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4,600 | As a geometrical application of Stirling's approximation, let denote the standard simplex in "n"-dimensional Euclidean space, and denote the simplex having all of its sides scaled up by a factor of . Then | https://en.wikipedia.org/wiki?curid=23601 |
4,601 | Ehrhart's volume conjecture is that this is the (optimal) upper bound on the volume of a convex body containing only one lattice point. | https://en.wikipedia.org/wiki?curid=23601 |
4,602 | The Riemann zeta function is used in many areas of mathematics. When evaluated at it can be written as | https://en.wikipedia.org/wiki?curid=23601 |
4,603 | Finding a simple solution for this infinite series was a famous problem in mathematics called the Basel problem. Leonhard Euler solved it in 1735 when he showed it was equal to . Euler's result leads to the number theory result that the probability of two random numbers being relatively prime (that is, having no shared... | https://en.wikipedia.org/wiki?curid=23601 |
4,604 | This probability can be used in conjunction with a random number generator to approximate using a Monte Carlo approach. | https://en.wikipedia.org/wiki?curid=23601 |
4,605 | The solution to the Basel problem implies that the geometrically derived quantity is connected in a deep way to the distribution of prime numbers. This is a special case of Weil's conjecture on Tamagawa numbers, which asserts the equality of similar such infinite products of "arithmetic" quantities, localized at each p... | https://en.wikipedia.org/wiki?curid=23601 |
4,606 | The zeta function also satisfies Riemann's functional equation, which involves as well as the gamma function: | https://en.wikipedia.org/wiki?curid=23601 |
4,607 | A consequence is that can be obtained from the functional determinant of the harmonic oscillator. This functional determinant can be computed via a product expansion, and is equivalent to the Wallis product formula. The calculation can be recast in quantum mechanics, specifically the variational approach to the spectru... | https://en.wikipedia.org/wiki?curid=23601 |
4,608 | The constant also appears naturally in Fourier series of periodic functions. Periodic functions are functions on the group of fractional parts of real numbers. The Fourier decomposition shows that a complex-valued function on can be written as an infinite linear superposition of unitary characters of . That is, continu... | https://en.wikipedia.org/wiki?curid=23601 |
4,609 | There is a unique character on , up to complex conjugation, that is a group isomorphism. Using the Haar measure on the circle group, the constant is half the magnitude of the Radon–Nikodym derivative of this character. The other characters have derivatives whose magnitudes are positive integral multiples of 2. As a res... | https://en.wikipedia.org/wiki?curid=23601 |
4,610 | The constant is connected in a deep way with the theory of modular forms and theta functions. For example, the Chudnovsky algorithm involves in an essential way the j-invariant of an elliptic curve. | https://en.wikipedia.org/wiki?curid=23601 |
4,611 | Modular forms are holomorphic functions in the upper half plane characterized by their transformation properties under the modular group formula_85 (or its various subgroups), a lattice in the group formula_86. An example is the Jacobi theta function | https://en.wikipedia.org/wiki?curid=23601 |
4,612 | which is a kind of modular form called a Jacobi form. This is sometimes written in terms of the nome formula_88. | https://en.wikipedia.org/wiki?curid=23601 |
4,613 | The constant is the unique constant making the Jacobi theta function an automorphic form, which means that it transforms in a specific way. Certain identities hold for all automorphic forms. An example is | https://en.wikipedia.org/wiki?curid=23601 |
4,614 | which implies that transforms as a representation under the discrete Heisenberg group. General modular forms and other theta functions also involve , once again because of the Stone–von Neumann theorem. | https://en.wikipedia.org/wiki?curid=23601 |
4,615 | The Cauchy distribution plays an important role in potential theory because it is the simplest Furstenberg measure, the classical Poisson kernel associated with a Brownian motion in a half-plane. Conjugate harmonic functions and so also the Hilbert transform are associated with the asymptotics of the Poisson kernel. Th... | https://en.wikipedia.org/wiki?curid=23601 |
4,616 | The constant is the unique (positive) normalizing factor such that "H" defines a linear complex structure on the Hilbert space of square-integrable real-valued functions on the real line. The Hilbert transform, like the Fourier transform, can be characterized purely in terms of its transformation properties on the Hilb... | https://en.wikipedia.org/wiki?curid=23601 |
4,617 | An occurrence of in the fractal called the Mandelbrot set was discovered by David Boll in 1991. He examined the behaviour of the Mandelbrot set near the "neck" at . When the number of iterations until divergence for the point is multiplied by , the result approaches as approaches zero. The point at the cusp of the larg... | https://en.wikipedia.org/wiki?curid=23601 |
4,618 | Although not a physical constant, appears routinely in equations describing fundamental principles of the universe, often because of 's relationship to the circle and to spherical coordinate systems. A simple formula from the field of classical mechanics gives the approximate period of a simple pendulum of length , swi... | https://en.wikipedia.org/wiki?curid=23601 |
4,619 | One of the key formulae of quantum mechanics is Heisenberg's uncertainty principle, which shows that the uncertainty in the measurement of a particle's position (Δ) and momentum (Δ) cannot both be arbitrarily small at the same time (where is Planck's constant): | https://en.wikipedia.org/wiki?curid=23601 |
4,620 | The fact that is approximately equal to 3 plays a role in the relatively long lifetime of orthopositronium. The inverse lifetime to lowest order in the fine-structure constant is | https://en.wikipedia.org/wiki?curid=23601 |
4,621 | The field of fluid dynamics contains in Stokes' law, which approximates the frictional force exerted on small, spherical objects of radius , moving with velocity in a fluid with dynamic viscosity : | https://en.wikipedia.org/wiki?curid=23601 |
4,622 | In electromagnetics, the vacuum permeability constant "μ" appears in Maxwell's equations, which describe the properties of electric and magnetic fields and electromagnetic radiation. Before 20 May 2019, it was defined as exactly | https://en.wikipedia.org/wiki?curid=23601 |
4,623 | A relation for the speed of light in vacuum, can be derived from Maxwell's equations in the medium of classical vacuum using a relationship between "μ" and the electric constant (vacuum permittivity), in SI units: | https://en.wikipedia.org/wiki?curid=23601 |
4,624 | Under ideal conditions (uniform gentle slope on a homogeneously erodible substrate), the sinuosity of a meandering river approaches . The sinuosity is the ratio between the actual length and the straight-line distance from source to mouth. Faster currents along the outside edges of a river's bends cause more erosion th... | https://en.wikipedia.org/wiki?curid=23601 |
4,625 | Piphilology is the practice of memorizing large numbers of digits of , and world-records are kept by the "Guinness World Records". The record for memorizing digits of , certified by Guinness World Records, is 70,000 digits, recited in India by Rajveer Meena in 9 hours and 27 minutes on 21 March 2015. In 2006, Akira Har... | https://en.wikipedia.org/wiki?curid=23601 |
4,626 | One common technique is to memorize a story or poem in which the word lengths represent the digits of : The first word has three letters, the second word has one, the third has four, the fourth has one, the fifth has five, and so on. Such memorization aids are called mnemonics. An early example of a mnemonic for pi, or... | https://en.wikipedia.org/wiki?curid=23601 |
4,627 | A few authors have used the digits of to establish a new form of constrained writing, where the word lengths are required to represent the digits of . The "Cadaeic Cadenza" contains the first 3835 digits of in this manner, and the full-length book "Not a Wake" contains 10,000 words, each representing one digit of . | https://en.wikipedia.org/wiki?curid=23601 |
4,628 | Perhaps because of the simplicity of its definition and its ubiquitous presence in formulae, has been represented in popular culture more than other mathematical constructs. | https://en.wikipedia.org/wiki?curid=23601 |
4,629 | In the 2008 Open University and BBC documentary co-production, "The Story of Maths", aired in October 2008 on BBC Four, British mathematician Marcus du Sautoy shows a visualization of the – historically first exact – formula for calculating when visiting India and exploring its contributions to trigonometry. | https://en.wikipedia.org/wiki?curid=23601 |
4,630 | In the Palais de la Découverte (a science museum in Paris) there is a circular room known as the "pi room". On its wall are inscribed 707 digits of . The digits are large wooden characters attached to the dome-like ceiling. The digits were based on an 1873 calculation by English mathematician William Shanks, which incl... | https://en.wikipedia.org/wiki?curid=23601 |
4,631 | In Carl Sagan's 1985 novel "Contact" it is suggested that the creator of the universe buried a message deep within the digits of . The digits of have also been incorporated into the lyrics of the song "Pi" from the 2005 album "Aerial" by Kate Bush. In the 1967 "" episode "Wolf in the Fold", an out-of-control computer i... | https://en.wikipedia.org/wiki?curid=23601 |
4,632 | In the United States, Pi Day falls on 14 March (written 3/14 in the US style), and is popular among students. and its digital representation are often used by self-described "math geeks" for inside jokes among mathematically and technologically minded groups. A college cheer variously attributed to the Massachusetts In... | https://en.wikipedia.org/wiki?curid=23601 |
4,633 | During the 2011 auction for Nortel's portfolio of valuable technology patents, Google made a series of unusually specific bids based on mathematical and scientific constants, including . | https://en.wikipedia.org/wiki?curid=23601 |
4,634 | In 1958 Albert Eagle proposed replacing by (tau), where , to simplify formulas, but this use of is otherwise unknown. Some propose , arguing that , as the number of radians in one turn or the ratio of a circle's circumference to its radius, is more natural than and simplifies many formulas. This use of has not made its... | https://en.wikipedia.org/wiki?curid=23601 |
4,635 | In 1897, an amateur mathematician attempted to persuade the Indiana legislature to pass the Indiana Pi Bill, which described a method to square the circle and contained text that implied various incorrect values for , including 3.2. The bill is notorious as an attempt to establish a value of mathematical constant by le... | https://en.wikipedia.org/wiki?curid=23601 |
4,636 | In contemporary internet culture, individuals and organizations frequently pay homage to the number . For instance, the computer scientist Donald Knuth let the version numbers of his program TeX approach . The versions are 3, 3.1, 3.14, and so forth. | https://en.wikipedia.org/wiki?curid=23601 |
4,637 | Sven Magnus Øen Carlsen (born 30 November 1990) is a Norwegian chess grandmaster who is the reigning five-time World Chess Champion. He is also a three-time World Rapid Chess Champion and five-time World Blitz Chess Champion. Carlsen has held the position in the FIDE world chess rankings since 1 July 2011 and trails on... | https://en.wikipedia.org/wiki?curid=442682 |
4,638 | A chess prodigy, Carlsen finished first in the C group of the Corus chess tournament shortly after he turned 13 and earned the title of grandmaster a few months later. At 15, he won the Norwegian Chess Championship, and at 17 he finished joint first in the top group of Corus. He surpassed a rating of 2800 at 18, the yo... | https://en.wikipedia.org/wiki?curid=442682 |
4,639 | Carlsen became World Chess Champion in 2013 by defeating Viswanathan Anand. He retained his title against Anand the following year and won both the 2014 World Rapid Championship and World Blitz Championship, becoming the first player to hold all three titles simultaneously, a feat which he repeated in 2019. He defended... | https://en.wikipedia.org/wiki?curid=442682 |
4,640 | Known for his attacking style as a teenager, Carlsen has since developed into a universal player. He uses a variety of openings to make it harder for opponents to prepare against him and reduce the utility of pre-game computer analysis. He has stated the middlegame is his favourite part of the game as it "comes down to... | https://en.wikipedia.org/wiki?curid=442682 |
4,641 | Carlsen was born in Tønsberg, Norway, on 30 November 1990 to Sigrun Øen, a chemical engineer, and Henrik Albert Carlsen, an IT consultant. The family spent one year in Espoo, Finland, and then in Brussels, Belgium, before returning to Norway in 1998, where they lived in Lommedalen, Bærum. They later moved to Haslum. Ca... | https://en.wikipedia.org/wiki?curid=442682 |
4,642 | His father, a keen amateur chess player, taught him to play at age 5, although he initially showed little interest in it. He has three sisters, and in 2010 stated that one of the things that first motivated him to take up chess seriously was the desire to beat his elder sister at the game. | https://en.wikipedia.org/wiki?curid=442682 |
4,643 | The first chess book Carlsen read was a booklet named "Find the Plan" by Bent Larsen, and his first book on openings was Eduard Gufeld's "The Complete Dragon". Carlsen developed his early chess skills playing by himself for hours on end—moving the pieces around, searching for combinations, and replaying games and posit... | https://en.wikipedia.org/wiki?curid=442682 |
4,644 | Carlsen was coached at the Norwegian College of Elite Sport by the country's top player, Grandmaster (GM) Simen Agdestein, who in turn cites Norwegian football manager Egil "Drillo" Olsen as a key inspiration for his coaching strategy. In 2000, Agdestein introduced Carlsen to Torbjørn Ringdal Hansen, a former Norwegian... | https://en.wikipedia.org/wiki?curid=442682 |
4,645 | Over the course of that year, Carlsen's rating rose from 904 in June 2000 to 1907. His breakthrough occurred in the Norwegian junior teams championship in September 2000, where he scored 3½/5 against the country's top junior players and gained a (TPR) of around 2000. Apart from chess, which he studied about three to fo... | https://en.wikipedia.org/wiki?curid=442682 |
4,646 | From autumn 2000 to the end of 2002, Carlsen played almost 300 rated tournament games, as well as in several blitz tournaments, and participated in other minor events. In October 2002, he placed sixth in the European Under-12 Championship in Peñiscola. The following month, he tied for first place in the 2002 World Unde... | https://en.wikipedia.org/wiki?curid=442682 |
4,647 | After finishing primary school, Carlsen took a year off to participate in international chess tournaments in Europe during the autumn of 2003, then returned to complete secondary education at a sports school. During the year away from school, he placed joint-third in the European Under-14 Championship and ninth in the ... | https://en.wikipedia.org/wiki?curid=442682 |
4,648 | Carlsen made headlines after his victory, at the age of 13, in the C group at the 2004 Corus chess tournament in Wijk aan Zee. He obtained a score of 10½/13, losing just one game (against the highest-rated player of the C group, Duško Pavasovič). As a result, he earned his first GM norm, and achieved a of 2702. Particu... | https://en.wikipedia.org/wiki?curid=442682 |
4,649 | Carlsen obtained his second GM norm at the Moscow Aeroflot Open in February. On 17 March, in a blitz chess tournament in Reykjavík, Iceland, he defeated former World Champion Anatoly Karpov. It was a preliminary event leading up to a rapid knockout tournament beginning the next day. In that event, Carlsen was paired wi... | https://en.wikipedia.org/wiki?curid=442682 |
4,650 | In the sixth Dubai Open Chess Championship, held 18–28 April, Carlsen obtained his third and final GM norm. It made him the world's youngest GM at the time, and the second-youngest GM in history at the time (after Sergey Karjakin, who earned the title at 12 years and 7 months). Carlsen played in the FIDE World Chess Ch... | https://en.wikipedia.org/wiki?curid=442682 |
4,651 | In July, Carlsen and Berge Østenstad, then the reigning Norwegian champion, tied for first in the Norwegian Chess Championship, each scoring 7/9. A two-game match between them was arranged to decide the title. Both games were drawn, which left Østenstad the champion because he had superior tiebreaks in the tournament. | https://en.wikipedia.org/wiki?curid=442682 |
4,652 | In the Smartfish Chess Masters event at the Drammen International Chess Festival 2004–05, Carlsen defeated Alexei Shirov, then ranked in the world, as well as the co-winner of the tournament. In the semifinals of the Ciudad de León rapid chess tournament in June, Carlsen played a four-game match against Viswanathan Ana... | https://en.wikipedia.org/wiki?curid=442682 |
4,653 | In the Norwegian Chess Championship, Carlsen again finished in shared first place, this time with his mentor Simen Agdestein. A playoff between them was played between 7 and 10 November. This time, Carlsen had the better tiebreaks, but the rule giving the title to the player with better tiebreak scores in the event of ... | https://en.wikipedia.org/wiki?curid=442682 |
4,654 | In October, Carlsen took first place at the Arnold Eikrem Memorial in Gausdal with a score 8/9 and a of 2792. | https://en.wikipedia.org/wiki?curid=442682 |
4,655 | At the end of 2005, Carlsen participated at the Chess World Cup in Khanty-Mansiysk, Russia. In the knockout tournament, he upset 44th-ranked Zurab Azmaiparashvili in round one, and proceeded to defeat Farrukh Amonatov and Ivan Cheparinov to reach the round of 16. There he lost to Evgeny Bareev, but won against Joël Lau... | https://en.wikipedia.org/wiki?curid=442682 |
4,656 | Carlsen qualified for a place in the Corus B group due to his first-place finish in Corus group C in 2004. His shared first place with Alexander Motylev with 9/13 (+6−1=6) qualified him to play in the Corus group A in 2007. | https://en.wikipedia.org/wiki?curid=442682 |
4,657 | At the 2006 international 'Bosna' tournament in Sarajevo, Carlsen shared first place with Liviu-Dieter Nisipeanu (who won on tiebreak evaluation) and Vladimir Malakhov; this could be regarded as Carlsen's first "A" elite tournament win, although it was not a clear first. | https://en.wikipedia.org/wiki?curid=442682 |
4,658 | Carlsen was close to winning the 2006 Norwegian Chess Championship outright, but a last-round loss to Berge Østenstad dropped him into another tie for first place with Agdestein. It also prevented Carlsen from beating Agdestein's record as the youngest Norwegian champion ever. Nonetheless, in the playoff held from 19 t... | https://en.wikipedia.org/wiki?curid=442682 |
4,659 | Carlsen won the Glitnir Blitz Tournament in Iceland. He achieved a 2–0 win over Viswanathan Anand in the semi-finals and achieved the same score in the finals. He scored 6/8 in the 37th Chess Olympiad and achieved a PR of 2820. | https://en.wikipedia.org/wiki?curid=442682 |
4,660 | In the Midnight Sun Chess Tournament in Tromsø, Carlsen finished second to Sergei Shipov. In the Biel Grandmaster Tournament, he placed second, beating the tournament winner Alexander Morozevich twice. | https://en.wikipedia.org/wiki?curid=442682 |
4,661 | In the NH Chess Tournament held in Amsterdam in August, Carlsen participated in an "Experience" vs. "Rising Stars" Scheveningen team match. The "Rising Stars" won the match 28–22, with Carlsen achieving the best individual score for the Rising Stars team (6½/10) and a 2700 PR, thus winning the right to participate in t... | https://en.wikipedia.org/wiki?curid=442682 |
4,662 | With a score of 7½/15, Carlsen placed 8th out of 16 participants at the World Blitz Championship in Rishon LeZion, Israel. In the rapid chess tournament "Rencontres nationales et internationales d'échecs" in Cap d'Agde, France, he reached the semi-final, losing there to Sergey Karjakin. In November, Carlsen achieved a ... | https://en.wikipedia.org/wiki?curid=442682 |
4,663 | Playing in the top group of the Corus chess tournament for the first time, Carlsen placed last with nine draws and four losses, scoring 4½/13. In the Linares chess tournament, Carlsen played against top-rated players Veselin Topalov, Viswanathan Anand, Peter Svidler, Alexander Morozevich, Levon Aronian, Peter Leko, and... | https://en.wikipedia.org/wiki?curid=442682 |
4,664 | Carlsen played for the first time in the Melody Amber blind and rapid chess tournament in Monte Carlo in March. In the 11 rounds, he achieved eight draws and three losses in the blindfold games, as well as three wins, seven draws and one loss in the rapid games. This resulted in a shared ninth place in the blindfold, s... | https://en.wikipedia.org/wiki?curid=442682 |
4,665 | In May and June, he participated in the Candidates Tournament for the FIDE World Chess Championship 2007, facing Levon Aronian in a six-game match at standard time controls, which Carlsen drew (+2−2=2) by coming from behind twice. The four-game rapid playoff was drawn as well (+1−1=2), with Carlsen winning the last gam... | https://en.wikipedia.org/wiki?curid=442682 |
4,666 | In July and August, Carlsen won the Biel Grandmaster Tournament with a 6/10 record and a PR of 2753. His score was matched by Alexander Onischuk and they played a match to break the tie. After drawing two rapid and two blitz games, Carlsen won the armageddon game. Immediately after the Biel tournament, Carlsen entered ... | https://en.wikipedia.org/wiki?curid=442682 |
4,667 | Carlsen reached the semi-final round of the World Chess Cup in December, after defeating Michael Adams in the round of 16 and Ivan Cheparinov in the quarterfinals. In the semi-final, he was eliminated by the eventual winner, Gata Kamsky, scoring ½–1½. | https://en.wikipedia.org/wiki?curid=442682 |
4,668 | In the top group A of the 69th Corus chess tournament, Carlsen scored 8/13, achieving a PR of 2830. Carlsen won five games, lost two and drew six, sharing first place with Levon Aronian. At the Linares chess tournament, Carlsen had another 2800+ PR, scoring 8/14. He finished in sole second place, ½ point behind the win... | https://en.wikipedia.org/wiki?curid=442682 |
4,669 | In March, Carlsen played for the second time in the Melody Amber blind and rapid chess tournament, held in Nice for the first time. In the 11 rounds he achieved four wins, four draws and two losses in the blindfold, and three wins, two losses, and six draws in the rapid. This resulted in a shared fifth place in the bli... | https://en.wikipedia.org/wiki?curid=442682 |
4,670 | Carlsen was one of 21 players in the six-tournament FIDE Grand Prix 2008–2010, a qualifier for the World Chess Championship 2012. In the first tournament, in Baku, Azerbaijan, he finished in a three-way tie for first place, with another 2800 PR. He later withdrew from the Grand Prix cycle despite his initial success, c... | https://en.wikipedia.org/wiki?curid=442682 |
4,671 | Carlsen won a rapid match against Peter Leko held in Miskolc, Hungary, scoring 5–3. In June, Carlsen won the annual Aerosvit chess tournament, finishing undefeated with 8/11 in a category 19 field and achieving a PR of 2877, his best PR at that point in his career. Playing in the category 18 Biel Grandmaster Tournament... | https://en.wikipedia.org/wiki?curid=442682 |
4,672 | In the Mainz World Rapid Chess Championship, Carlsen finished in second place after losing the final to defending champion Anand 3–1. In the qualification round Carlsen scored 1½–½ against Judit Polgár, 1–1 against Anand and 1–1 against Alexander Morozevich. In the category 22 Bilbao Masters, Carlsen tied for second wi... | https://en.wikipedia.org/wiki?curid=442682 |
4,673 | Playing in Group A of the 71st Corus chess tournament, Carlsen tied for fifth with a 2739 PR. In the Linares chess tournament, Carlsen finished third with a 2777 PR. Carlsen tied for second place with Veselin Topalov at the M-Tel Masters (category 21) tournament in Sofia, Bulgaria. He lost to eventual winner Alexei Shi... | https://en.wikipedia.org/wiki?curid=442682 |
4,674 | Carlsen won the category 21 Nanjing Pearl Spring tournament, 2½ points ahead of second-place finisher Topalov, the world's highest-rated player at the time. He scored an undefeated 8/10, winning every game as white (against Topalov, Wang Yue, Leko, Teimour Radjabov, and Dmitry Jakovenko), and also winning as black agai... | https://en.wikipedia.org/wiki?curid=442682 |
4,675 | In the Tal Memorial, played from 5 to 14 November, Carlsen started with seven straight draws, but finished with wins over former FIDE World Champion Ruslan Ponomariov and Peter Leko. This result put Carlsen in shared second place behind former World Champion Vladimir Kramnik and equal with Ivanchuk. After the Tal Memor... | https://en.wikipedia.org/wiki?curid=442682 |
4,676 | Carlsen entered the London Chess Classic as the top seed in a field including Kramnik, Hikaru Nakamura, Michael Adams, Nigel Short, Ni Hua, Luke McShane and David Howell. He defeated Kramnik in round one and went on to win the tournament with 13/21 (three points were awarded for a win, and one for a draw; using classic... | https://en.wikipedia.org/wiki?curid=442682 |
4,677 | Based on his average ranking from the July 2009 and January 2010 FIDE lists, Carlsen qualified for the Candidates Tournament that would determine the challenger to World Champion Viswanathan Anand in the World Chess Championship 2012. In November 2010, however, Carlsen announced he was withdrawing from the Candidates T... | https://en.wikipedia.org/wiki?curid=442682 |
4,678 | In early 2009 Carlsen engaged former World Champion Garry Kasparov as a personal trainer. In September their partnership was revealed to the public by Norwegian newspapers. | https://en.wikipedia.org/wiki?curid=442682 |
4,679 | Responding to a question in an interview with "Time" magazine in December 2009 as to whether he used computers when studying chess, Carlsen explained that he does not use a chess set when studying on his own. | https://en.wikipedia.org/wiki?curid=442682 |
4,680 | Carlsen won the 72nd Corus chess tournament played 16–31 January with 8½ points. His ninth-round loss to Kramnik ended a streak of 36 rated games undefeated. Carlsen appeared to struggle in the last round against Fabiano Caruana, but saved a draw, leaving him half a point ahead of Kramnik and Shirov. | https://en.wikipedia.org/wiki?curid=442682 |
4,681 | In March it was announced that Carlsen had split from Kasparov and would no longer use him as a trainer, although this was put into different context by Carlsen himself in an interview with the German magazine "Der Spiegel", in which he stated that they would remain in contact and he would continue to attend training s... | https://en.wikipedia.org/wiki?curid=442682 |
4,682 | Carlsen shared first place alongside Ivanchuk in the Amber blindfold and rapid tournament. Scoring 6½/11 in the blindfold and 8/11 in the rapid, Carlsen accumulated 14½ from a possible 22 points. In May it was revealed that Carlsen had helped Anand prepare for the World Chess Championship 2010 against challenger Veseli... | https://en.wikipedia.org/wiki?curid=442682 |
4,683 | Carlsen played in the Bazna Kings Tournament in Romania on 14–25 June. The tournament was a double round robin involving Wang Yue, Boris Gelfand, Ruslan Ponomariov, Teimour Radjabov, and Liviu-Dieter Nisipeanu. He finished with 7½/10 and a 2918 PR, winning the tournament by two points ahead of Radjabov and Gelfand. Car... | https://en.wikipedia.org/wiki?curid=442682 |
4,684 | Carlsen's next tournament was the Grand Slam Masters Final on 9–15 October, which he had qualified for automatically by winning three of the previous year's four Grand Slam chess events (2009 Nanjing Pearl Spring, 2010 Corus, 2010 Bazna Kings). Along with Carlsen, the finals consisted of World Champion Anand and the hi... | https://en.wikipedia.org/wiki?curid=442682 |
4,685 | Carlsen's next tournament was the Pearl Spring chess tournament on 19–30 October in Nanjing, China, against Anand, Topalov, Vugar Gashimov, Wang Yue, and Étienne Bacrot. This was the only tournament in 2010 to feature Anand, Carlsen and Topalov, at the time the top three players in the world, and was the first tourname... | https://en.wikipedia.org/wiki?curid=442682 |
4,686 | On 5 November, Carlsen withdrew from the 2011 Candidates Tournament, having qualified as the highest rated challenger, citing dissatisfaction with the World Championship cycle format. | https://en.wikipedia.org/wiki?curid=442682 |
4,687 | In the World Blitz Championship, held in Moscow on 16–18 November, Carlsen attempted to defend his 2009 title. With a score of 23½/38, he finished in third place behind Radjabov and winner Levon Aronian. After the tournament, Carlsen played a private 40-game blitz match against Hikaru Nakamura, winning with a score of ... | https://en.wikipedia.org/wiki?curid=442682 |
4,688 | Carlsen won the London Chess Classic on 8–15 December in a field comprising World Champion Anand, Vladimir Kramnik, Nakamura, and British players Adams, Nigel Short, David Howell, and Luke McShane. Carlsen had a rocky start, losing his games to McShane and Anand in rounds 1 and 3, but winning with white against Adams a... | https://en.wikipedia.org/wiki?curid=442682 |
4,689 | Carlsen competed in the GM-A group of the 73rd Tata Steel Chess Tournament (formerly called the Corus chess tournament) on 14–30 January in Wijk aan Zee in an attempt to defend his title; the field included World Champion Viswanathan Anand, Levon Aronian, former World Champion Vladimir Kramnik, Alexander Grischuk, Hika... | https://en.wikipedia.org/wiki?curid=442682 |
4,690 | The first tournament victory of the year came in the Bazna Kings tournament, a double round robin played in Mediaș, Romania on 11–21 June. Carlsen finished with 6½/10, equal with Sergey Karjakin but with a better tiebreak score. Carlsen won his White games against Nakamura, Nisipeanu, and Ivanchuk and drew the rest of ... | https://en.wikipedia.org/wiki?curid=442682 |
4,691 | Carlsen won the 44th Biel Grandmaster tournament, held from 16 to 29 July. He took clear first place with a score of 19/30 (+5−1=4; three points for a win) in a field comprising Fabiano Caruana, Maxime Vachier-Lagrave, Alexander Morozevich, Alexey Shirov and Yannick Pelletier, two points ahead of Morozevich. This was C... | https://en.wikipedia.org/wiki?curid=442682 |
4,692 | The Grand Slam Chess Final was held as a double round robin with six players, in São Paulo (25 September – 1 October) and Bilbao (5–11 October). Although Carlsen had a slow start, including a loss against bottom-ranked Francisco Vallejo Pons, he finished +3−1=6, equal with Ivanchuk (whose +4−3=3 finish was equal due to... | https://en.wikipedia.org/wiki?curid=442682 |
4,693 | Another tournament victory was achieved in the Tal Memorial in Moscow 16–25 November as a round robin with ten players. Carlsen won two games, against Gelfand and Nakamura, and drew the rest. Although he finished equal on points with Aronian, he placed ahead since the tiebreak was determined by the number of black game... | https://en.wikipedia.org/wiki?curid=442682 |
4,694 | In the London Chess Classic, played 3–12 December, Carlsen's streak of tournament victories ended when he finished third, behind Kramnik and Nakamura. Carlsen won three games and drew five. Although he did not win the tournament, Carlsen gained rating points, rising to a new personal record of 2835. | https://en.wikipedia.org/wiki?curid=442682 |
4,695 | At the 74th Tata Steel Chess Tournament held on 14–29 January in Wijk aan Zee, Carlsen finished in a shared second place with 8/13, behind Aronian, and equal with Radjabov and Caruana. Carlsen defeated Gashimov, Aronian, Gelfand, and Topalov, but lost against Karjakin. At the blitz chess tournament at Tal Memorial, hel... | https://en.wikipedia.org/wiki?curid=442682 |
4,696 | Carlsen then went on to finish second in the Biel Grandmaster Tournament, with 18 points, just one point behind Wang Hao using the 3–1–0 scoring system. As in the Tal Memorial earlier in 2012, Carlsen managed to finish the tournament without any losses (+4−0=6). He also defeated the winner Wang in both of their individ... | https://en.wikipedia.org/wiki?curid=442682 |
4,697 | The Grand Slam Chess Final was again held as a double round robin with six players, in São Paulo and Bilbao. Carlsen started with a loss against Caruana, but after three wins in the second (Bilbao) round, finished +4−1=5, equal first with Caruana, and ahead of Aronian, Karjakin and Anand. Carlsen won the tournament by ... | https://en.wikipedia.org/wiki?curid=442682 |
4,698 | From 24 to 25 November, Carlsen took part in the chess festival "Segunda Gran Fiesta Internacional de Ajedrez" in Mexico City. As part of it, Carlsen took on an online audience (dubbed as "The World") with the white pieces and won. He then took part in the knockout exhibition event "Cuadrangular UNAM". Carlsen first be... | https://en.wikipedia.org/wiki?curid=442682 |
4,699 | Carlsen won the London Chess Classic in December with five wins (over McShane, Aronian, Gawain Jones, Adams and Judit Polgár) and three draws (against Kramnik, Nakamura and Anand). This win, the third time Carlsen had won the tournament in the past four years, increased his rating from 2848 to a new record of 2861, bre... | https://en.wikipedia.org/wiki?curid=442682 |
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