coast of Western Australia, mainly on Rottnest Island near Perth, and Bald Island near Albany.
Quokka 
 A small number live on the main land in the protected area of Two Peoples Bay, which they share with Gilbert's Potoroo.
Quokka 
 They can become very sick if fed with things like bread, given to them by visitors to Rottnest Island.
Quokka 
 Quokkas are not scared of people, so you are able to get quite close to them, particularly on Rottnest Island.
Quokka 
 These fines have been used in some unusual cases where quokka have been hurt or killed by visitors to Rottnest.
Quokka 
 There are a lot of quokkas living on the small offshore islands, because this is only a small area they are listed as vulnerable.
Quokka 
 On the mainland, they are attacked by dingoes, as well as introduced animals like foxes, dogs and cats.
Quokka 
 In 1696, Willem de Vlamingh thought they were rats and named the island "Rottenest", Dutch for "rat nest".
Salzburgerland 
 Salzburgerland or Salzburg (; ; literally "Salt Fortress"; ), officially Land Salzburg, (German: Land Salzburg, East Central Austro-Bavarian: Laund Soizbuerg) is one of the states of Austria.
A Mathematician's Apology 
 He spent time writing the essay instead because discovering new mathematical ideas was now too hard for him.
A Mathematician's Apology 
 He believed that mathematics should be investigated for interest, instead of for making other things like weapons.
White Hart Lane railway station 
 White Hart Lane station in Tottenham, (London) was originally a station on the Stoke Newington & Edmonton Railway.
Bruce Grove railway station 
 Bruce Grove railway station in Tottenham was originally a station on the Stoke Newington & Edmonton Railway.
Clapham Junction (disambiguation) 
 Clapham Junction rail crash, a railway disaster which happened near Clapham Junction railway station
Public transport in Enfield 
 Public transport in the London Borough of Enfield, which is northeast of the centre of London, is a mix of National Rail, London Underground and London Buses services.
List of London railway stations 
 This list, by their present names, of heavy rail passenger stations in the Greater London region excludes stations served only by the London Underground, Tramlink and Docklands Light Railway systems.
List of London railway stations 
 Other station lists for the area (whose limits are a matter of debate, see this article's Talk) are:
List of London railway stations 
 All railway stations in and around London are shown on the non-geographic copyright London Connections map.
List of London railway stations 
 Repeated links (overlinkage) in this, a list, allows finding linked articles and expanding abbreviations without scrolling searches.
List of London railway stations 
 Official names by this site  for Blackfriars, Waterloo East and eleven absolute termini (which means "route ends") (not Moorgate) all start with "London".
List of London railway stations 
 Queenstown Road is labelled "Queenstown Road (Battersea)" on maps and timetables, though its name is unique within London.
List of London railway stations 
 White, H.P. (1963) A Regional History of the Railways of Great Britain: Volume III: Greater London, Phoenix House, London
Seven Sisters station 
 Seven Sisters station is a London Overground and London Underground Victoria Line station in the Seven Sisters area of the London Borough of Haringey, north London.
Seven Sisters station 
 Seven Sisters lies between Finsbury Park and Tottenham Hale on the Victoria Line and between Stamford Hill and Bruce Grove on the London Overground from Liverpool Street Station.
Xenu 
 Scientology teaches that Xenu (pronounced  (ZEE-noo)) was the dictator of a galactic confederacy of 76 planets, who was captured and imprisoned on Earth 75 million years ago after bringing billions of his people to Earth, placing them around volcanoes and killing them by using hydrogen bombs.
Xenu 
 Xenu is very important to the beliefs of Scientology because the story of Xenu explains the believed origin of what are known as body thetans from humans.
Xenu 
 Body thetans are believed to be the essence of Xenu's people that gather around humans and cause them spiritual harm.
Xenu 
 The existence of Xenu has been reported by L. Ron Hubbard's writings and by Scientology spokesman Tommy Davis in an interview ABC affiliate KESQ-TV.
Charlotte, Princess Royal 
 The Princess Charlotte, Princess Royal (Charlotte Augusta Matilda; later Queen Charlotte of Württemberg; 29 September 1766 – 5 October 1828) was the fourth  child and oldest daughter of George III of the United Kingdom.
Henry the Young King 
 Henry the Young King (28 February 1155 – near Limoges, France, 11 June 1183) was the junior king to his father Henry II of England.
Henry the Young King 
 The meaning of this is that Henry II's territory covered much of northern France as well as England and Ireland.
Henry the Young King 
 The idea may have been to have an official deputy for legal actions when Henry was in France, and to indicate the succession to the throne.
Henry the Young King 
 According to his tutor, William Marshal, he spent his time in France going from one knights' tournament to another.
Henry the Young King 
 The boy was married as a child to Marguerite of France (1158–1197), daughter of the French King Louis VII.
Henry the Young King 
 A civil war (1173/74) occurred in which Young Henry and his mother, with Scots and French support, fought against Henry II.
Rod cell 
 Rod cells are one of two types of photoreceptor cells that can be found in the retina of the eyes of humans and other mammals.
Rod cell 
 They counted only 3 million cone cells, the other kind of receptor, which are bigger and perceive color.
Three Gorges Dam 
 The Three Gorges Dam () is a dam in the Three Gorges region on the Yangtze River in Sandouping, in the country of China.
Three Gorges Dam 
 Being one of the largest dams in the world, it also generates the biggest amount of hydroelectric power (22,250 megawatts), pushing the massive Itaipu Dam in Brazil from first place to second place.
Three Gorges Dam 
 The dam covers a lot of historic sites and has caused 1.24 million people to lose their homes under the rising water.
Three Gorges Dam 
 The Japanese drew up a plan (the Otani plan) for the dam, only to realize later that China would remain under Chinese control.
Three Gorges Dam 
 Later, in 1944, the United States helped make plans for the dam, but all work on the dam stopped in 1947, because of the Chinese Civil War.
Three Gorges Dam 
 Some new plans, such as a set of 6 new power generators under construction, became operational in the year 2011.
Three Gorges Dam 
 The Three Gorges Dam consists of a main dam wall, and a section on the right with a set of five locks, which are devices used to raise boats and ships.
Three Gorges Dam 
 While this cost seems huge, it actually was $20 billion yuan (about $3.3 billion USD) less than the original budget of $203.9 billion yuan (about $34 billion USD).
Three Gorges Dam 
 In the event of a flood, there are 22 cubic kilometers (18 million acre feet) of space behind the dam to hold back the flood waters.
Three Gorges Dam 
 In the dry season, the water is released down the river, and the reservoir level drops to prepare for the next flood.
Three Gorges Dam 
 Another reason the dam was built was for water navigation, or the transport of people and goods by ship.
Three Gorges Dam 
 Each lock is  long,  wide, and  deep, which is similar in size to the original locks of the Panama Canal, one of the biggest canals in the world.
Three Gorges Dam 
 The reservoir behind the dam floods dangerous sections of the river, so boats and ships can go safely and easily.
Three Gorges Dam 
 There is also a "ship lift" (an elevator for ships) that can lift ships that weigh up to 3,000 tons.
Three Gorges Dam 
 The Three Gorges Dam generates 22,250 megawatts, which makes it the biggest single hydroelectric power source in the world.
Three Gorges Dam 
 This is more electricity than the entire electricity generation of Glen Canyon Dam, one of the biggest dams in the United States.)
Three Gorges Dam 
 The generating capacity of the dam is 10,000 MWh (megawatt-hours), or the amount of megawatts generated per hour.
Three Gorges Dam 
 The water drops  from the reservoir to the generator, which uses a type of turbine called a Francis turbine.
Three Gorges Dam 
 The amount of water that goes into the turbine can be from 1,968 cubic feet (600 m3) to 3,116 cubic feet (950 m3) per second.
Three Gorges Dam 
 The full power (9,800 megawatts) of the north side generators was first tested on October 18, 2006, when the reservoir had risen to  above sea level.
Three Gorges Dam 
 From its completion to March 2009, the Three Gorges Dam has generated about 296,550,000 MWh (Megawatt-hours) of electricity.
Three Gorges Dam 
 Three power lines send electricity away from the dam, to three electricity grids called the East, Central, and South China grids.
Three Gorges Dam 
 Because of reducing electricity needs on fossil fuels like coal and oil, the Three Gorges Dam has saved 31 million tons of coal per year, and prevented:
Three Gorges Dam 
 Fuel saved by the dam by replacing land transportation by water transportation has cut carbon dioxide by 10 million tons.
Three Gorges Dam 
 In response to the dam, many sewage pipes that once dumped sewage straight into the Yangtze River now have to be treated.
Three Gorges Dam 
 The dam also persuaded the government of China to think seriously about the pollution in the Yangtze River and the rest of China.
Three Gorges Dam 
 A total of 1.24 million people had to move to different places because their homes were flooded by the dam.
Three Gorges Dam 
 This number is about 1.5% of the total population of Hubei Province (60.3 million) and Chongqing City (31.44 million) where the reservoir is located.
Three Gorges Dam 
 4 million more people will ultimately have to move to Chongqing from their homes near the Three Gorges Dam.
Three Gorges Dam 
 These include the endangered Siberian Crane, the Yangtze river dolphin (baiji), and Yangtze sturgeon.
Three Gorges Dam 
 The dam has stopped this dirty water from being washed away to Shanghai, and led to serious pollution problems.
Three Gorges Dam 
 The Three Gorges Dam will become much less spectacular, because the water level will rise up to  in places, reducing the depth of the canyons.
Three Gorges Dam 
 Also, because the river's silt doesn't go downstream anymore, the city of Shanghai will suffer because there has been no silt to replace land that is washed away at the river's mouth.
Three Gorges Dam 
 In a high-silt content river like the Yangtze, sediment can clog the dam's outlets, and it cannot release water.
Three Gorges Dam 
 The water would back up behind the dam and have nowhere to go, and would eventually go over the dam, making it collapse.
Three Gorges Dam 
 The Gezhouba Dam (Gezhouba Water Control Project, Chinese: 长江葛洲坝水利枢纽工程) is an afterbay (smaller dam in front) of the Three Gorges Dam.
Three Gorges Dam 
 About four dams are planned on the stretch of the Yangtze River, and they will produce 38,500 megawatts in total.
Three Gorges Dam 
 Eight dams are planned on the Jinsha River, and eight more upstream of it, and one original plan called for a dam in the Tiger Leaping Gorge, one of the deepest river canyons in the world.
Three Gorges Dam 
 This plan was, however, scrapped in December 21, 2007, because of the gorge's status as a World Heritage site.
Ericaceae 
 The genus Epacris was treated in a separate family, Epacridaceae, but Epacris is now in this family.
Alternation of generations 
 The term alternation of generations is used to describe an alternation of forms in the life cycle of  plants (and some protists).
Alternation of generations 
 In sexual reproduction, organisms have a haploid phase with one set of chromosomes and a diploid phase with two sets of chromosomes.
Alternation of generations 
 The classic example is the mosses, where the green plant is a haploid gametophyte, and the reproductive phase is the diploid sporophyte.
Alternation of generations 
 The term alternation of generations refers only to the sexual cycle: organisms may have asexual reproduction as well.
Alternation of generations 
 The term should not be confused with life cycle stages in animals, which may look very different, but where all cells have two sets of chromosomes.
Alternation of generations 
 In mosses and their relatives (Bryophytes), the haploid gametophyte is the dominant generation, and the diploid sporophytes are sporangium-bearing stalks growing from the gametophytes.
Alternation of generations 
 In ferns, the diploid sporophyte is much larger, and the haploid gametophyte is a little plant that can grow for a long time.
Alternation of generations 
 For flowering plants (Angiosperms), the sporophyte generation is almost the whole life cycle (the green plant, roots etc.)
Alternation of generations 
 Both the spores and the resulting gametophyte are haploid, meaning they have half as many chromosomes.
Alternation of generations 
 The fusion of male and female gametes (fertilization) produces a diploid zygote which develops into a new sporophyte.