1.
Gibson ES-335
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The Gibson ES-335 is the worlds first commercial thinline archtop semi-acoustic electric guitar. Released by the Gibson Guitar Corporation as part of its ES series in 1958, it is fully hollow nor fully solid, instead. The side wings formed by the two cutaways into its upper bouts are hollow, and the top has two violin-style f-holes over the hollow chambers, before 1952 Gibson produced only hollow-body guitars, which are prone to feedback when amplified loudly. By 1958 Gibson was making a few models which had much lower feedback and better sustain but lacked the darker, warmer tone. The ES-335 was an attempt to find a ground, a warmer tone than a solid body produced with almost as little feedback. With a basic price of $267.50, it became a best-seller. The first major update came in mid 1962, with the most visible change being the markers on neck, early models had dots, later models had blocks. Notable users were Larry Carlton, Robben Ford, John Scofield, Lee Ritenour, Alvin Lee, Richie Blackmore, Noel Gallagher, some models feature a coil split switch, which allows the humbuckers to produce a single-coil sound. The ES-335 Pro, ES-335TD CRS and CRR models were equipped with Gibson Dirty Fingers humbuckers, other signature models have included the heavily customized Alvin Lee Big Red 335. A reissue of the 1963 model was a 2014 Editors pick in Guitar Player magazine, the ES-345 also featured an optional stereophonic output jack, gold-plated hardware, large split parallelogram fingerboard inlays, and a thicker three-ply edge binding than that of the ES-335. Notable users were B. B. King, Freddie King, Bill Nelson, John McLaughlin, Jorma Kaukonen, Fred Frith, Porl Thompson of The Cure, Steve Howe and Elvin Bishop. The ES-345 was discontinued in 1981, one year after the Gibson Lucille, as of 2012, the ES-345 is available as a limited edition from Gibsons discount line, Epiphone Guitars, as well as the ES-355. The differences between two models are, The ES-355TD was at the top of Gibsons range of thinline semi-acoustic guitars and it was manufactured from 1958 to 1982, fitted with Varitone Stereo option, as ES-355TD-SV released in 1959. The headstock has a split-diamond inlay rather than the crown inlay on the 335/345. The fingerboard inlays are inlaid mother-of-pearl blocks, beginning at the first position of the fretboard, in addition to the headstock, binding is also applied to the fretboard and both the front and the back edges of the body. Rather than the rosewood fretboard on a 335 or 345, both variations of the 355 have an ebony fingerboard for a smoother sound, early models of Epiphones limited edition budget version had an ebony fingerboard but the later issues had a rosewood board. The ES-355 was available with a Vibrola vibrato unit or a Bigsby vibrato tailpiece and it was also available with a stereo output and Varitone tone filter circuitry. When fitted with the optional stereo wiring and Varitone, the model was known as the ES-355TD-SV, the best-known user of this guitar is probably B. B. King, whose trademark guitar, Lucille, was the basis for a 1981 signature model
2.
British Rail Class 390
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The Class 390 Pendolino is a type of electric high-speed train operated by Virgin Trains in the United Kingdom. They are electric multiple units using Fiat Ferroviarias tilting train Pendolino technology, fifty-three 9-car units were originally built between 2001 and 2004 for operation on the West Coast Main Line, with an additional four trains and also a further 62 cars built between 2009 and 2012. The trains of the batch were the last to be assembled at Alstoms Washwood Heath plant. The remaining trains in the fleet were built in Italy, the fleet is maintained at the Alstom Manchester Train Depot near Piccadilly station. Virgin placed an order with Alstom/Fiat Ferroviaria, Tilting trains were not new on the West Coast Main Line. Twenty years previously, British Rail had developed the revolutionary, but ultimately unsuccessful, Fiat Ferroviaria supplied much of the content of the Class 390 units, including the bodyshell and the bogies, while final assembly was carried out at Washwood Heath. The tilting technology was developed by SIG Switzerland, two electromechanical actuators are used per car to achieve the desired tilting angle on curved stretches of track. The train can tilt to a maximum of eight degrees, at which point one side of the train is 380 mm higher above the track than the other. In contrast to other Fiat Ferroviaria tilting trains which use hydraulic tilting actuators, the new trains were intended to run at 140 mph, but the West Coast Main Line modernisation programme, which was an upgrade to the infrastructure to allow faster line speeds, ran over budget. Although this are well below BRs hopes for APT of 155 mph, the original order was for 53 sets,34 eight-carriage sets and 19 nine-carriage sets. The eight-carriage sets each had an additional carriage added in 2004, to increase capacity,4 eleven-carriage sets and an additional 62 extra carriages were ordered to increase 31 sets to eleven carriages. These were delivered between 2009 and 2012, each 11-car set is identified by having 100 added to its unit number. During use, the Dellner coupling of carriages A and K may be exposed during use and it is not uncommon for the front to be open like this as the main intention is emergencies. Joining a set of nine cars with another would create an 18-car set, therefore, they only travel as the original 9-car or 11-car set. Following criticisms of the pressure- operated automatic gangway doors of the older Mark 3, all seats originally had an on-board entertainment system with a number of pre-recorded music channels. This feature was disabled in March 2010 to make way for new on-board WiFi provided by T-Mobile, each seating row has a dot-matrix LCD display to indicate the reservation status of each seat, removing the need for conventional printed labels inserted manually by train crew. The coaches also incorporate steps which automatically extend to level when the doors are opened. This feature was first seen on the APT-P, which as mentioned above is a distant ancestor of the Pendolino, the windows are fitted with roll-down blinds
3.
Dada
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Dada or Dadaism was an art movement of the European avant-garde in the early 20th century, with early centers in Zürich, Switzerland at the Cabaret Voltaire, in New York, and after 1920, in Paris. The art of the movement spanned visual, literary, and sound media, including collage, sound poetry, cut-up writing, Dadaist artists expressed their discontent with violence, war, and nationalism, and maintained political affinities with the radical left. Others note that it suggests the first words of a child, evoking a childishness, still others speculate that the word might have been chosen to evoke a similar meaning in any language, reflecting the movements internationalism. The roots of Dada lay in pre-war avant-garde, the term anti-art, a precursor to Dada, was coined by Marcel Duchamp around 1913 to characterize works which challenge accepted definitions of art. Cubism and the development of collage and abstract art would inform the movements detachment from the constraints of reality, the work of French poets, Italian Futurists and the German Expressionists would influence Dadas rejection of the tight correlation between words and meaning. Works such as Ubu Roi by Alfred Jarry, and the ballet Parade by Erik Satie would also be characterized as proto-Dadaist works, the Dada movements principles were first collected in Hugo Balls Dada Manifesto in 1916. The movement influenced later styles like the avant-garde and downtown music movements, Dada was an informal international movement, with participants in Europe and North America. The beginnings of Dada correspond to the outbreak of World War I, avant-garde circles outside France knew of pre-war Parisian developments. Futurism developed in response to the work of various artists, many Dadaists believed that the reason and logic of bourgeois capitalist society had led people into war. They expressed their rejection of that ideology in artistic expression that appeared to reject logic and embrace chaos, for example, George Grosz later recalled that his Dadaist art was intended as a protest against this world of mutual destruction. According to Hans Richter Dada was not art, it was anti-art, Dada represented the opposite of everything which art stood for. Where art was concerned with aesthetics, Dada ignored aesthetics. If art was to appeal to sensibilities, Dada was intended to offend, as Hugo Ball expressed it, For us, art is not an end in itself. But it is an opportunity for the perception and criticism of the times we live in. A reviewer from the American Art News stated at the time that Dada philosophy is the sickest, most paralyzing and most destructive thing that has ever originated from the brain of man. Art historians have described Dada as being, in large part, a systematic work of destruction and demoralization. In the end it became nothing but an act of sacrilege, to quote Dona Budds The Language of Art Knowledge, Dada was born out of negative reaction to the horrors of the First World War. This international movement was begun by a group of artists and poets associated with the Cabaret Voltaire in Zürich, Dada rejected reason and logic, prizing nonsense, irrationality and intuition
4.
Volvo 340
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The Volvo 300 Series is a rear wheel drive small family car sold as both a hatchback and a conventional saloon from 1976 to 1991. It was launched in the Netherlands shortly after Volvo acquired a stake in the passenger car division of DAF in 1973. The series consisted of the Volvo 340 and the later Volvo 360, the 300 series was unusual in having the gearbox mounted to the De Dion tube rear axle as a transaxle, with the 2 liter models having the driveshaft enclosed in a torque tube. III Ford Escort and the Opel Kadett E/Mk, overall, the 300 series was considered heavy and unrewarding to drive but reliable and safe by the standards of its day. However, early 360GLT versions were regarded by more enthusiastic drivers, with the unusual gearbox location ensuring good weight distribution and unusually good balance. After building a series of cars, DAF sought a partner to bring its new larger model, codenamed P900 and intended to become the DAF77. Several manufacturers were approached, including Audi, BMW, and Volvo, Volvo was not originally interested due to the cost, but they were later persuaded by DAFs access to Renault engines. This helped Volvo expand its model line-up without the large expenditures associated with developing a new model, building cars in the Netherlands also helped the Swedish Volvo to access the markets of the EEC, of which Sweden was then not yet a member. Volvo purchased a share in DAF in 1973, increasing to a three-quarters stake in 1975. Free of its car division, DAFs commercial vehicle division, DAF Trucks. The Volvo 343 was introduced in 1976, DAF had already begun development of this car as a replacement for the Volvo 66. It was fitted with a 1.4 litre Renault engine in the front and DAFs radical Variomatic continuously variable transmission unusually mounted in the rear, helping weight distribution. To add to the appeal of the car and boost it sales, Volvo adapted the M45 manual transmission from the 200 series to fit in place of the CVT, and was sold alongside the CVT models from 1979. The CVT continued to be offered but sold in more marginal numbers. A five-door model, the 345, was added in August 1979 for the 1980 model year, the extra doors added 30 kg, other modifications included better brakes, a slightly larger track due to wider rims, and interval wipers. During 1980 larger wrap around bumpers were introduced,1981 saw the addition of an additional engine option, the Volvo designed B19, only available with the manual transmission. A revised bonnet, grille and front lamp arrangement and slightly different wings signalled a facelift in summer 1981, from having been mostly a DAF design, the dashboard gradually became more aligned with the design of other Volvos over the years. The overall length crept up to 4,300 mm, the third digit designating the number of doors was dropped from model designations in 1983
5.
Ferrari 348
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The Ferrari 348 is a mid-engined, rear-wheel-drive V8-powered 2-seat sports car by Ferrari, replacing the 328 in 1989 and continuing until 1995. It was the final V8 mid-engine model developed by Enzo Ferrari before his death, the 348, badged 348 tb for the coupé and 348 ts and the 348sp versions, features a normally aspirated 3. 4-litre version of the quad-cam, four-valve-per-cylinder V8 engine. As with its predecessors, the number was derived from this configuration. The engine, which produced 300 hp, was mounted longitudinally and coupled to a manual gearbox. The T in the model name 348 tb and ts refers to the position of the gearbox. Overall,2,895 examples of the 348 tb and 4,230 of the 348 ts were produced, the F355 that replaced it returned to the styling cues of the 328 with round tail lights and rounded side air scoops. Fifty-seven Challenge models were built for owners who wanted a more track-ready car, the 348 was fitted with dual-computer engine management using twin Bosch Motronic ECUs, double-redundant anti-lock brakes, and self-diagnosing air conditioning and heating systems. Late versions have Japanese-made starter motors and Nippondenso power generators to improve reliability, U. S. spec 348s have OBD-I engine management systems, though European variants do not come with the self-test push button installed, which is needed to activate this troubleshooting feature. This also had the effect of making the doors very wide. The 348 was equipped with an oil system to prevent oil starvation at high speeds. The oil level can only be checked on the dipstick when the motor is running due to this setup. The 348 was fitted with adjustable suspension and a removable rear sub-frame to speed up the removal of the engine for maintenance. This vehicle also served as a test mule for the Ferrari Enzo, between 1992 and 1993 Ferrari made 100 units of 348 Serie Speciale of its tb and ts versions. It was a limited edition made for the US market. During 1992 -1993 there were only 35 TB Serie Speciales manufactured with the remainder being the TS Serie Speciale, Ferrari indicates a 0-60 mph time of 5.3 seconds and a standing ¼ mile of 13.75 seconds. The cars were offered with F40 style sport seats in Connolly leather, the door panels were also modified and made of leather. Each car is numbered, with a 348 Serie Speciale plate on the passengers side door-post, in 1994, a further 15 units were produced, bringing the total production of this limited edition to 115. The Ferrari Challenge was initiated by Ferrari Club Nederland and designated for the Ferrari 348, using the un-modified engine, the only changes of the car were slick tyres, better brake-pads, roll-bar, smaller battery in a different position and seat belts
6.
BMW 315
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The BMW303 was a small family saloon produced by BMW in 1933 and 1934. It was the first BMW motor car with a six-cylinder engine, the 303 platform was also used for the BMW 315/1 and BMW 319/1. These were high-performance versions of the 315 and 319 respectively, with tuned engines, the 315/1 and 319/1 were replaced by the BMW328 in 1936. Upon its introduction in 1933, the 303 was the largest car BMW had made, the wheelbase of the 303 was 2,400 millimetres, an increase of 300 millimetres over the 3/20. The track,1,150 millimetres at the front and 1,220 millimetres at the rear, was wider than the 3/20s 1,100 millimetres front. Unlike the 3/20s backbone chassis, the 303 had a frame made from tubular side members. The independent front suspension used a transverse mounted leaf spring mounted above the centre line. The hubs were located with the spring mounts at the top, the rear suspension used a live axle on semi-elliptic leaf springs, a conventional system neither as advanced nor as troublesome as the 3/20s swing axles. The 303 was the first German car in its size and price class to have automatic one-shot chassis lubrication. Each wheel had a brake, all four were operated through the pedal using rods and levers. The 303 was the first BMW car to use a straight-6 engine, the M781182 cc six-cylinder engine was developed from the four-cylinder engine used in the 3/20. The crankshaft ran in four plain bearings, the 303 was the first BMW to use the kidney grill, which has since become a defining feature of the companys models. Two-door saloon and cabriolet bodies were manufactured, at first by Daimler-Benzs coachworks in Sindelfingen, Ambi-Budd would also offer a two-seat sports cabriolet for the 303. At the time it was being made, the 303 was the least expensive car in Germany. However, it was considered underpowered, with a top speed of 56 miles per hour, the combination of soft spring rates at the front and hard spring rates at the rear caused understeer, body roll, and a generally unsettling pitching movement. 2300 BMW 303s were produced up to 1934, when the 303 was replaced by the 315, the BMW309 was a development of the 303. A replacement for the 3/20, the 309 was a 303 with an engine developed from the M78 six-cylinder engine used in the 303. The 309s engine had the bore increased from 56 mm to 58 mm which, with a stroke of 80 mm, gave a capacity of 845 cc, in addition to the body styles offered with the 303, the 309 was also available as a tourer
7.
BMW 328
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The BMW328 is a sports car made by BMW between 1936 and 1940, with the body design credited to Peter Szymanowski, who became BMW chief of design after World War II. In 1999 the BMW328 was named one of 25 finalists for Car of the Century by a panel of automotive journalists. The 328 was introduced at the Eifelrennen race at the Nürburgring in 1936, the 328 had more than 100 class wins in 1937, including the RAC Tourist Trophy, the Österreichische Alpenfahrt, and the La Turbie hillclimb. In 1938, the 328 won its class at Le Mans, the RAC Tourist Trophy, the Alpine Rally, the 328 won the RAC Rally in 1939 and came in fifth overall and first in class in the 193924 Hours of Le Mans. Frank Pratt won the 1948 Australian Grand Prix driving a 328, in 1938, BMW328 became a class winner in Mille Miglia. In 1940, the Mille Miglia Touring Coupe won the Mille Miglia with an speed of 166.7 km/h. In 2004, the BMW328 Mille Miglia Touring Coupe became the first car to win both the Mille Miglia and the classical version of the race. One of the Mille Miglia 328s and BMWs technical plans for the car were taken from the bombed BMW factory by English representatives from the Bristol Aeroplane Company, fiedler, the BMW engineer, was persuaded to come, too. Bristol Cars was set up to complete cars, called Bristols. The first Bristol car, the 400, was based on the BMW plans. This Bristol engine was also an option in AC cars, before the Cobra, BMW328, From roadster to legend. Norbye, Jan P. BMW - Bavarias Driving Machines, BMW328 - the legendary roadster. Archived from the original on 2010-01-03, BMW328 specifications Jalopnik BMW328 Carsguide - 75th Anniversary of BMW Roadsters - Gallery
8.
Porsche 356
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The Porsche 356 is a luxury sports car which was first produced by Austrian company Porsche Konstruktionen GesmbH, and then by German company Dr. Ing. h. c. It was Porsches first production automobile, earlier cars designed by the Austrian company include Cisitalia Grand Prix race car, the Volkswagen Beetle, and Auto Union Grand Prix cars. The 356 is a lightweight and nimble-handling, rear-engine, rear-wheel drive, two-door, sports car available in hardtop coupé, engineering innovations continued during the years of manufacture, contributing to its motorsports success and popularity. Production started in 1948 at Gmünd, Austria, where approximately 50 cars were built, in 1950 the factory relocated to Zuffenhausen, Germany, and general production of the 356 continued until April 1965, well after the replacement model 911 made its autumn 1963 debut. Of the 76,000 originally produced, approximately half survive, prior to World War II Porsche designed and built three Type 64 cars for a 1939 Berlin-to-Rome race that was cancelled. In 1948 the mid-engine, tubular chassis 356 prototype called No.1 was completed and this led to some debate as to the first Porsche automobile, but the 356 is considered by Porsche to be its first production model. The 356 was created by Ferdinand Ferry Porsche, who founded the Austrian company with his sister, like its cousin, the Volkswagen Beetle, the 356 is a four-cylinder, air-cooled, rear-engine, rear-wheel drive car with unitized pan and body construction. Ferry Porsche described the thinking behind the development of the 356 in an interview with the editor of Panorama, …. I had always driven very speedy cars. I had an Alfa Romeo, also a BMW and others, …. By the end of the war I had a Volkswagen Cabriolet with a supercharged engine and that was the basic idea. I saw that if you had enough power in a car it is nicer to drive than if you have a big car which is also overpowered. On this basic idea we started the first Porsche prototype, to make the car lighter, to have an engine with more horsepower…that was the first two seater that we built in Carinthia. The first 356 was road certified in Austria on June 8,1948, Porsche re-engineered and refined the car with a focus on performance. Fewer and fewer parts were shared between Volkswagen and Porsche as the 1950s progressed, the early 356 automobile bodies produced at Gmünd were handcrafted in aluminum, but when production moved to Zuffenhausen, Germany in 1950, models produced there were steel-bodied. The aluminium bodied cars from very small company are what are now referred to as prototypes. Porsche contracted Reutter to build the bodies and eventually bought the Reutter company in 1963. The Reutter company retained the seat manufacturing part of the business, little noticed at its inception, mostly by a small number of auto racing enthusiasts, the first 356s sold primarily in Austria and Germany. It took Porsche two years, starting with the first prototype in 1948, to manufacture the first 50 automobiles, by the early 1950s the 356 had gained some renown among enthusiasts on both sides of the Atlantic for its aerodynamics, handling, and excellent build quality. The class win at Le Mans in 1951 was a factor and it was common for owners to race the car as well as drive them on the streets
9.
350.org
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350. org was founded by author Bill McKibben and a group of students from Middlebury College. The organizing effort drew its name from NASA climate scientist James Hansens contention that any concentration of CO2 above 350 parts per million was unsafe. Carbon dioxide, the greenhouse gas, rose by 2.6 parts per million to 396 ppm in 2013 from the previous year. It already crossed 400 ppm in May 2012 on monitors in the industrialized Northern Hemispheres Arctic region, McKibben first started to organize against climate change with a walk across Vermont, his home state. His Step It Up campaign in 2007 involved 1,400 demonstrations at famous sites across the United States, McKibben credits these activities with making Hillary Clinton and Barack Obama change their energy policies during the presidential campaign. Starting in 2008,350. org built upon the Step It Up campaign, McKibben called news of Pachauris embrace of the 350ppm target amazing. Some media have indicated that Pachauris endorsement of the 350 ppm target was a victory for 350. orgs activism, the organization had a lift in prominence after McKibben appeared on The Colbert Report television show on Monday August 17,2009. McKibben promotes the organization on speaking tours and by writing articles about it for major newspapers and media, such as the Los Angeles Times. In 2012 the organization was presented with the 2012 Katerva Award for Behavioural Change, the 350. org movement considers the atmospheric concentration 350ppm of CO2 as a safe upper limit. This limit was the focus a 2009 COP15 international treaty,350. orgs goal is to have governments adopt policies to lower carbon dioxide emissions. In spite of this goal, n 2013, CO2 levels surpassed 400 ppm for the first time in recorded history,350. org reports, This March, global levels of CO2 passed 400 parts per million. 350. org aims to build a global, grassroots movement to take on the fuel industry. Through online campaigns, grassroots organizing, and mass actions,350. org has mobilized thousands of volunteer organizers in over 188 countries. Climate safety and climate justice for people across the globe is a part of 350. orgs mission. By working with community groups,350. org aims to hold corporations and world leaders accountable to the realities of science. 350 parts per million is what scientists, climate experts, the amount of CO2 in the atmosphere is continuing to rise at about 2 ppm every year. 2 °C was agreed upon during the 2009 Copenhagen Accord as a limit for global temperature rise, the accord formally recognized the scientific view that the increase in global temperature should be below two degrees Celsius. The next paragraph declared that we agree that deep cuts in global emissions are required, so as to hold the increase in global temperature below two degrees Celsius
10.
AL 333
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AL333, commonly referred to as the First Family, is a collection of prehistoric hominid teeth and bones. They are generally thought to be members of the species Australopithecus afarensis, there are multiple theories about the hominids’ cause of death and some debate over their species and sexual dimorphism. Also known as the Danakil depression or Afar depression, this triangle is the lowest point in Ethiopia and they soon settled on working in the Hadar Formation, a sedimentary geological formation within the region. The four men established the International Afar Research Expedition, with Johanson in charge of the aspect of the expedition. Historically, the Afar Triangle had been unexplored because it was remote, however, the IARE chose to explore the region for other reasons. The geological sequence of the Hadar Formation consists of nearly 200 meters of strata, or rock layers, furthermore, the area had feldspars and volcanic glass that would be valuable for chronometric dating. From 1973 to 1977, the IARE campaigns resulted in the discovery of about 250 hominid fossils, the most famous of the Hadar discoveries is Lucy, the most complete A. afarensis skeleton that has been discovered. However, in 1975, this formation also witnessed the discovery of numerous remains from another site. These remains became known as the “First Family, ” and represent at least thirteen different individuals, of the 216 specimens,197 were surface finds, and 19 were found within 80 cm in the ground, suggesting a common time of death. Further visits to AL333 resulted in the discovery of 23 additional postcranial and 3 mandibular and this increased the estimate from 13 to at least 17 individuals. In 2000, a fossil of the fourth metatarsal was recovered from AL333. The morphology of this suggests that A. afarensis had transverse and longitudinal foot arches. The discovery of all of the fossils at AL333 aligned close together in one geological stratum is a sign that they died at about the same time. But absolute dating had to be used to ascertain that time, because the specimens were found between two layers of volcanic ash, potassium-argon dating was used. Potassium-argon dating measures the ratio of potassium and the argon it decays into. It is ideal for dating volcanic material, in the case of AL333, this method yielded an age of 3. 18-3.21 million years. The unique grouping of such a number of individuals in the same place. One popular theory was a flood, but more detailed study of the geological formation of the site has largely discredited this idea
11.
Tupolev Tu-334
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The Tupolev Tu-334 was a Russian short-to-medium range airliner project that was developed to replace the ageing Tu-134s and Yak-42s in service around the world. The airframe was based on a shortened Tu-204 fuselage and a version of that aircrafts wing. Unlike the Tu-204, however, the Tu-334 has a T-tail, with the rationalisation of the Russian aircraft companies in 2009 to form United Aircraft Corporation it was decided not to continue with the programme. Work commenced on the Tu-334 in the early 1990s, but proceeded slowly due to funding problems arising from the breakup of the Soviet Union, a prototype was displayed in 1995, but this was little more than a mockup with few systems installed. A functional aircraft first flew on February 8,1999, and later that year, a Russian type certificate was obtained – after some delay – on December 30,2003. Since then, development remained slow due to protracted budget problems, in turn, the certification of the aircraft and its planned entry into serial production was delayed multiple times. The price per unit for the version is estimated to be around $43–44 million. One of the customers for the type was Iran. The Iran Aviation Industries Organization was in negotiations to purchase licenses to assemble the aircraft in Iran by 2011, nothing concrete became of these negotiations before the cancellation of the Tu-334 programme. However, this date passed without any reported progress on Tu-334 serial production. In mid-2009, the decision was taken to not continue with the Tu-334 programme and instead focus efforts on the Sukhoi Superjet 100, the Antonov An-148, Tu-334-100 Basic version, with accommodation for 72 passengers in mixed-class configuration or 102 passengers in high-density layout. Two 73.6 kN Progress D-436T1 turbofans, tu-334-100C Proposed combi version of Tu-334-100. Tu-334-120 Planned derivative of Tu-334-100, powered by two 88.9 kN Rolls-Royce BR715-55 engines, fuselage stretched by 54 cm and longer span wing. Powered by two 80.4 kN Progress D-436T2 engines, tu-334-120D Based on the Tu-334-100D, but with two Rolls-Royce BR-715-55 engines. Tu-336 Proposed liquid natural gas-fueled version, with fuel tanks above the passenger cabin. Tu-354 Further stretched version, originally designated Tu-334-200, stretched by 390 cm over Tu-334-100, with accommodation for up to 126 passengers. Powered by two Progress D-436T2 or Rolls-Royce BR-715-55 engines, the Tu-354s landing gear was strengthened to use four-wheel bogies
12.
Boeing 377
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The Boeing 377 Stratocruiser was a large long-range airliner developed from the C-97 Stratofreighter military transport, itself a derivative of the B-29 Superfortress. The Stratocruisers first flight was on July 8,1947 and its design was advanced for its day, its innovative features included two passenger decks and a pressurized cabin, a relatively new feature on transport aircraft. It could carry up to 100 passengers on the main deck plus 14 in the lower deck lounge, typical seating was for 63 or 84 passengers or 28 berthed, the Stratocruiser was larger than the Douglas DC-6 and Lockheed Constellation and cost more to buy and operate. Its reliability was poor, chiefly due to problems with the four 28-cylinder Pratt & Whitney Wasp Major radial engines, only 55 Model 377s were built for airlines, along with the single prototype. The Boeing 377 Stratocruiser was a derivative of the Boeing Model 367, the Boeing C-97 Stratofreighter. William Allen, who had become President of The Boeing Company in September 1945, although in a recession in late 1945, Allen ordered 50 Stratocruisers, spending capital on the project without an airline customer. On November 29,1945 Pan American World Airways became the customer with the largest commercial aircraft order in history. Earlier in 1945 a Boeing C-97 had flown from Seattle to Washington, outside diameter of the upper lobe was 132 inches, compared to 125 inches for the DC-6 and other Douglas types. The lower deck served as a lounge, seating 14, the wing was the Boeing 117 airfoil, regarded as the fastest wing of its time. In all,4,000,000 man-hours went into the engineering of the 377, First flight of the 377 was on July 8,1947, two years after the first commercial order. The flight test fleet of three 377s underwent 250,000 mi of flying to test its limits before certification, as the launch customer, Pan Am was the first to begin scheduled service, from San Francisco to Honolulu in April 1949. By the fall of 1950, Northwest Orient was serving New York City, Chicago, Detroit, paul, Milwaukee and Spokane with the aircraft and was also operating the Stratocruiser nonstop between Seattle and Honolulu. For a short time Pan Am flew their B377s to Beirut, also in 1954, United was operating nonstop service with the Stratocruiser between Los Angeles and Honolulu and also between Seattle and San Francisco. According to its August 1,1954 system timeable, Uniteds service between Honolulu and Los Angeles and San Francisco operated with the B377 featured an all first class cabin at this time as well, in 1955 BOAC B377s had 50 First Class seats or 81 Tourist seats. In 1956 Pan Am was flying the B377 from Los Angeles and San Francisco to Sydney with stops at Honolulu, Canton Island and Suva. By 1958 Pan Am was operating the Stratocruiser between Seattle and Fairbanks, Juneau and Ketchikan in Alaska and between Seattle and Whitehorse in the Yukon Territory of Canada, a total of 56 were built, one prototype and 55 production aircraft. In these first six years, the Stratocruiser fleet had flown 169,859,579 miles and it was also one of but a few double deck airliners, another being its French contemporary, the Breguet Deux-Ponts, as well as Boeings own 747 and the Airbus A380. The last 377 was delivered to BOAC in May 1950, on this delivery flight, Boeing engineer Wellwood Beall accompanied the final 377 to England, and returned with news of the De Havilland Comet, the first jet airliner, and its appeal
13.
343 Industries
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343 Industries is an American video game developer located in Redmond, Washington. Halo 4 was the first title released by 343 Industries in which played a lead development role. The newest release from the company was Halo Wars 2 in 2017,343 Industries was founded in 2007, after the former Halo studio, Bungie, separated from Microsoft. It was named after Halo character 343 Guilty Spark, Bungie continued making Halo games until Halo, Reach in 2010. In July 2009, it was announced that 343 Industries was working on a seven-part Halo anime series called Halo Legends, later that year the studio created Halo Waypoint, a downloadable application that tracks a users Halo accomplishments. 343i also increased staff for Halo development, recruiting 20 staff from the now defunct Pandemic Studios, 343i also developed Halo, Reachs second and third map packs, entitled Defiant and Anniversary respectively, in conjunction with Certain Affinity. Following Bungies departure from Microsoft in 2007,343 Industries was eventually given complete control of the Halo franchise including servers, the studios development of Halo 4, which began in 2009, was completed ahead of schedule the same year in September. It was released on November 6,2012, as the first title of a new Halo Reclaimer Trilogy which will include at least two more installments over the years, at E32013, Microsoft and 343i announced the next Halo installment set for release on the Xbox One. Shortly after the announcement, the Reclaimer Trilogy was confirmed by Microsoft Studios corporate vice president Phil Spencer to be expanded into a Reclaimer Saga. The following year at E32014, the title was revealed as Halo 5. Microsoft, in a contract with Mega Bloks, is in conjunction with 343i to manufacture a new line of toys, Halo 5, Guardians was released on October 27,2015, with semi-exclusive content to those who purchased select Mega Bloks sets. 343 Industries has since released free monthly content updates since Halo 5s launch
14.
Integer
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An integer is a number that can be written without a fractional component. For example,21,4,0, and −2048 are integers, while 9.75, 5 1⁄2, the set of integers consists of zero, the positive natural numbers, also called whole numbers or counting numbers, and their additive inverses. This is often denoted by a boldface Z or blackboard bold Z standing for the German word Zahlen, ℤ is a subset of the sets of rational and real numbers and, like the natural numbers, is countably infinite. The integers form the smallest group and the smallest ring containing the natural numbers, in algebraic number theory, the integers are sometimes called rational integers to distinguish them from the more general algebraic integers. In fact, the integers are the integers that are also rational numbers. Like the natural numbers, Z is closed under the operations of addition and multiplication, that is, however, with the inclusion of the negative natural numbers, and, importantly,0, Z is also closed under subtraction. The integers form a ring which is the most basic one, in the following sense, for any unital ring. This universal property, namely to be an object in the category of rings. Z is not closed under division, since the quotient of two integers, need not be an integer, although the natural numbers are closed under exponentiation, the integers are not. The following lists some of the properties of addition and multiplication for any integers a, b and c. In the language of algebra, the first five properties listed above for addition say that Z under addition is an abelian group. As a group under addition, Z is a cyclic group, in fact, Z under addition is the only infinite cyclic group, in the sense that any infinite cyclic group is isomorphic to Z. The first four properties listed above for multiplication say that Z under multiplication is a commutative monoid. However, not every integer has an inverse, e. g. there is no integer x such that 2x =1, because the left hand side is even. This means that Z under multiplication is not a group, all the rules from the above property table, except for the last, taken together say that Z together with addition and multiplication is a commutative ring with unity. It is the prototype of all objects of algebraic structure. Only those equalities of expressions are true in Z for all values of variables, note that certain non-zero integers map to zero in certain rings. The lack of zero-divisors in the means that the commutative ring Z is an integral domain
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Negative number
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In mathematics, a negative number is a real number that is less than zero. If positive represents movement to the right, negative represents movement to the left, if positive represents above sea level, then negative represents below level. If positive represents a deposit, negative represents a withdrawal and they are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset, if a quantity may have either of two opposite senses, then one may choose to distinguish between those senses—perhaps arbitrarily—as positive and negative. In the medical context of fighting a tumor, an expansion could be thought of as a negative shrinkage, negative numbers are used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. The laws of arithmetic for negative numbers ensure that the common idea of an opposite is reflected in arithmetic. For example, − −3 =3 because the opposite of an opposite is the original thing, negative numbers are usually written with a minus sign in front. For example, −3 represents a quantity with a magnitude of three, and is pronounced minus three or negative three. To help tell the difference between a subtraction operation and a number, occasionally the negative sign is placed slightly higher than the minus sign. Conversely, a number that is greater than zero is called positive, the positivity of a number may be emphasized by placing a plus sign before it, e. g. +3. In general, the negativity or positivity of a number is referred to as its sign, every real number other than zero is either positive or negative. The positive whole numbers are referred to as natural numbers, while the positive and negative numbers are referred to as integers. In bookkeeping, amounts owed are often represented by red numbers, or a number in parentheses, Liu Hui established rules for adding and subtracting negative numbers. By the 7th century, Indian mathematicians such as Brahmagupta were describing the use of negative numbers, islamic mathematicians further developed the rules of subtracting and multiplying negative numbers and solved problems with negative coefficients. Western mathematicians accepted the idea of numbers by the 17th century. Prior to the concept of numbers, mathematicians such as Diophantus considered negative solutions to problems false. Negative numbers can be thought of as resulting from the subtraction of a number from a smaller. For example, negative three is the result of subtracting three from zero,0 −3 = −3, in general, the subtraction of a larger number from a smaller yields a negative result, with the magnitude of the result being the difference between the two numbers
16.
100 (number)
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100 or one hundred is the natural number following 99 and preceding 101. In medieval contexts, it may be described as the hundred or five score in order to differentiate the English. The standard SI prefix for a hundred is hecto-,100 is the basis of percentages, with 100% being a full amount. 100 is the sum of the first nine prime numbers, as well as the sum of pairs of prime numbers e. g.3 +97,11 +89,17 +83,29 +71,41 +59. 100 is the sum of the cubes of the first four integers and this is related by Nicomachuss theorem to the fact that 100 also equals the square of the sum of the first four integers,100 =102 =2. 26 +62 =100, thus 100 is a Leyland number and it is divisible by the number of primes below it,25 in this case. It can not be expressed as the difference between any integer and the total of coprimes below it, making it a noncototient and it can be expressed as a sum of some of its divisors, making it a semiperfect number. 100 is a Harshad number in base 10, and also in base 4, there are exactly 100 prime numbers whose digits are in strictly ascending order. 100 is the smallest number whose common logarithm is a prime number,100 senators are in the U. S One hundred is the atomic number of fermium, an actinide. On the Celsius scale,100 degrees is the temperature of pure water at sea level. The Kármán line lies at an altitude of 100 kilometres above the Earths sea level and is used to define the boundary between Earths atmosphere and outer space. There are 100 blasts of the Shofar heard in the service of Rosh Hashana, a religious Jew is expected to utter at least 100 blessings daily. In Hindu Religion - Mythology Book Mahabharata - Dhritarashtra had 100 sons known as kauravas, the United States Senate has 100 Senators. Most of the currencies are divided into 100 subunits, for example, one euro is one hundred cents. The 100 Euro banknotes feature a picture of a Rococo gateway on the obverse, the U. S. hundred-dollar bill has Benjamin Franklins portrait, the Benjamin is the largest U. S. bill in print. American savings bonds of $100 have Thomas Jeffersons portrait, while American $100 treasury bonds have Andrew Jacksons portrait, One hundred is also, The number of years in a century. The number of pounds in an American short hundredweight, in Greece, India, Israel and Nepal,100 is the police telephone number. In Belgium,100 is the ambulance and firefighter telephone number, in United Kingdom,100 is the operator telephone number
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Factorization
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In mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 ×5, in all cases, a product of simpler objects is obtained. The aim of factoring is usually to reduce something to “basic building blocks”, such as numbers to prime numbers, factoring integers is covered by the fundamental theorem of arithmetic and factoring polynomials by the fundamental theorem of algebra. Viètes formulas relate the coefficients of a polynomial to its roots, the opposite of polynomial factorization is expansion, the multiplying together of polynomial factors to an “expanded” polynomial, written as just a sum of terms. Integer factorization for large integers appears to be a difficult problem, there is no known method to carry it out quickly. Its complexity is the basis of the security of some public key cryptography algorithms. A matrix can also be factorized into a product of matrices of special types, One major example of this uses an orthogonal or unitary matrix, and a triangular matrix. There are different types, QR decomposition, LQ, QL, RQ and this situation is generalized by factorization systems. By the fundamental theorem of arithmetic, every integer greater than 1 has a unique prime factorization. Given an algorithm for integer factorization, one can factor any integer down to its constituent primes by repeated application of this algorithm, for very large numbers, no efficient classical algorithm is known. Modern techniques for factoring polynomials are fast and efficient, but use sophisticated mathematical ideas and these techniques are used in the construction of computer routines for carrying out polynomial factorization in Computer algebra systems. This article is concerned with classical techniques. While the general notion of factoring just means writing an expression as a product of simpler expressions, when factoring polynomials this means that the factors are to be polynomials of smaller degree. Thus, while x 2 − y = is a factorization of the expression, another issue concerns the coefficients of the factors. It is not always possible to do this, and a polynomial that can not be factored in this way is said to be irreducible over this type of coefficient, thus, x2 -2 is irreducible over the integers and x2 +4 is irreducible over the reals. In the first example, the integers 1 and -2 can also be thought of as real numbers, and if they are, then x 2 −2 = shows that this polynomial factors over the reals. Similarly, since the integers 1 and 4 can be thought of as real and hence complex numbers, x2 +4 splits over the complex numbers, i. e. x 2 +4 =. The fundamental theorem of algebra can be stated as, Every polynomial of n with complex number coefficients splits completely into n linear factors
18.
Greek numerals
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Greek numerals are a system of writing numbers using the letters of the Greek alphabet. These alphabetic numerals are known as Ionic or Ionian numerals, Milesian numerals. In modern Greece, they are used for ordinal numbers. For ordinary cardinal numbers, however, Greece uses Arabic numerals, attic numerals, which were later adopted as the basis for Roman numerals, were the first alphabetic set. They were acrophonic, derived from the first letters of the names of the numbers represented and they ran =1, =5, =10, =100, =1000, and =10000. 50,500,5000, and 50000 were represented by the letter with minuscule powers of ten written in the top right corner, the same system was used outside of Attica, but the symbols varied with the local alphabets, in Boeotia, was 1000. The present system probably developed around Miletus in Ionia, 19th-century classicists placed its development in the 3rd century BC, the occasion of its first widespread use. The present system uses the 24 letters adopted by Euclid as well as three Phoenician and Ionic ones that were not carried over, digamma, koppa, and sampi. The position of characters within the numbering system imply that the first two were still in use while the third was not. Greek numerals are decimal, based on powers of 10, the units from 1 to 9 are assigned to the first nine letters of the old Ionic alphabet from alpha to theta. Each multiple of one hundred from 100 to 900 was then assigned its own separate letter as well and this alphabetic system operates on the additive principle in which the numeric values of the letters are added together to obtain the total. For example,241 was represented as, in ancient and medieval manuscripts, these numerals were eventually distinguished from letters using overbars, α, β, γ, etc. In medieval manuscripts of the Book of Revelation, the number of the Beast 666 is written as χξϛ, although the Greek alphabet began with only majuscule forms, surviving papyrus manuscripts from Egypt show that uncial and cursive minuscule forms began early. These new letter forms sometimes replaced the ones, especially in the case of the obscure numerals. The old Q-shaped koppa began to be broken up and simplified, the numeral for 6 changed several times. During antiquity, the letter form of digamma came to be avoided in favor of a special numerical one. By the Byzantine era, the letter was known as episemon and this eventually merged with the sigma-tau ligature stigma. In modern Greek, a number of changes have been made
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Roman numerals
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The numeric system represented by Roman numerals originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet, Roman numerals, as used today, are based on seven symbols, The use of Roman numerals continued long after the decline of the Roman Empire. The numbers 1 to 10 are usually expressed in Roman numerals as follows, I, II, III, IV, V, VI, VII, VIII, IX, Numbers are formed by combining symbols and adding the values, so II is two and XIII is thirteen. Symbols are placed left to right in order of value. Named after the year of its release,2014 as MMXIV, the year of the games of the XXII Olympic Winter Games The standard forms described above reflect typical modern usage rather than a universally accepted convention. Usage in ancient Rome varied greatly and remained inconsistent in medieval, Roman inscriptions, especially in official contexts, seem to show a preference for additive forms such as IIII and VIIII instead of subtractive forms such as IV and IX. Both methods appear in documents from the Roman era, even within the same document, double subtractives also occur, such as XIIX or even IIXX instead of XVIII. Sometimes V and L are not used, with such as IIIIII. Such variation and inconsistency continued through the period and into modern times. Clock faces that use Roman numerals normally show IIII for four o’clock but IX for nine o’clock, however, this is far from universal, for example, the clock on the Palace of Westminster in London uses IV. Similarly, at the beginning of the 20th century, different representations of 900 appeared in several inscribed dates. For instance,1910 is shown on Admiralty Arch, London, as MDCCCCX rather than MCMX, although Roman numerals came to be written with letters of the Roman alphabet, they were originally independent symbols. The Etruscans, for example, used
20.
Binary number
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The base-2 system is a positional notation with a radix of 2. Because of its implementation in digital electronic circuitry using logic gates. Each digit is referred to as a bit, the modern binary number system was devised by Gottfried Leibniz in 1679 and appears in his article Explication de lArithmétique Binaire. Systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, Leibniz was specifically inspired by the Chinese I Ching. The scribes of ancient Egypt used two different systems for their fractions, Egyptian fractions and Horus-Eye fractions, the method used for ancient Egyptian multiplication is also closely related to binary numbers. This method can be seen in use, for instance, in the Rhind Mathematical Papyrus, the I Ching dates from the 9th century BC in China. The binary notation in the I Ching is used to interpret its quaternary divination technique and it is based on taoistic duality of yin and yang. Eight trigrams and a set of 64 hexagrams, analogous to the three-bit and six-bit binary numerals, were in use at least as early as the Zhou Dynasty of ancient China. The Song Dynasty scholar Shao Yong rearranged the hexagrams in a format that resembles modern binary numbers, the Indian scholar Pingala developed a binary system for describing prosody. He used binary numbers in the form of short and long syllables, Pingalas Hindu classic titled Chandaḥśāstra describes the formation of a matrix in order to give a unique value to each meter. The binary representations in Pingalas system increases towards the right, the residents of the island of Mangareva in French Polynesia were using a hybrid binary-decimal system before 1450. Slit drums with binary tones are used to encode messages across Africa, sets of binary combinations similar to the I Ching have also been used in traditional African divination systems such as Ifá as well as in medieval Western geomancy. The base-2 system utilized in geomancy had long been applied in sub-Saharan Africa. Leibnizs system uses 0 and 1, like the modern binary numeral system, Leibniz was first introduced to the I Ching through his contact with the French Jesuit Joachim Bouvet, who visited China in 1685 as a missionary. Leibniz saw the I Ching hexagrams as an affirmation of the universality of his own beliefs as a Christian. Binary numerals were central to Leibnizs theology and he believed that binary numbers were symbolic of the Christian idea of creatio ex nihilo or creation out of nothing. Is not easy to impart to the pagans, is the ex nihilo through Gods almighty power. In 1854, British mathematician George Boole published a paper detailing an algebraic system of logic that would become known as Boolean algebra
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Ternary numeral system
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The ternary numeral system has three as its base. Analogous to a bit, a digit is a trit. One trit is equivalent to bits of information. Representations of integer numbers in ternary do not get uncomfortably lengthy as quickly as in binary, for example, decimal 365 corresponds to binary 101101101 and to ternary 111112. However, they are far less compact than the corresponding representations in bases such as decimal – see below for a compact way to codify ternary using nonary. The value of a number with n bits that are all 1 is 2n −1. Then N = M, N = /, and N = bd −1, for a three-digit ternary number, N =33 −1 =26 =2 ×32 +2 ×31 +2 ×30 =18 +6 +2. Nonary or septemvigesimal can be used for representation of ternary. A base-three system is used in Islam to keep track of counting Tasbih to 99 or to 100 on a hand for counting prayers. In certain analog logic, the state of the circuit is often expressed ternary and this is most commonly seen in Transistor–transistor logic using 7406 open collector logic. The output is said to either be low, high, or open, in this configuration the output of the circuit is actually not connected to any voltage reference at all. Where the signal is usually grounded to a reference, or at a certain voltage level. Thus, the voltage level is sometimes unpredictable. A rare ternary point is used to denote fractional parts of an inning in baseball, since each inning consists of three outs, each out is considered one third of an inning and is denoted as.1. For example, if a player pitched all of the 4th, 5th and 6th innings, plus 2 outs of the 7th inning, his Innings pitched column for that game would be listed as 3.2, meaning 3⅔. In this usage, only the part of the number is written in ternary form. Ternary numbers can be used to convey self-similar structures like the Sierpinski triangle or the Cantor set conveniently, additionally, it turns out that the ternary representation is useful for defining the Cantor set and related point sets, because of the way the Cantor set is constructed. The Cantor set consists of the points from 0 to 1 that have an expression that does not contain any instance of the digit 1
22.
Quaternary numeral system
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Quaternary is the base-4 numeral system. It uses the digits 0,1,2 and 3 to represent any real number. Four is the largest number within the range and one of two numbers that is both a square and a highly composite number, making quaternary a convenient choice for a base at this scale. Despite being twice as large, its economy is equal to that of binary. However, it no better in the localization of prime numbers. See decimal and binary for a discussion of these properties, as with the octal and hexadecimal numeral systems, quaternary has a special relation to the binary numeral system. Each radix 4,8 and 16 is a power of 2, so the conversion to and from binary is implemented by matching each digit with 2,3 or 4 binary digits, for example, in base 4,302104 =11001001002. Although octal and hexadecimal are widely used in computing and computer programming in the discussion and analysis of binary arithmetic and logic, by analogy with byte and nybble, a quaternary digit is sometimes called a crumb. There is a surviving list of Ventureño language number words up to 32 written down by a Spanish priest ca, the Kharosthi numerals have a partial base 4 counting system from 1 to decimal 10. Quaternary numbers are used in the representation of 2D Hilbert curves, here a real number between 0 and 1 is converted into the quaternary system. Every single digit now indicates in which of the respective 4 sub-quadrants the number will be projected, parallels can be drawn between quaternary numerals and the way genetic code is represented by DNA. The four DNA nucleotides in order, abbreviated A, C, G and T, can be taken to represent the quaternary digits in numerical order 0,1,2. With this encoding, the complementary digit pairs 0↔3, and 1↔2 match the complementation of the pairs, A↔T and C↔G. For example, the nucleotide sequence GATTACA can be represented by the quaternary number 2033010, quaternary line codes have been used for transmission, from the invention of the telegraph to the 2B1Q code used in modern ISDN circuits
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Quinary
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Quinary is a numeral system with five as the base. A possible origination of a system is that there are five fingers on either hand. The base five is stated from 0–4, in the quinary place system, five numerals, from 0 to 4, are used to represent any real number. According to this method, five is written as 10, twenty-five is written as 100, today, the main usage of base 5 is as a biquinary system, which is decimal using five as a sub-base. Another example of a system, is sexagesimal, base 60. Each quinary digit has log25 bits of information, many languages use quinary number systems, including Gumatj, Nunggubuyu, Kuurn Kopan Noot, Luiseño and Saraveca. Gumatj is a true 5–25 language, in which 25 is the group of 5. The Gumatj numerals are shown below, In the video game Riven and subsequent games of the Myst franchise, a decimal system with 2 and 5 as a sub-bases is called biquinary, and is found in Wolof and Khmer. Roman numerals are a biquinary system, the numbers 1,5,10, and 50 are written as I, V, X, and L respectively. Eight is VIII and seventy is LXX, most versions of the abacus use a biquinary system to simulate a decimal system for ease of calculation. Urnfield culture numerals and some tally mark systems are also biquinary, units of currencies are commonly partially or wholly biquinary. A vigesimal system with 4 and 5 as a sub-bases is found in Nahuatl, pentimal system Quibinary Yan Tan Tethera References, Quinary Base Conversion, includes fractional part, from Math Is Fun Media related to Quinary numeral system at Wikimedia Commons
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Senary
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The senary numeral system has six as its base. It has been adopted independently by a number of cultures. Like decimal, it is a semiprime, though being the product of the two consecutive numbers that are both prime it has a high degree of mathematical properties for its size. As six is a highly composite number, many of the arguments made in favor of the duodecimal system also apply to this base-6. Senary may be considered interesting in the study of numbers, since all primes other than 2 and 3. That is, for every number p greater than 3, one has the modular arithmetic relations that either p ≡1 or 5. This property maximizes the probability that the result of an integer multiplication will end in zero, E. g. if three fingers are extended on the left hand and four on the right, 34senary is represented. This is equivalent to 3 ×6 +4 which is 22decimal, flipping the sixes hand around to its backside may help to further disambiguate which hand represents the sixes and which represents the units. While most developed cultures count by fingers up to 5 in very similar ways, beyond 5 non-Western cultures deviate from Western methods, such as with Chinese number gestures. More abstract finger counting systems, such as chisanbop or finger binary, allow counting to 99,1,023, or even higher depending on the method. The English monk and historian Bede, in the first chapter of De temporum ratione, titled Tractatus de computo, vel loquela per gestum digitorum, the Ndom language of Papua New Guinea is reported to have senary numerals. Mer means 6, mer an thef means 6 ×2 =12, nif means 36, another example from Papua New Guinea are the Morehead-Maro languages. In these languages, counting is connected to ritualized yam-counting and these languages count from a base six, employing words for the powers of six, running up to 66 for some of the languages. One example is Kómnzo with the numerals, nimbo, féta, tarumba, ntamno, wärämäkä. Some Niger-Congo languages have been reported to use a number system, usually in addition to another. For some purposes, base 6 might be too small a base for convenience. The choice of 36 as a radix is convenient in that the digits can be represented using the Arabic numerals 0–9 and the Latin letters A–Z, this choice is the basis of the base36 encoding scheme. Base36 encoding scheme Binary Ternary Duodecimal Sexagesimal Shacks Base Six Dialectic Digital base 6 clock Analog Clock Designer capable of rendering a base 6 clock Senary base conversion
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Octal
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The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Octal numerals can be made from binary numerals by grouping binary digits into groups of three. For example, the representation for decimal 74 is 1001010. Two zeroes can be added at the left,1001010, corresponding the octal digits 112, in the decimal system each decimal place is a power of ten. For example,7410 =7 ×101 +4 ×100 In the octal system each place is a power of eight. The Yuki language in California and the Pamean languages in Mexico have octal systems because the speakers count using the spaces between their fingers rather than the fingers themselves and it has been suggested that the reconstructed Proto-Indo-European word for nine might be related to the PIE word for new. Based on this, some have speculated that proto-Indo-Europeans used a number system. In 1716 King Charles XII of Sweden asked Emanuel Swedenborg to elaborate a number based on 64 instead of 10. Swedenborg however argued that for people with less intelligence than the king such a big base would be too difficult, in 1718 Swedenborg wrote a manuscript, En ny rekenkonst som om vexlas wid Thalet 8 i stelle then wanliga wid Thalet 10. The numbers 1-7 are there denoted by the l, s, n, m, t, f, u. Thus 8 = lo,16 = so,24 = no,64 = loo,512 = looo etc, numbers with consecutive consonants are pronounced with vowel sounds between in accordance with a special rule. Writing under the pseudonym Hirossa Ap-Iccim in The Gentlemans Magazine, July 1745, Hugh Jones proposed a system for British coins, weights. In 1801, James Anderson criticized the French for basing the Metric system on decimal arithmetic and he suggested base 8 for which he coined the term octal. In the mid 19th century, Alfred B. Taylor concluded that Our octonary radix is, therefore, so, for example, the number 65 would be spoken in octonary as under-un. Taylor also republished some of Swedenborgs work on octonary as an appendix to the above-cited publications, in the 2009 film Avatar, the language of the extraterrestrial Navi race employs an octal numeral system, probably due to the fact that they have four fingers on each hand. In the TV series Stargate SG-1, the Ancients, a race of beings responsible for the invention of the Stargates, in the tabletop game series Warhammer 40,000, the Tau race use an octal number system. Octal became widely used in computing systems such as the PDP-8, ICL1900. Octal was an abbreviation of binary for these machines because their word size is divisible by three
26.
Duodecimal
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The duodecimal system is a positional notation numeral system using twelve as its base. In this system, the number ten may be written by a rotated 2 and this notation was introduced by Sir Isaac Pitman. These digit forms are available as Unicode characters on computerized systems since June 2015 as ↊ and ↋, other notations use A, T, or X for ten and B or E for eleven. The number twelve is written as 10 in duodecimal, whereas the digit string 12 means 1 dozen and 2 units. Similarly, in duodecimal 100 means 1 gross,1000 means 1 great gross, the number twelve, a superior highly composite number, is the smallest number with four non-trivial factors, and the smallest to include as factors all four numbers within the subitizing range. As a result, duodecimal has been described as the number system. Of its factors,2 and 3 are prime, which means the reciprocals of all 3-smooth numbers have a representation in duodecimal. In particular, the five most elementary fractions all have a terminating representation in duodecimal. This all makes it a convenient number system for computing fractions than most other number systems in common use, such as the decimal, vigesimal, binary. Although the trigesimal and sexagesimal systems do even better in respect, this is at the cost of unwieldy multiplication tables. In this section, numerals are based on decimal places, for example,10 means ten,12 means twelve. Languages using duodecimal number systems are uncommon, germanic languages have special words for 11 and 12, such as eleven and twelve in English. However, they are considered to come from Proto-Germanic *ainlif and *twalif, historically, units of time in many civilizations are duodecimal. There are twelve signs of the zodiac, twelve months in a year, traditional Chinese calendars, clocks, and compasses are based on the twelve Earthly Branches. There are 12 inches in a foot,12 troy ounces in a troy pound,12 old British pence in a shilling,24 hours in a day. The Romans used a system based on 12, including the uncia which became both the English words ounce and inch. The importance of 12 has been attributed to the number of cycles in a year. It is possible to count to 12 with the acting as a pointer
27.
Hexadecimal
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In mathematics and computing, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, Hexadecimal numerals are widely used by computer system designers and programmers. As each hexadecimal digit represents four binary digits, it allows a more human-friendly representation of binary-coded values, one hexadecimal digit represents a nibble, which is half of an octet or byte. For example, a byte can have values ranging from 00000000 to 11111111 in binary form. In a non-programming context, a subscript is typically used to give the radix, several notations are used to support hexadecimal representation of constants in programming languages, usually involving a prefix or suffix. The prefix 0x is used in C and related languages, where this value might be denoted as 0x2AF3, in contexts where the base is not clear, hexadecimal numbers can be ambiguous and confused with numbers expressed in other bases. There are several conventions for expressing values unambiguously, a numerical subscript can give the base explicitly,15910 is decimal 159,15916 is hexadecimal 159, which is equal to 34510. Some authors prefer a text subscript, such as 159decimal and 159hex, or 159d and 159h. example. com/name%20with%20spaces where %20 is the space character, thus ’, represents the right single quotation mark, Unicode code point number 2019 in hex,8217. In the Unicode standard, a value is represented with U+ followed by the hex value. Color references in HTML, CSS and X Window can be expressed with six hexadecimal digits prefixed with #, white, CSS allows 3-hexdigit abbreviations with one hexdigit per component, #FA3 abbreviates #FFAA33. *nix shells, AT&T assembly language and likewise the C programming language, to output an integer as hexadecimal with the printf function family, the format conversion code %X or %x is used. In Intel-derived assembly languages and Modula-2, hexadecimal is denoted with a suffixed H or h, some assembly languages use the notation HABCD. Ada and VHDL enclose hexadecimal numerals in based numeric quotes, 16#5A3#, for bit vector constants VHDL uses the notation x5A3. Verilog represents hexadecimal constants in the form 8hFF, where 8 is the number of bits in the value, the Smalltalk language uses the prefix 16r, 16r5A3 PostScript and the Bourne shell and its derivatives denote hex with prefix 16#, 16#5A3. For PostScript, binary data can be expressed as unprefixed consecutive hexadecimal pairs, in early systems when a Macintosh crashed, one or two lines of hexadecimal code would be displayed under the Sad Mac to tell the user what went wrong. Common Lisp uses the prefixes #x and #16r, setting the variables *read-base* and *print-base* to 16 can also used to switch the reader and printer of a Common Lisp system to Hexadecimal number representation for reading and printing numbers. Thus Hexadecimal numbers can be represented without the #x or #16r prefix code, MSX BASIC, QuickBASIC, FreeBASIC and Visual Basic prefix hexadecimal numbers with &H, &H5A3 BBC BASIC and Locomotive BASIC use & for hex. TI-89 and 92 series uses a 0h prefix, 0h5A3 ALGOL68 uses the prefix 16r to denote hexadecimal numbers, binary, quaternary and octal numbers can be specified similarly
28.
Vigesimal
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The vigesimal or base 20 numeral system is based on twenty. In a vigesimal system, twenty individual numerals are used. One modern method of finding the extra needed symbols is to write ten as the letter A20, to write nineteen as J20, and this is similar to the common computer-science practice of writing hexadecimal numerals over 9 with the letters A–F. Another method skips over the letter I, in order to avoid confusion between I20 as eighteen and one, so that the number eighteen is written as J20, the number twenty is written as 1020. According to this notation,2020 means forty in decimal = + D020 means two hundred and sixty in decimal = +10020 means four hundred in decimal = + +, in the rest of this article below, numbers are expressed in decimal notation, unless specified otherwise. For example,10 means ten,20 means twenty, in decimal, dividing by three twice only gives one digit periods because 9 is the number below ten. 21, however, the adjacent to 20 that is divisible by 3, is not divisible by 9. Ninths in vigesimal have six-digit periods, the prime factorization of twenty is 22 ×5, so it is not a perfect power. However, its part,5, is congruent to 1. Thus, according to Artins conjecture on primitive roots, vigesimal has infinitely many cyclic primes, but the fraction of primes that are cyclic is not necessarily ~37. 395%. An UnrealScript program that computes the lengths of recurring periods of various fractions in a set of bases found that, of the first 15,456 primes. In many European languages,20 is used as a base, vigesimal systems are common in Africa, for example in Yoruba. Ogún,20, is the basic numeric block, ogójì,40, =20 multiplied by 2. Ogota,60, =20 multiplied by 3, ogorin,80, =20 multiplied by 4. Ogorun,100, =20 multiplied by 5, twenty was a base in the Maya and Aztec number systems. The Maya used the names for the powers of twenty, kal, bak, pic, calab, kinchil. See also Maya numerals and Maya calendar, Mayan languages, Yucatec, the Aztec called them, cempoalli, centzontli, cenxiquipilli, cempoalxiquipilli, centzonxiquipilli and cempoaltzonxiquipilli. Note that the ce prefix at the beginning means one and is replaced with the number to get the names of other multiples of the power
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Base 36
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The senary numeral system has six as its base. It has been adopted independently by a number of cultures. Like decimal, it is a semiprime, though being the product of the two consecutive numbers that are both prime it has a high degree of mathematical properties for its size. As six is a highly composite number, many of the arguments made in favor of the duodecimal system also apply to this base-6. Senary may be considered interesting in the study of numbers, since all primes other than 2 and 3. That is, for every number p greater than 3, one has the modular arithmetic relations that either p ≡1 or 5. This property maximizes the probability that the result of an integer multiplication will end in zero, E. g. if three fingers are extended on the left hand and four on the right, 34senary is represented. This is equivalent to 3 ×6 +4 which is 22decimal, flipping the sixes hand around to its backside may help to further disambiguate which hand represents the sixes and which represents the units. While most developed cultures count by fingers up to 5 in very similar ways, beyond 5 non-Western cultures deviate from Western methods, such as with Chinese number gestures. More abstract finger counting systems, such as chisanbop or finger binary, allow counting to 99,1,023, or even higher depending on the method. The English monk and historian Bede, in the first chapter of De temporum ratione, titled Tractatus de computo, vel loquela per gestum digitorum, the Ndom language of Papua New Guinea is reported to have senary numerals. Mer means 6, mer an thef means 6 ×2 =12, nif means 36, another example from Papua New Guinea are the Morehead-Maro languages. In these languages, counting is connected to ritualized yam-counting and these languages count from a base six, employing words for the powers of six, running up to 66 for some of the languages. One example is Kómnzo with the numerals, nimbo, féta, tarumba, ntamno, wärämäkä. Some Niger-Congo languages have been reported to use a number system, usually in addition to another. For some purposes, base 6 might be too small a base for convenience. The choice of 36 as a radix is convenient in that the digits can be represented using the Arabic numerals 0–9 and the Latin letters A–Z, this choice is the basis of the base36 encoding scheme. Base36 encoding scheme Binary Ternary Duodecimal Sexagesimal Shacks Base Six Dialectic Digital base 6 clock Analog Clock Designer capable of rendering a base 6 clock Senary base conversion
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Hebrew numerals
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The system of Hebrew numerals is a quasi-decimal alphabetic numeral system using the letters of the Hebrew alphabet. The system was adapted from that of the Greek numerals in the late 2nd century BC, the current numeral system is also known as the Hebrew alphabetic numerals to contrast with earlier systems of writing numerals used in classical antiquity. The Greek system was adopted in Hellenistic Judaism and had been in use in Greece since about the 5th century BC, in this system, there is no notation for zero, and the numeric values for individual letters are added together. Each unit is assigned a letter, each tens a separate letter. The later hundreds are represented by the sum of two or three letters representing the first four hundreds, to represent numbers from 1,000 to 999,999, the same letters are reused to serve as thousands, tens of thousands, and hundreds of thousands. In Israel today, the system of Arabic numerals is used in almost all cases. The Hebrew numerals are used only in cases, such as when using the Hebrew calendar, or numbering a list. Numbers in Hebrew from zero to one million, Hebrew alphabet are used to a limited extent to represent numbers, widely used on calendars. In other situations Arabic numerals are used, cardinal and ordinal numbers must agree in gender with the noun they are describing. If there is no such noun, the form is used. For ordinal numbers greater than ten the cardinal is used and numbers above the value 20 have no gender, note, For ordinal numbers greater than 10, cardinal numbers are used instead. Note, For numbers greater than 20, gender does not apply, cardinal and ordinal numbers must agree in gender with the noun they are describing. If there is no such noun, the form is used. Ordinal numbers must also agree in number and definite status like other adjectives, the cardinal number precedes the noun, except for the number one which succeeds it. The number two is special - shnayim and shtayim become shney and shtey when followed by the noun they count, for ordinal numbers greater than ten the cardinal is used. The Hebrew numeric system operates on the principle in which the numeric values of the letters are added together to form the total. For example,177 is represented as קעז which corresponds to 100 +70 +7 =177, mathematically, this type of system requires 27 letters. In practice the last letter, tav is used in combination with itself and/or other letters from kof onwards, to numbers from 500
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Natural number
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In mathematics, the natural numbers are those used for counting and ordering. In common language, words used for counting are cardinal numbers, texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, but in other writings, that term is used instead for the integers. These chains of extensions make the natural numbers canonically embedded in the number systems. Properties of the numbers, such as divisibility and the distribution of prime numbers, are studied in number theory. Problems concerning counting and ordering, such as partitioning and enumerations, are studied in combinatorics, the most primitive method of representing a natural number is to put down a mark for each object. Later, a set of objects could be tested for equality, excess or shortage, by striking out a mark, the first major advance in abstraction was the use of numerals to represent numbers. This allowed systems to be developed for recording large numbers, the ancient Egyptians developed a powerful system of numerals with distinct hieroglyphs for 1,10, and all the powers of 10 up to over 1 million. A stone carving from Karnak, dating from around 1500 BC and now at the Louvre in Paris, depicts 276 as 2 hundreds,7 tens, and 6 ones, and similarly for the number 4,622. A much later advance was the development of the idea that 0 can be considered as a number, with its own numeral. The use of a 0 digit in place-value notation dates back as early as 700 BC by the Babylonians, the Olmec and Maya civilizations used 0 as a separate number as early as the 1st century BC, but this usage did not spread beyond Mesoamerica. The use of a numeral 0 in modern times originated with the Indian mathematician Brahmagupta in 628, the first systematic study of numbers as abstractions is usually credited to the Greek philosophers Pythagoras and Archimedes. Some Greek mathematicians treated the number 1 differently than larger numbers, independent studies also occurred at around the same time in India, China, and Mesoamerica. In 19th century Europe, there was mathematical and philosophical discussion about the nature of the natural numbers. A school of Naturalism stated that the numbers were a direct consequence of the human psyche. Henri Poincaré was one of its advocates, as was Leopold Kronecker who summarized God made the integers, in opposition to the Naturalists, the constructivists saw a need to improve the logical rigor in the foundations of mathematics. In the 1860s, Hermann Grassmann suggested a recursive definition for natural numbers thus stating they were not really natural, later, two classes of such formal definitions were constructed, later, they were shown to be equivalent in most practical applications. The second class of definitions was introduced by Giuseppe Peano and is now called Peano arithmetic and it is based on an axiomatization of the properties of ordinal numbers, each natural number has a successor and every non-zero natural number has a unique predecessor. Peano arithmetic is equiconsistent with several systems of set theory
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Triangular number
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A triangular number or triangle number counts the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangular number is the number of dots composing a triangle with n dots on a side and it represents the number of distinct pairs that can be selected from n +1 objects, and it is read aloud as n plus one choose two. Carl Friedrich Gauss is said to have found this relationship in his early youth, however, regardless of the truth of this story, Gauss was not the first to discover this formula, and some find it likely that its origin goes back to the Pythagoreans 5th century BC. The two formulae were described by the Irish monk Dicuil in about 816 in his Computus, the triangular number Tn solves the handshake problem of counting the number of handshakes if each person in a room with n +1 people shakes hands once with each person. In other words, the solution to the problem of n people is Tn−1. The function T is the analog of the factorial function. In the limit, the ratio between the two numbers, dots and line segments is lim n → ∞ T n L n =13, Triangular numbers have a wide variety of relations to other figurate numbers. Most simply, the sum of two triangular numbers is a square number, with the sum being the square of the difference between the two. Algebraically, T n + T n −1 = + = + = n 2 =2, alternatively, the same fact can be demonstrated graphically, There are infinitely many triangular numbers that are also square numbers, e. g.1,36,1225. Some of them can be generated by a recursive formula. All square triangular numbers are found from the recursion S n =34 S n −1 − S n −2 +2 with S0 =0 and S1 =1. Also, the square of the nth triangular number is the same as the sum of the cubes of the integers 1 to n and this can also be expressed as ∑ k =1 n k 3 =2. The sum of the all triangular numbers up to the nth triangular number is the nth tetrahedral number, more generally, the difference between the nth m-gonal number and the nth -gonal number is the th triangular number. For example, the sixth heptagonal number minus the sixth hexagonal number equals the triangular number,15. Every other triangular number is a hexagonal number, knowing the triangular numbers, one can reckon any centered polygonal number, the nth centered k-gonal number is obtained by the formula C k n = k T n −1 +1 where T is a triangular number. The positive difference of two numbers is a trapezoidal number. Triangular numbers correspond to the case of Faulhabers formula. Alternating triangular numbers are also hexagonal numbers, every even perfect number is triangular, given by the formula M p 2 p −1 = M p 2 = T M p where Mp is a Mersenne prime