|Divisors||1, 2, 4|
|Roman numeral (unicode)||Ⅳ, ⅳ|
|Greek||δ (or Δ)|
4 is the smallest squared prime (p2) and the only even number in this form. 4 is also the only square one more than a prime number.
A number is a multiple of 4 if its last two digits are a multiple of 4. For example, 1092 is a multiple of 4 because 92 = 4 × 23.
In addition, 2 + 2 = 2 × 2 = 22 = 4. Continuing the pattern in Knuth's up-arrow notation, 2 ↑↑ 2 = 2 ↑↑↑ 2 = 4, and so on, for any number of up arrows. (That is, 2 [n] 2 = 4 for every positive integer n, where a [n] b is the hyperoperation.)
A four-sided plane figure is a quadrilateral (quadrangle) which include kites, rhombi, rectangles and squares, sometimes also called a tetragon. A circle divided by 4 makes right angles and four quadrants. Because of it, four (4) is the base number of the plane (mathematics). Four cardinal directions, four seasons, the duodecimal system, and the vigesimal system are based on four.
A solid figure with four faces as well as four vertices is a tetrahedron, and 4 is the smallest possible number of faces (as well as vertices) of a polyhedron. The regular tetrahedron is the simplest Platonic solid. A tetrahedron, which can also be called a 3-simplex, has four triangular faces and four vertices. It is the only self-dual regular polyhedron.
Four-dimensional space is the highest-dimensional space featuring more than three convex regular figures:
Four is the only integer n for which the (non trivial) alternating group An is not simple.
The four-color theorem states that a planar graph (or, equivalently, a flat map of two-dimensional regions such as countries) can be colored using four colors, so that adjacent vertices (or regions) are always different colors. Three colors are not, in general, sufficient to guarantee this. The largest planar complete graph has four vertices.
Lagrange's four-square theorem states that every positive integer can be written as the sum of at most four square numbers. Three are not always sufficient; 7 for instance cannot be written as the sum of three squares.
Each natural number divisible by 4 is a difference of squares of two natural numbers, i.e. 4x = y2 − z2.
The four fours game, there are known solutions for all integers from 0 to 880 (but not 881).
|4 × x||4||8||12||16||20||24||28||32||36||40||44||48||52||56||60||64||68||72||76||80||84||88||92||96||100||200||400||4000|
|4 ÷ x||4||2||1.3||1||0.8||0.6||0.571428||0.5||0.4||0.4||0.36||0.3||0.307692||0.285714||0.26||0.25|
|x ÷ 4||0.25||0.5||0.75||1||1.25||1.5||1.75||2||2.25||2.5||2.75||3||3.25||3.5||3.75||4|
Representing 1, 2 and 3 in as many lines as the number represented worked well. The Brahmin Indians simplified 4 by joining its four lines into a cross that looks like the modern plus sign. The Shunga would add a horizontal line on top of the numeral, and the Kshatrapa and Pallava evolved the numeral to a point where the speed of writing was a secondary concern. The Arabs' 4 still had the early concept of the cross, but for the sake of efficiency, was made in one stroke by connecting the "western" end to the "northern" end; the "eastern" end was finished off with a curve. The Europeans dropped the finishing curve and gradually made the numeral less cursive, ending up with a glyph very close to the original Brahmin cross.
Television stations that operate on channel 4 have occasionally made use of another variation of the "open 4", with the open portion being on the side, rather than the top. This version resembles the Canadian Aboriginal syllabics letter ᔦ or the Coptic letter Ϥ. The magnetic ink character recognition "CMC-7" font also uses this variety of "4".
The 2014–15 UEFA Champions League was the 60th season of Europe's premier club football tournament organised by UEFA, and the 23rd season since it was renamed from the European Champion Clubs' Cup to the UEFA Champions League.
The 2015 UEFA Champions League Final was played at the Olympiastadion in Berlin, Germany, with Spanish side Barcelona defeating Italian side Juventus by 3–1 to win their fifth title and complete their treble. Real Madrid were the title holders, but they were eliminated by Juventus in the semi-finals.
This season was the first where clubs must comply with UEFA Financial Fair Play Regulations in order to participate. Moreover, this season was the first where a club from Gibraltar competed in the tournament, after the Gibraltar Football Association was accepted as the 54th UEFA member at the UEFA Congress in May 2013. They were granted one spot in the Champions League, which was taken by Lincoln Red Imps, the champions of the 2013–14 Gibraltar Premier Division.On 17 July 2014, the UEFA emergency panel ruled that Ukrainian and Russian clubs would not be drawn against each other "until further notice" due to the political unrest between the countries. Another ruling centred in regional instability was also made where Israeli teams were prohibited from hosting any UEFA competitions due to the 2014 Israel–Gaza conflict. The rules regarding suspension due to yellow card accumulation were also changed such that all bookings expired on completion of the quarter-finals and were not carried forward to the semi-finals. Moreover, this was the first season in which vanishing spray was used.2015–16 UEFA Champions League
The 2015–16 UEFA Champions League was the 61st season of Europe's premier club football tournament organised by UEFA, and the 24th season since it was renamed from the European Champion Clubs' Cup to the UEFA Champions League. Barcelona were the title holders, but were eliminated by Atlético Madrid in the quarter-finals.
The 2016 UEFA Champions League Final was played between Real Madrid and Atlético Madrid at the San Siro in Milan, Italy. It was the second time in the tournament's history that both finalists were from the same city, after the same clubs faced each other in the 2014 final. Real Madrid defeated Atlético Madrid 5–3 on penalties (1–1 after extra time) in the final to win a record-extending eleventh European Cup/Champions League title.
As the winners of the 2015–16 UEFA Champions League, Real Madrid qualified as the UEFA representative at the 2016 FIFA Club World Cup in Japan (their third Club World Cup appearance), and also earned the right to play against the winners of the 2015–16 UEFA Europa League, Sevilla, in the 2016 UEFA Super Cup.2017–18 UEFA Champions League
The 2017–18 UEFA Champions League was the 63rd season of Europe's premier club football tournament organised by UEFA, the 26th season since it was renamed from the European Champion Clubs' Cup to the UEFA Champions League.
The final was played between Real Madrid and Liverpool at the NSC Olimpiyskiy Stadium in Kiev, Ukraine. Real Madrid, the defending champions, beat Liverpool 3–1 to win a record-extending 13th title and their third title in a row.
As winners, Real Madrid qualified as the UEFA representative for the 2018 FIFA Club World Cup in the United Arab Emirates, and also earned the right to play against the winners of the 2017–18 UEFA Europa League, Atlético Madrid, in the 2018 UEFA Super Cup. Moreover, they would also have been automatically qualified for the 2018–19 UEFA Champions League group stage, but since they had already qualified through their league performance, the berth reserved was given to the champions of the 2017–18 Czech First League, the 11th-ranked association according to next season's access list.2018–19 FA Cup
The 2018–19 FA Cup (also known as the Football Association Challenge Cup) is the 138th edition of the oldest recognised football tournament in the world. It is sponsored by Emirates and known as The Emirates FA Cup for sponsorship purposes. It started with the Extra Preliminary Round on the weekend of 11 August 2018 and will conclude with the final on 18 May 2019. The winner will qualify for the 2019–20 UEFA Europa League group stage.
Premier League side Chelsea were the defending champions, but they were eliminated by Manchester United in the fifth round on 18 February 2019 in a rematch of the previous year's final.2018–19 UEFA Europa League
The 2018–19 UEFA Europa League is the 48th season of Europe's secondary club football tournament organised by UEFA, and the 10th season since it was renamed from the UEFA Cup to the UEFA Europa League.
The final will be played at the Olympic Stadium in Baku, Azerbaijan. The winners of the 2018–19 UEFA Europa League will earn the right to play against the winners of the 2018–19 UEFA Champions League in the 2019 UEFA Super Cup. They will also automatically qualify for the 2019–20 UEFA Champions League group stage, and if they have already qualified through their league performance, the berth reserved will be given to the third-placed team of the 2018–19 Ligue 1, the 5th-ranked association according to next season's access list.For the first time, the video assistant referee (VAR) system will be used in the competition, where it will be implemented in the final.As the title holders of Europa League, Atlético Madrid qualified for the 2018–19 UEFA Champions League, although they had already qualified before the final through their league performance. They are unable to defend their title as they advanced to the Champions League knockout stage.ASCII
ASCII ( (listen) ASS-kee), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Most modern character-encoding schemes are based on ASCII, although they support many additional characters.
ASCII is the traditional name for the encoding system; the Internet Assigned Numbers Authority (IANA) prefers the updated name US-ASCII, which clarifies that this system was developed in the US and based on the typographical symbols predominantly in use there.ASCII is one of the IEEE milestones.ATP Tour Masters 1000
The ATP Masters 1000 (previously known as the ATP Championship Series, Single-Week, ATP Mercedes-Benz Super 9, Tennis Masters Series, and ATP Masters Series) is the third highest tier of annual men's tennis tournament after the four Grand Slam tournaments and the ATP Finals.
Results in ATP Masters 1000 events earn players more world ranking points than regular tournaments, though not as many as Grand Slam events or the year-end ATP Finals. Up until 2007, most Masters Series finals were contested as best of five-set matches. Currently, all Masters Series matches (including the finals) are decided in best of three-set matches.
In singles, Rafael Nadal holds the record for the most titles with 33 since the Masters series began in 1990. Novak Djokovic is the only player to have won all nine Masters singles titles and became the first player to complete the Career Golden Masters. Djokovic has the second most titles holding 32. Rafael Nadal, Roger Federer, Andre Agassi, and Andy Murray have each won 7 different titles. Djokovic holds the record for the most singles titles in a year, winning 6 in 2015. Additionally, Djokovic and Nadal are the only two players to win four singles titles in a row and Nadal is the only person to complete the feat in the same calendar year when he won Madrid, Rome, Canada, and Cincinnati in 2013. Nadal and Djokovic together held all 9 Masters 1000 crowns starting with the 2013 Monte Carlo title through the 2014 Miami title, which was the first time that 2 players possessed all nine of the titles.
In doubles, the Bryan brothers (Bob and Mike) have won a record 38 doubles titles, all as a team. Daniel Nestor and the Bryan brothers have each won all 9 titles throughout their careers. The Bryans have won 6 titles in a single year once (2014) and 5 titles in a single year twice (2007 and 2013).
Currently, the following 9 tournaments are part of the series: Canadian Open (alternating yearly between Montreal and Toronto), Cincinnati Masters, Indian Wells Masters, Italian Open (Rome), Madrid Open, Miami Open, Monte-Carlo Masters, Paris Masters, and Shanghai Masters.Android version history
The version history of the Android mobile operating system began with the public release of the Android beta on November 5, 2007. The first commercial version, Android 1.0, was released on September 23, 2008. Android is continually developed by Google and the Open Handset Alliance, and it has seen a number of updates to its base operating system since the initial release.Aspect ratio (image)
The aspect ratio of an image describes the proportional relationship between its width and its height. It is commonly expressed as two numbers separated by a colon, as in 16:9. For an x:y aspect ratio, no matter how big or small the image is, if the width is divided into x units of equal length and the height is measured using this same length unit, the height will be measured to be y units.
For example, in a group of images that all have an aspect ratio of 16:9, one image might be 16 inches wide and 9 inches high, another 16 centimeters wide and 9 centimeters high, and a third might be 8 yards wide and 4.5 yards high. Thus, aspect ratio concerns the relationship of the width to the height, not an image's actual size.Bugatti Veyron
The Bugatti Veyron EB 16.4 is a mid-engine sports car, designed and developed in Germany by the Volkswagen Group and manufactured in Molsheim, France, by French automobile manufacturer Bugatti. It was named after the racing driver Pierre Veyron.
The original version has a top speed of 407 km/h (253 mph). It was named Car of the Decade and best car award (2000–2009) by the BBC television programme Top Gear. The standard Bugatti Veyron also won Top Gear's Best Car Driven All Year award in 2005.
The Super Sport version of the Veyron is recognised by Guinness World Records as the fastest street-legal production car in the world, with a top speed of 431.072 km/h (267.856 mph). The Veyron Grand Sport Vitesse was the fastest roadster in the world, reaching an averaged top speed of 408.84 km/h (254.04 mph) in a test on 6 April 2013.The Veyron's chief designer was Hartmut Warkuß and the exterior was designed by Jozef Kabaň of Volkswagen, with much of the engineering work being conducted under the guidance of engineering chief Wolfgang Schreiber. The Veyron includes a sound system designed and built by Burmester Audiosysteme.Several special variants have been produced. In December, 2010, Bugatti began offering prospective buyers the ability to customise exterior and interior colours by using the Veyron 16.4 Configurator application on the marque's official website. The Bugatti Veyron was discontinued in late 2014. But special edition models continued production til 2015.Channel 4
Channel 4 is a British public-service free-to-air television network that began transmission on 2 November 1982. Although largely commercially- self-funded, it is ultimately publicly-owned; originally a subsidiary of the Independent Broadcasting Authority (IBA), the station is now owned and operated by Channel Four Television Corporation, a public corporation of the Department for Digital, Culture, Media and Sport, which was established in 1990 and came into operation in 1993. With the conversion of the Wenvoe transmitter group in Wales to digital terrestrial broadcasting on 31 March 2010, Channel 4 became a UK-wide TV channel for the first time.
The channel was established to provide a fourth television service to the United Kingdom in addition to the licence-funded BBC One and BBC Two, and the single commercial broadcasting network ITV.Creative Commons license
A Creative Commons (CC) license is one of several public copyright licenses that enable the free distribution of an otherwise copyrighted "work". A CC license is used when an author wants to give other people the right to share, use, and build upon a work that he or she (that author) has created. CC provides an author flexibility (for example, he or she might choose to allow only non-commercial uses of a given work) and protects the people who use or redistribute an author's work from concerns of copyright infringement as long as they abide by the conditions that are specified in the license by which the author distributes the work.There are several types of Creative Commons licenses. The licenses differ by several combinations that condition the terms of distribution. They were initially released on December 16, 2002 by Creative Commons, a U.S. non-profit corporation founded in 2001. There have also been five versions of the suite of licenses, numbered 1.0 through 4.0. As of December 2018, the 4.0 license suite is the most current.
In October 2014 the Open Knowledge Foundation approved the Creative Commons CC BY, CC BY-SA and CC0 licenses as conformant with the "Open Definition" for content and data.Indian Wells Masters
The Indian Wells Masters, also known as BNP Paribas Open and the WTA Indian Wells Open, is an annual tennis tournament held in early- and mid-March at the Indian Wells Tennis Garden in Indian Wells, California, United States. The current owner is Larry Ellison, CTO and co-founder of Oracle. The current tournament director is former world No. 2 player Tommy Haas.
The tournament is a Masters 1000 event on the men's tour and is a Premier Mandatory event on the women's tour. Between 1974 and 1986 it was a secondary tournament of the Grand Prix Tennis Tour but in 1987 it was upgraded to be part of the Grand Prix Super Series, the series of nine tournaments just below the four majors and the year-end finals in importance. It took the place of the Philadelphia Indoor event as the first Super Series event of the year. The event is one of two tour events (along with the Miami Open), other than the Majors, in which main draw play extends beyond eight days. The women's main draw usually starts on Wednesday and the men's main draw starts on Thursday. Both finals are held on Sunday of the following week. Both singles main draws include 96 players in a 128-player grid, with the 32 seeded players getting a bye (a free pass) to the second round.
The tournament is played on hardcourt and is the best-attended tennis tournament outside the four Grand Slam tournaments. It has the second-largest permanent tennis stadium in the world (the Arthur Ashe Stadium being the largest).List of NBA champions
The National Basketball Association (NBA) (formerly Basketball Association of America (BAA) from 1946 to 1949) Finals is the championship series for the NBA and the conclusion of the NBA's postseason. All Finals have been played in a best-of-seven format, and contested between the winners of the Eastern Conference and the Western Conference (formerly Divisions before 1970), except in 1950 in which the Eastern Division champion faced the winner between the Western and Central Division champions. Prior to 1949, the playoffs were instituted a three-stage tournament where the two semifinal winners played each other in the finals. The winning team of the series receives the Larry O'Brien Championship Trophy.
The home-and-away format in the NBA Finals is in a 2–2–1–1–1 format (the team with the better regular season record plays on their home court in Games 1, 2, 5 and 7) during 1947–1948, 1950–1952, 1957–1970, 1972–1974, 1976–1977, 1979–1984, 2014–present. It was previously in a 2–3–2 format (the team with the better regular season record plays on their home court in Games 1, 2, 6 and 7) during 1949, 1953–1955, and 1985–2013, in a 1–1–1–1–1–1–1 format during 1956 and 1971 and in a 1–2–2–1–1 format during 1975 and 1978.The Eastern Conference/Division leads the Western Conference/Division in series won (38–32). The defunct Central Division won one championship. The Boston Celtics and the Minneapolis/Los Angeles Lakers alone own almost half of the titles, having won a combined 33 of 72 championships.List of busiest airports by passenger traffic
The world's busiest airports by passenger traffic are measured by total passengers (data from Airports Council International), defined as passengers enplaned plus passengers deplaned plus direct-transit passengers. Hartsfield–Jackson Atlanta International Airport has been the world's busiest airport every year since 2000; with all airports combined London has the world's busiest city airport system by passenger count. As of 2018, six countries have at least two airports in the top 50; the United States of America has 15, Greater China has 10, and the United Kingdom, Germany, India and Spain have two airports each.List of cities and towns in California
California is a state located in the Western United States. It is the most populous state and the third largest by area after Alaska and Texas. According to the 2010 United States Census, California has 37,253,956 inhabitants and 155,779.22 square miles (403,466.3 km2) of land.California has been inhabited by numerous Native American peoples since antiquity. The Spanish, the Russians, and other Europeans began exploring and colonizing the area in the 16th and 17th centuries, with the Spanish establishing its first California mission at what is now San Diego in 1769. After the Mexican Cession of 1848, the California Gold Rush brought worldwide attention to the area. The growth of the movie industry in Los Angeles and Hollywood, high tech in San Francisco and Silicon Valley, tourism, agriculture, and other areas in the ensuing decades fueled the creation of a $1.85 trillion economy, the ninth-largest in the world.California is divided into 58 counties and contains 482 municipalities. One, San Francisco, is a consolidated city-county. California law makes no distinction between "city" and "town", and municipalities may use either term in their official names. They can be organized as either a charter municipality, governed by its own charter, or a general-law municipality, governed by state law.According to the 2010 Census, 30,908,614 of California's 37,253,956 residents lived in urban areas, accounting for 82.97% of the population. The first municipality to incorporate was Sacramento on February 27, 1850, while the most recent was Jurupa Valley on July 1, 2011. Eight cities were incorporated before the state's September 9, 1850, admission to the Union. The largest municipality by population and land area is Los Angeles with 3,792,621 residents and 468.67 square miles (1,213.8 km2). The smallest by population is Vernon with 112 people, while the smallest by land area is Amador City at 0.31 square miles (0.80 km2).McDonnell Douglas F-4 Phantom II
The McDonnell Douglas F-4 Phantom II is a tandem two-seat, twin-engine, all-weather, long-range supersonic jet interceptor and fighter-bomber originally developed for the United States Navy by McDonnell Aircraft. It first entered service in 1960 with the U.S. Navy. Proving highly adaptable, it was also adopted by the U.S. Marine Corps and the U.S. Air Force, and by the mid-1960s had become a major part of their air arms.The Phantom is a large fighter with a top speed of over Mach 2.2. It can carry more than 18,000 pounds (8,400 kg) of weapons on nine external hardpoints, including air-to-air missiles, air-to-ground missiles, and various bombs. The F-4, like other interceptors of its time, was designed without an internal cannon. Later models incorporated an M61 Vulcan rotary cannon. Beginning in 1959, it set 15 world records for in-flight performance, including an absolute speed record, and an absolute altitude record.The F-4 was used extensively during the Vietnam War. It served as the principal air superiority fighter for the U.S. Air Force, Navy, and Marine Corps and became important in the ground-attack and aerial reconnaissance roles late in the war. During the Vietnam War, one U.S. Air Force pilot, two weapon systems officers (WSOs), one U.S. Navy pilot and one radar intercept officer (RIO) became aces by achieving five aerial kills against enemy fighter aircraft. The F-4 continued to form a major part of U.S. military air power throughout the 1970s and 1980s, being gradually replaced by more modern aircraft such as the F-15 Eagle and F-16 Fighting Falcon in the U.S. Air Force, the F-14 Tomcat in the U.S. Navy, and the F/A-18 Hornet in the U.S. Navy and U.S. Marine Corps.
The F-4 Phantom II remained in use by the U.S. in the reconnaissance and Wild Weasel (Suppression of Enemy Air Defenses) roles in the 1991 Gulf War, finally leaving service in 1996. It was also the only aircraft used by both U.S. flight demonstration teams: the USAF Thunderbirds (F-4E) and the US Navy Blue Angels (F-4J). The F-4 was also operated by the armed forces of 11 other nations. Israeli Phantoms saw extensive combat in several Arab–Israeli conflicts, while Iran used its large fleet of Phantoms, acquired before the fall of the Shah, in the Iran–Iraq War. Phantom production ran from 1958 to 1981, with a total of 5,195 built, making it the most produced American supersonic military aircraft. As of 2018, 60 years after its first flight, the F-4 remains in service with Iran, Japan, South Korea, Greece, and Turkey. The aircraft has most recently been in service against the Islamic State group in the Middle East.PlayStation 4
The PlayStation 4 (PS4) is an eighth-generation home video game console developed by Sony Interactive Entertainment. Announced as the successor to the PlayStation 3 in February, 2013, it was launched on November 15 in North America, November 29 in Europe, South America and Australia, and on February 22, 2014, in Japan. It competes with Microsoft's Xbox One and Nintendo's Wii U and Switch.
Moving away from the more complex Cell microarchitecture of its predecessor, the console features an AMD Accelerated Processing Unit (APU) built upon the x86-64 architecture, which can theoretically peak at 1.84 teraflops; AMD stated that it was the "most powerful" APU it had developed to date. The PlayStation 4 places an increased emphasis on social interaction and integration with other devices and services, including the ability to play games off-console on PlayStation Vita and other supported devices ("Remote Play"), the ability to stream gameplay online or to friends, with them controlling gameplay remotely ("Share Play"). The console's controller was also redesigned and improved over the PlayStation 3, with improved buttons and analog sticks, and an integrated touchpad among other changes. The console also supports HDR10 High-dynamic-range video and playback of 4K resolution multimedia.
The PlayStation 4 was released to acclaim, with critics praising Sony for acknowledging its consumers' needs, embracing independent game development, and for not imposing the restrictive digital rights management schemes similarly to those announced by Microsoft for Xbox One. Critics and third-party studios also praised the capabilities of the PlayStation 4 in comparison to its competitors; developers described the performance difference between the console and Xbox One as "significant" and "obvious". Heightened demand also helped Sony top global console sales. By the end of December 2018, over 94 million PlayStation 4 consoles had been shipped worldwide, surpassing lifetime sales of its predecessor, the PlayStation 3. As of December 2018, 91.6 million PlayStation 4 consoles had been sold through to customers worldwide.
On September 7, 2016, Sony unveiled the PlayStation 4 Pro, a high-end version of the console with an upgraded GPU and higher CPU clock rate to support enhanced performance and 4K resolution on supported games. The company also released a variant of the original model with a smaller form factor, and the release of a patch to add HDR support to all existing consoles.