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Federer Spectral Sequence
Roger Federer (; born 8 August 1981) is a Swiss former professional tennis player. He was ranked world No. 1 by the Association of Tennis Professionals (ATP) for 310 weeks, including a record 237 consecutive weeks, and finished as the year-end No. 1 five times. He won 103 ATP singles titles, the second most of all time, including 20 Grand Slam singles titles, a record eight men's singles Wimbledon titles, an Open Era record-tying five men's singles US Open titles, and a record-tying six year-end championships. Federer played during an era where he dominated men's tennis along with Rafael Nadal and Novak Djokovic as the Big Three, collectively considered by some to be the three most successful male tennis players of all time. Federer's 20 Grand Slam singles titles also put him at third most of all time, only behind Djokovic with 21 and record holder Nadal with 22, as of the end of 2022 season when Federer retired. A Wimbledon junior champion in 1998 and former ball boy, Fed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2016 Wimbledon Championships
The 2016 Wimbledon Championships was a Grand Slam (tennis), Grand Slam tennis tournament which took place at All England Lawn Tennis and Croquet Club in Wimbledon, London, United Kingdom. The main draw commenced on 27 June 2016 and concluded on 10 July 2016. 2016 was the 130th edition of The Championships, Wimbledon, Wimbledon, the 49th in the Open Era (tennis), Open Era and the third Grand Slam (tennis), Grand Slam tournament of the year. It was played on grass courts and was part of the 2016 ATP World Tour, ATP World Tour, the 2016 WTA Tour, WTA Tour, the ITF Junior tour and the NEC Tour. The tournament was organised by All England Lawn Tennis Club and International Tennis Federation. For the first time in the Championships' history, singles events were held in the wheelchair competitions. Thus, all four Grand Slam (tennis)#Tournaments, majors now hold wheelchair singles events, making a complete Grand Slam (tennis), Grand Slam in the discipline possible. Novak Djokovic was t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laver Cup
The Laver Cup is an international indoor hard court men's team tennis tournament between Team Europe and Team World, the latter of which is composed of players from all other continents except Europe. Usually held annually since 2017, the tournament is intended to be the Ryder Cup of the tennis world. It normally takes place two weeks after the US Open, with the location rotating between various host cities (that usually do not have an ATP Tour event); alternating yearly between European cities and cities in the rest of the world. In addition to the guaranteed participation fees which are based upon the players' ATP rankings, each member of the winning team gets $250,000 in prize money, but the tournament itself does not count towards the players' point totals in the ATP Tour for that year. In May 2019, the Laver Cup became an officially sanctioned ATP Tour event. Matches during the Laver Cup tournament differ from conventional 3-set matches played on the ATP Tour; in the event ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2006 Wimbledon Championships – Men's Singles
6 (six) is the natural number following 5 and preceding 7. It is a composite number and the smallest perfect number. In mathematics Six is the smallest positive integer which is neither a square number nor a prime number; it is the second smallest composite number, behind 4; its proper divisors are , and . Since 6 equals the sum of its proper divisors, it is a perfect number; 6 is the smallest of the perfect numbers. It is also the smallest Granville number, or \mathcal-perfect number. As a perfect number: *6 is related to the Mersenne prime 3, since . (The next perfect number is 28.) *6 is the only even perfect number that is not the sum of successive odd cubes. *6 is the root of the 6-aliquot tree, and is itself the aliquot sum of only one other number; the square number, . Six is the only number that is both the sum and the product of three consecutive positive numbers. Unrelated to 6's being a perfect number, a Golomb ruler of length 6 is a "perfect ruler". Six is a con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2005 Wimbledon Championships – Men's Singles
5 (five) is a number, numeral and digit. It is the natural number, and cardinal number, following 4 and preceding 6, and is a prime number. It has attained significance throughout history in part because typical humans have five digits on each hand. In mathematics 5 is the third smallest prime number, and the second super-prime. It is the first safe prime, the first good prime, the first balanced prime, and the first of three known Wilson primes. Five is the second Fermat prime and the third Mersenne prime exponent, as well as the third Catalan number, and the third Sophie Germain prime. Notably, 5 is equal to the sum of the ''only'' consecutive primes, 2 + 3, and is the only number that is part of more than one pair of twin primes, ( 3, 5) and (5, 7). It is also a sexy prime with the fifth prime number and first prime repunit, 11. Five is the third factorial prime, an alternating factorial, and an Eisenstein prime with no imaginary part and real part of the form 3p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2004 Wimbledon Championships – Men's Singles
4 (four) is a number, numeral and digit. It is the natural number following 3 and preceding 5. It is the smallest semiprime and composite number, and is considered unlucky in many East Asian cultures. In mathematics Four is the smallest composite number, its proper divisors being and . Four is the sum and product of two with itself: 2 + 2 = 4 = 2 x 2, the only number b such that a + a = b = a x a, which also makes four the smallest squared prime number p^. In Knuth's up-arrow notation, , and so forth, for any number of up arrows. By consequence, four is the only square one more than a prime number, specifically three. The sum of the first four prime numbers two + three + five + seven is the only sum of four consecutive prime numbers that yields an odd prime number, seventeen, which is the fourth super-prime. Four lies between the first proper pair of twin primes, three and five, which are the first two Fermat primes, like seventeen, which is the third. On the other ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2003 Wimbledon Championships – Men's Singles
3 (three) is a number A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers c ..., numeral (linguistics), numeral and numerical digit, digit. It is the natural number following 2 and preceding 4, and is the smallest odd prime number and the only prime preceding a square number. It has religious or cultural significance in many societies. Evolution of the Arabic digit The use of three lines to denote the number 3 occurred in many writing systems, including some (like Roman and Chinese numerals) that are still in use. That was also the original representation of 3 in the Brahmic numerals, Brahmic (Indian) numerical notation, its earliest forms aligned vertically. However, during the Gupta Empire the sign was modified by the addition of a curve on each line. The Nāgarī script rotated t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2009 French Open – Men's Singles
9 (nine) is the natural number following and preceding . Evolution of the Arabic digit In the beginning, various Indians wrote a digit 9 similar in shape to the modern closing question mark without the bottom dot. The Kshatrapa, Andhra and Gupta started curving the bottom vertical line coming up with a -look-alike. The Nagari continued the bottom stroke to make a circle and enclose the 3-look-alike, in much the same way that the sign @ encircles a lowercase ''a''. As time went on, the enclosing circle became bigger and its line continued beyond the circle downwards, as the 3-look-alike became smaller. Soon, all that was left of the 3-look-alike was a squiggle. The Arabs simply connected that squiggle to the downward stroke at the middle and subsequent European change was purely cosmetic. While the shape of the glyph for the digit 9 has an ascender in most modern typefaces, in typefaces with text figures the character usually has a descender, as, for example, in . The mod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2018 Australian Open – Men's Singles
Defending champion Roger Federer defeated Marin Čilić in the final, 6–2, 6–7(5–7), 6–3, 3–6, 6–1 to win the men's singles tennis title at the 2018 Australian Open. It was his record-equalling sixth Australian Open title (tied with Roy Emerson and Novak Djokovic), and his record-extending 20th and last major title overall. With the win, Federer became the oldest man to win a major singles title since Ken Rosewall in 1972. This was the 10th time that Federer defended a major title, the last time being at the 2008 US Open. Čilić became the first Croatian to reach an Australian Open singles final. This was the first time since the 2008 Wimbledon Championships that two unseeded players (Chung Hyeon and Kyle Edmund) reached the semifinals of a men's singles major, and the first time at the Australian Open since 1999. Chung became the first South Korean player to reach a major quarterfinal and semifinal. Seeds All seedings per ATP rankings. Draw Finals Top half ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2017 Australian Open – Men's Singles
Roger Federer defeated Rafael Nadal in the final, 6–4, 3–6, 6–1, 3–6, 6–3 to win the men's singles tennis title at the 2017 Australian Open. It was his fifth Australian Open title and record-extending 18th major title overall. Federer became the oldest men's singles major champion since Ken Rosewall at the 1972 Australian Open. Nadal was attempting to become the first man in the Open Era to achieve a double career Grand Slam. Novak Djokovic was the two-time defending champion, but lost in the second round to Denis Istomin. It was the first time since the 2008 Wimbledon Championships that Djokovic failed to reach the third round of a major and the first time since 2006 that he failed to do so at the Australian Open. With top-seed Andy Murray losing in the fourth round, this marked the first time since the 2004 French Open that the top two seeds both failed to reach the quarterfinals of a men's singles major. This marked the first major tournament for future world No. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2010 Australian Open – Men's Singles
1 (one, unit, unity) is a number representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of ''unit length'' is a line segment of length 1. In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer. It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number, following 0. The fundamental mathematical property of 1 is to be a multiplicative identity, meaning that any number multiplied by 1 equals the same number. Most if not all properties of 1 can be deduced from this. In advanced mathematics, a multiplicative identity is often denoted 1, even if it is not a number. 1 is by convention not considered a prime number; this was not universally accepted until the mid-20th century. Additionally, 1 is the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2007 Australian Open – Men's Singles
7 (seven) is the natural number following 6 and preceding 8. It is the only prime number preceding a cube. As an early prime number in the series of positive integers, the number seven has greatly symbolic associations in religion, mythology, superstition and philosophy. The seven Classical planets resulted in seven being the number of days in a week. It is often considered lucky in Western culture and is often seen as highly symbolic. Unlike Western culture, in Vietnamese culture, the number seven is sometimes considered unlucky. It is the first natural number whose pronunciation contains more than one syllable. Evolution of the Arabic digit In the beginning, Indians wrote 7 more or less in one stroke as a curve that looks like an uppercase vertically inverted. The western Ghubar Arabs' main contribution was to make the longer line diagonal rather than straight, though they showed some tendencies to making the digit more rectilinear. The eastern Arabs developed the digit fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2006 Australian Open – Men's Singles
6 (six) is the natural number following 5 and preceding 7. It is a composite number and the smallest perfect number. In mathematics Six is the smallest positive integer which is neither a square number nor a prime number; it is the second smallest composite number, behind 4; its proper divisors are , and . Since 6 equals the sum of its proper divisors, it is a perfect number; 6 is the smallest of the perfect numbers. It is also the smallest Granville number, or \mathcal-perfect number. As a perfect number: *6 is related to the Mersenne prime 3, since . (The next perfect number is 28.) *6 is the only even perfect number that is not the sum of successive odd cubes. *6 is the root of the 6-aliquot tree, and is itself the aliquot sum of only one other number; the square number, . Six is the only number that is both the sum and the product of three consecutive positive numbers. Unrelated to 6's being a perfect number, a Golomb ruler of length 6 is a "perfect ruler". Six is a con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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