the-french-artist/wikipedia_20220301.simple_sentence_embeddings huggingface dataset:
Octahedron 
 If the edge length of a regular octahedron is a, the radius of a circumscribed sphere (one that touches the octahedron at all vertices) is
Octahedron 
 The octahedron has four special orthogonal projections, centered, on an edge, vertex, face, and normal to a face.
Octahedron 
 The octahedron can also be represented as a spherical tiling, and projected onto the plane via a stereographic projection.
Octahedron 
 An octahedron with edge length  can be placed with its center at the origin and its vertices on the coordinate axes; the Cartesian coordinates of the vertices are then
Octahedron 
 In an x–y–z Cartesian coordinate system, the octahedron with center coordinates (a, b, c) and radius r is the set of all points (x, y, z) such that
Octahedron 
 Thus the volume is four times that of a regular tetrahedron with the same edge length, while the surface area is twice (because we have 8 rather than 4 triangles).
Octahedron 
 The interior of the compound of two dual tetrahedra is an octahedron, and this compound, called the stella octangula, is its first and only stellation.
Octahedron 
 Correspondingly, a regular octahedron is the result of cutting off from a regular tetrahedron, four regular tetrahedra of half the linear size (i.e. rectifying the tetrahedron).
Octahedron 
 The vertices of the octahedron lie at the midpoints of the edges of the tetrahedron, and in this sense it relates to the tetrahedron in the same way that the cuboctahedron and icosidodecahedron relate to the other Platonic solids.
Octahedron 
 One can also divide the edges of an octahedron in the ratio of the golden mean to define the vertices of an icosahedron.
Octahedron 
 This is done by first placing vectors along the octahedron's edges such that each face is bounded by a cycle, then similarly partitioning each edge into the golden mean along the direction of its vector.
Octahedron 
 There are five octahedra that define any given icosahedron in this fashion, and together they define a regular compound.
Octahedron 
 Octahedra and tetrahedra can be alternated to form a vertex, edge, and face-uniform tessellation of space, called the octet truss by Buckminster Fuller.
Octahedron 
 This is the only such tiling save the regular tessellation of cubes, and is one of the 28 convex uniform honeycombs.
Octahedron 
 The octahedron is unique among the Platonic solids in having an even number of faces meeting at each vertex.
Octahedron 
 Consequently, it is the only member of that group to possess mirror planes that do not pass through any of the faces.
Octahedron 
 Using the standard nomenclature for Johnson solids, an octahedron would be called a square bipyramid.
Octahedron 
 The octahedron is 4-connected, meaning that it takes the removal of four vertices to disconnect the remaining vertices.
Octahedron 
 It is one of only four 4-connected simplicial well-covered polyhedra, meaning that all of the maximal independent sets of its vertices have the same size.
Octahedron 
 The other three polyhedra with this property are the pentagonal dipyramid, the snub disphenoid, and an irregular polyhedron with 12 vertices and 20 triangular faces.
Octahedron 
 There are 3 uniform colorings of the octahedron, named by the triangular face colors going around each vertex: 1212, 1112, 1111.
Octahedron 
 This group's subgroups include D3d (order 12), the symmetry group of a triangular antiprism; D4h (order 16), the symmetry group of a square bipyramid; and Td (order 24), the symmetry group of a rectified tetrahedron.
Octahedron 
 The uniform tetrahemihexahedron is a tetrahedral symmetry faceting of the regular octahedron, sharing edge and vertex arrangement.
Rounder Records 
 Over the years, some of the artists and bands that have been signed to the label include Alison Krauss, Ween, and Bela Fleck.
Columbia Records 
 Over the years, some of the artists and bands that have been signed to the label include Aretha Franklin, System of a Down, Johnny Cash, Bob Dylan, Bela Fleck, Janis Joplin, Paul McCartney, John Lennon,  Prince, Willie Nelson, Dolly Parton, and hundreds of other artists.
Origin of life 
 It is not known how this early life form evolved, but scientists think it was a natural process which happened about 3,900 million years ago.
Origin of life 
 The main hypothesis which supports genetics first is the RNA world hypothesis, and the one which supports metabolism first is the protein world hypothesis.
Origin of life 
 Melvin Calvin, winner of the Nobel Prize in Chemistry, wrote a book on the subject, and so did Alexander Oparin.
Origin of life 
 What links most of the early work on the origin of life is the idea that before life began there must have been a process of chemical change.
Origin of life 
 Another question which has been discussed by J.D. Bernal and others is the origin of the cell membrane.
Origin of life 
 What we call life has only been verified in things that include RNA, mechanisms for encoding and decoding RNA, and mechanisms for building proteins from amino acids.
Origin of life 
 They were found in iron and silica-rich rocks which were once  hydrothermal vents in the Nuvvuagittuq greenstone belt of Quebec, Canada.
Origin of life 
 If this is the oldest record of life on Earth, it suggests "an almost instantaneous emergence of life" after oceans formed 4.4 billion years ago.
Origin of life 
 According to Stephen Blair Hedges, "If life arose relatively quickly on Earth… then it could be common in the universe".
Origin of life 
 A scientific study from 2002 showed that geological formations of stromatolites 3.45 billion years old contain fossilized cyanobacteria.
Origin of life 
 At the time it was widely agreed that stromatolites were the oldest known lifeforms on Earth which had left a record of its existence.
Origin of life 
 Therefore, if life originated on Earth, this happened sometime between 4.4 billion years ago, when water vapor first liquefied, and 3.5 billion years ago.
Origin of life 
 The earliest evidence of life comes from the Isua supercrustal belt in Western Greenland, and from similar formations in the nearby Akilia Islands.
Origin of life 
 With this evidence, Mojzis suggested that life existed on the planet already by 3.85 billion years ago.
Origin of life 
 A few scientists think life might have been carried from planet to planet by the transport of spores.
Origin of life 
 Until the early 19th century many people  believed in the regular spontaneous generation of life from non-living matter.
Origin of life 
 In a letter to Joseph Dalton Hooker on 11 February 1871, Charles Darwin proposed a natural process for the origin of life.
Origin of life 
 He suggested that the original spark of life may have begun in a "warm little pond, with all sorts of ammonia and phosphoric salts, lights, heat, electricity, etc.
Origin of life 
 He went on to explain that "at the present day such matter would be instantly devoured or absorbed, which would not have been the case before living creatures were formed".
Origin of life 
 No real progress was made until 1924 when Alexander Oparin reasoned that atmospheric oxygen prevented the synthesis of the organic molecules.
Origin of life 
 In his The Origin of Life, Oparin argued that a "primordial soup" of organic molecules could be created in an oxygen-less atmosphere through the action of sunlight.
Origin of life 
 These droplets would "grow" by fusion with other droplets, and "reproduce" through fission into daughter droplets, and so have a primitive metabolism in which those factors which promote "cell integrity" survive, those that do not become extinct.
Origin of life 
 Around the same time J.B.S. Haldane also suggested that the Earth's pre-biotic oceans, which were very different from what oceans are now, would have formed a "hot dilute soup".
Origin of life 
 This idea was called biopoiesis, the process of living matter evolving from self-replicating but nonliving molecules.
Origin of life 
 There was a time, between 3.8 and 4.1 billion years ago, which is known as the Late Heavy Bombardment.
Origin of life 
 Several people have suggested that the chemicals in the cell give clues as to what the early seas must have been like.
Origin of life 
 In 1926, Macallum noted that the inorganic composition of the cell cytosol dramatically differs from that of modern sea water: "the cell… has endowments transmitted from a past almost as remote as the origin of life on earth".
Origin of life 
 For example: "All cells contain much more potassium, phosphate, and transition metals than modern ... oceans, lakes, or rivers". "
Origin of life 
 Under the anoxic, CO2-dominated primordial atmosphere, the chemistry of inland basins at geothermal fields would [be like the chemistry inside] modern cells".
Origin of life 
 If life evolved in the deep ocean, near a hydrothermal vent, it could have originated as early as 4 to 4.2 billion years ago.
Origin of life 
 If, on the other hand, life originated at the surface of the planet, a common opinion is it could only have done so between 3.5 and 4 billion years ago.
Origin of life 
 Lazcano and Miller (1994) suggest that the pace of molecular evolution was dictated by the rate of recirculating water through mid-ocean submarine vents.
Origin of life 
 Complete recirculation takes 10 million years, so any organic compounds produced by then would be altered or destroyed by temperatures exceeding 300 °C.
Origin of life 
 They estimate that the development of a 100 kilobase genome of a DNA/protein primitive heterotroph into a 7000 gene filamentous cyanobacterium would have required only 7 million years.
Origin of life 
 Most organisms today need oxygen for their metabolism; only a few can use other sources for respiration.
Origin of life 
 So it is expected that the first proto-organisms were chemoautotrophs, and did not use aerobic respiration.
Origin of life 
 This was proved by the Miller–Urey experiment by Stanley L. Miller and Harold C. Urey in 1953, and we now know these basic building blocks are common throughout space.
Origin of life 
 The ribosome is critical to protein synthesis in present-day cells, but we have no idea as to how it evolved.
Origin of life 
 Early on, ribonucleic acids would have been catalysts, but later, nucleic acids are specialised for genomic use.
Origin of life 
 The origin of the basic biomolecules, while not settled, is less controversial than the significance and order of steps 2 and 3.
Origin of life 
 Estimates of these sources suggest that the heavy bombardment before 3.5 billion years ago made available quantities of organics comparable to those produced by other energy sources.
Origin of life 
 In 1953 a graduate student, Stanley Miller, and his professor, Harold Urey, performed an experiment that showed how organic molecules could have formed on early Earth from inorganic precursors.
Origin of life 
 The now-famous Miller–Urey experiment used a highly reduced mixture of gases – methane, ammonia and hydrogen – to form basic organic monomers, such as amino acids.
Origin of life 
 We do know now that for more than the first half of the Earth's history its atmosphere had almost no oxygen.
Origin of life 
 In the 1950s and 1960s, Sidney W. Fox studied the spontaneous formation of peptide structures under conditions that might have existed early in Earth's history.
Origin of life 
 These amino acids and small peptides could be encouraged to form closed spherical membranes, called microspheres.
Origin of life 
 Clay theory suggests complex organic molecules arose gradually on a pre-existing non-organic platform, namely, silicate crystals in solution.
Origin of life 
 In the 1970s, Thomas Gold proposed the theory that life first developed not on the surface of the Earth, but several kilometers below the surface.
Origin of life 
 The discovery in the late 1990s of nanobes (filamental structures that are smaller than bacteria, but that may contain DNA in deep rocks)  might support Gold's theory.
Origin of life 
 It is now reasonably well established that microbial life is plentiful at shallow depths in the Earth (up to five kilometers below the surface) in the form of extremophile archaea, rather than the better-known eubacteria (which live in more accessible conditions).
Origin of life 
 Gold asserted that a trickle of food from a deep, unreachable, source is needed for survival because life arising in a puddle of organic material is likely to consume all of its food and become extinct.
Origin of life 
 Gold's theory was that the flow of food is due to out-gassing of primordial methane from the Earth's mantle.
Origin of life 
 For example, Martin and Russel showed that cell membranes separating contents from the environment and self-organization of self-contained redox reactions are the most conserved attributes of living things.
Origin of life 
 The RNA world hypothesis proposes that life based on ribonucleic acid (RNA) pre-dates the current world of life based on deoxyribonucleic acid (DNA), RNA and proteins.
Origin of life 
 RNA is able both to store genetic information, like DNA, and to catalyze chemical reactions, like an enzyme.
Origin of life 
 This is the idea suggested by Arrhenius, and developed by Fred Hoyle, that life developed elsewhere in the universe and arrived on Earth in the form of spores.
Origin of life 
 The molecules which combined to form genetic material are more complex than the "primordial soup" of organic (carbon-based) chemicals that existed on Earth four billion years ago.
Origin of life 
 If RNA was the first genetic material, then minerals containing boron and molybdenum could assist in its formation.
Origin of life 
 However, the Bible does not explicitly state the age of the Earth, only that 'In the beginning, God created the heavens and the earth' (Genesis 1:1)
Timeline of the 2006 Atlantic hurricane season 
 Below is a timeline of the 2006 Atlantic hurricane season, listing all the storm formations, strengthening, weakening, landfalls, extratropical transitions, as well as dissipation.
Timeline of the 2006 Atlantic hurricane season 
 The 2006 Atlantic hurricane season was a season in which an El Niño event stopped much tropical cyclone activity, especially later in the season.
Timeline of the 2006 Atlantic hurricane season 
 The timeline also includes information which was not operationally released, meaning that information from post-storm reviews by the National Hurricane Center, such as information on a storm that was not operationally warned on, have been included.
Timeline of the 2006 Atlantic hurricane season 
 The graphical bar above gives a brief overview of storm activity during the season, and for convenience, the storm's maximum intensity is included as a color bar.
Timeline of the 2006 Atlantic hurricane season 
 Tropical Storm Zeta from 2005 persisted into 2006, therefore a January section has been included in the text timeline.
Timeline of the 2006 Atlantic hurricane season 
 0000 UTC - The year 2006 begins with Tropical Storm Zeta still active from the previous season, making Zeta only the second cross-season North Atlantic storm ever recorded.
Timeline of the 2006 Atlantic hurricane season 
 5 p.m. AST (2100 UTC) - The National Hurricane Center issues its last advisory on dissipating Tropical Depression Zeta, finally ending the 2005 season.
Timeline of the 2006 Atlantic hurricane season 
 1 a.m. CDT (0600 UTC) - Tropical Depression One forms 120 nautical miles (140 miles, 220 km) south of the western tip of Cuba.
Timeline of the 2006 Atlantic hurricane season 
 12:30 p.m. EDT (1630 UTC) - Tropical Storm Alberto makes landfall near Adams Beach, Florida, with 45 mph winds.
Timeline of the 2006 Atlantic hurricane season 
 5 p.m. EDT (2100 UTC) - The HPC issues its first and only advisory on the remnants of Tropical Depression Alberto.
Timeline of the 2006 Atlantic hurricane season 
 0600 UTC - A previously-extratropical low pressure area becomes a tropical depression about 210 nautical miles (245 miles, 390 km) southeast of Nantucket, Massachusetts.
Timeline of the 2006 Atlantic hurricane season 
 However, this depression is not assigned a number operationally, or warned on, by the National Hurricane Center.
Timeline of the 2006 Atlantic hurricane season 
 1200 UTC - The tropical depression near Nantucket strengthens into a tropical storm, but is not operationally named.
Timeline of the 2006 Atlantic hurricane season 
 8 a.m. EDT (1200 UTC) - Tropical Depression Two forms 250 nautical miles (290 miles, 645 km) east-southeast of Wilmington, North Carolina.
Timeline of the 2006 Atlantic hurricane season 
 2:45 a.m. EDT (0645 UTC) - Tropical Storm Beryl makes landfall on the island of Nantucket, Massachusetts, with 50 mph winds.
Timeline of the 2006 Atlantic hurricane season 
 8 p.m. EDT (0000 UTC August 1) - Tropical Depression Three forms 205 nautical miles (235 miles, 380 km) east-southeast of Barbuda.
Timeline of the 2006 Atlantic hurricane season 
 2 p.m. AST (1800 UTC) - Tropical Depression Four forms 225 nautical miles (260 miles, 415 km) south-southeast of Praia, Cape Verde.
Timeline of the 2006 Atlantic hurricane season 
 2 p.m. AST (1800 UTC) - Tropical Depression Five forms in the Caribbean Sea about 40 nautical miles (45 miles, 75 km) north-northwest of Grenada.
Timeline of the 2006 Atlantic hurricane season 
 7:15 a.m. EDT (1115 UTC) - Tropical Storm Ernesto makes a first landfall in Cuba at Playa Cazonal with 40 mph winds.
Timeline of the 2006 Atlantic hurricane season 
 11 p.m. EDT (0300 UTC) - Tropical Storm Ernesto makes a second landfall at Plantation Key, Florida, with 45 mph winds.
Timeline of the 2006 Atlantic hurricane season 
 1 a.m. EDT (0500 UTC) - Tropical Storm Ernesto makes a third landfall in southwestern Miami-Dade County with 45 mph winds.
Timeline of the 2006 Atlantic hurricane season 
 11:40 p.m. EDT (0340 UTC September 1) - Tropical Storm Ernesto makes a fourth landfall at Oak Island, North Carolina, with 70 mph winds.
Timeline of the 2006 Atlantic hurricane season 
 11 p.m. EDT (0300 UTC September 3) - The HPC releases its final advisory on the extratropical remnants of Ernesto.
Timeline of the 2006 Atlantic hurricane season 
 2 p.m. AST (1800 UTC) - Tropical Depression Six forms 855 nautical miles (990 miles, 1585 km) west of the Cape Verde Islands.
Timeline of the 2006 Atlantic hurricane season 
 2 p.m. EDT (1800 UTC) - Tropical Depression Seven forms 470 nautical miles (545 miles, 870 km) east-northeast of the Leeward Islands.
Timeline of the 2006 Atlantic hurricane season 
 8 a.m. EDT (1200 UTC) - Tropical Depression Eight forms 200 nautical miles (230 miles, 370 km) south-southeast of the Cape Verde Islands.
Timeline of the 2006 Atlantic hurricane season 
 8 p.m. AST (0000 UTC September 14) - Hurricane Gordon reaches Category 3 intensity, becoming the first major hurricane of the season.
Timeline of the 2006 Atlantic hurricane season 
 8 p.m. AST (0000 UTC September 14) - Tropical Depression Eight strengthens into Tropical Storm Helene.
Timeline of the 2006 Atlantic hurricane season 
 8 p.m. AST (0000 UTC September 18) - Hurricane Helene reaches to Category 3 intensity, becoming the second major hurricane of the season.
Timeline of the 2006 Atlantic hurricane season 
 11 p.m. AST (0300 UTC September 20) - Hurricane Gordon passes near the Central Azores with the eye staying offshore.
Timeline of the 2006 Atlantic hurricane season 
 2 p.m. EDT (1800 UTC) - Tropical Depression Nine forms 810 nautical miles (940 miles, 1500 km) east-southeast of Bermuda.
Atlantic Standard Time Zone 
 The Atlantic Standard Time Zone (AST) is a geographic region that keeps time by subtracting four hours from Greenwich Mean Time (GMT), resulting in GMT-4 (UTC-4).
Atlantic Standard Time Zone 
 The clock time in this zone is based on the mean solar time of the 60th degree meridian west of the Greenwich Observatory.
Atlantic Standard Time Zone 
 The Canadian provinces of New Brunswick, Nova Scotia and Prince Edward Island keep time by subtracting four hours from UTC.
Atlantic Standard Time Zone 
 Other parts of the world that keep time by subtracting four hours from UTC include: many Caribbean islands, including Puerto Rico, the U.S. Virgin Islands, and several South American countries, such as Paraguay, Chile, Bolivia, and parts of Brazil.
Atlantic Standard Time Zone 
 Venezuela used AST until December 9, 2007, when it switched to UTC-4:30, but switched back to AST on May 1, 2016, at 2:30 a.m. local time.
Figueirense FC 
 Figueirense Futebol Clube, also known as Figueirense, is a Brazilian football team in Florianópolis, Santa Catarina.
Figueirense FC 
 In 1987, the club played at Campeonato Catarinense Second Division, and won the promotion to the First Division.
Figueirense FC 
 In 2001, the club was Campeonato Brasileiro Second Division runner-up, and was promoted to the following year's First Division.
Figueirense FC 
 Champion of Campeonato Catarinense (State Championship) in  1932, 1935, 1936, 1937, 1939, 1941, 1972, 1974, 1994, 1999, 2002, 2003, 2004, 2006, 2008, 2014, 2015, 2018
C Sharp (programming language) 
 Free implementation of C# and .NET like Mono developed by Novell, or dotGNU developed by the Free Software Foundation.
C Sharp (programming language) 
 // The piece of code below is optional, but is needed to prevent the program from closing immediately.
C Sharp (programming language) 
 C# can be edited in a number of IDEs (Integrated Development Environments), some of which are listed below:
Wilmington, North Carolina 
 It was named in honor of Spencer Compton, the Earl of Wilmington, who was Prime Minister at the same time as George II was King of England.
Wilmington, North Carolina 
 It was the site of the 1898 insurrection where many white people killed African-American politicians in the city.
Plantation Key 
 It is in the upper Florida Keys on U.S. Route 1 (or the Overseas Highway), between Key Largo and Windley Key.
Oak Island, North Carolina 
 Oak Island, North Carolina is a town mostly on Oak Island (which also contains the town of Caswell Beach and the North Carolina Baptist Assembly at Fort Caswell) in Brunswick County, North Carolina; a small part of the town extends onto the mainland north of the island's bridge.
Avegno, Switzerland 
 In 1982, the Swiss Heritage Society gave the Wakker Prize to Avegno for the saving of its historical buildings.
Wakker Prize 
 The Wakker Prize (in German: Wakkerpreis, in French Prix Wakker) is given every year by the Swiss Heritage Society to a municipality of Switzerland for the making and saving of its historical buildings.
Ehrendingen 
 Ehrendingen was created on 1 January 2006 from the former municipalities of Oberehrendingen and Unterehrendingen.
Barbengo 
 Barbengo is a former municipality until 2008, when it was moved to the municipality of Lugano and in the district of Lugano in the canton of Ticino in Switzerland.
Hurricane Fabian 
 Hurricane Fabian was a powerful Cape Verde-type hurricane that hit Bermuda in early September during the 2003 Atlantic hurricane season.
Hurricane Fabian 
 It moved west-northwestward under the influence of the subtropical ridge to its north, and steadily strengthened in an area of warm water temperatures and light wind shear.
Hurricane Fabian 
 The hurricane attained a peak intensity of 145 mph (230 km/h) on September 1, and it slowly weakened as it turned northward.
Hurricane Fabian 
 On September 5, Fabian made a direct hit on the island of Bermuda with wind speeds of over 120 mph (195 km/h).
Hurricane Fabian 
 After passing the island, the hurricane turned to the northeast, and became extratropical on September 8.
Hurricane Fabian 
 The hurricane's powerful winds resulted in moderate damage and destroyed roofs throughout the island.
Hurricane Fabian 
 A strong storm surge associated with the hurricane killed four people crossing a causeway on Bermuda, temporarily closing the only link between two islands.
Hurricane Fabian 
 The endangered Bermuda Petrel, better known as the Cahow, was threatened by the hurricane, which destroyed ten nests, although volunteer work transported the species to a safer location.
Hurricane Fabian 
 Strong swells resulted in damage in northern Puerto Rico and the Dominican Republic, and also caused four people to drown along the United States' Atlantic coast.