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Pafnuty Chebyshev

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53-535: Pafnuty Lvovich Chebyshev (Russian: Пафну́тий Льво́вич Чебышёв , IPA: [pɐfˈnutʲɪj ˈlʲvovʲɪtɕ tɕɪbɨˈʂof] ) (16 May [ O.S. 4 May] 1821 – 8 December [ O.S. 26 November] 1894) was a Russian mathematician and considered to be the founding father of Russian mathematics. Chebyshev is known for his fundamental contributions to the fields of probability , statistics , mechanics , and number theory . A number of important mathematical concepts are named after him, including

106-466: A prime number p {\displaystyle p} such that n < p < 2 n {\displaystyle n<p<2n} . This is a consequence of the Chebyshev inequalities for the number π ( n ) {\displaystyle \pi (n)} of prime numbers less than n {\displaystyle n} : Fifty years later, in 1896,

159-453: A straightedge if a single circle and its center is given. Swiss mathematician Jakob Steiner proved this theorem in 1833, leading to the name of the theorem. The constructions that this theorem states are possible are known as Steiner constructions. In geometry , Poncelet's porism (sometimes referred to as Poncelet's closure theorem ) states that whenever a polygon is inscribed in one conic section and circumscribes another one,

212-599: A bitter priority dispute over the Principle of Duality. In 1825, he became the professor of mechanics at the École d'Application in Metz, a position he held until 1835. During his tenure at this school, he improved the design of turbines and water wheels , deriving his work from the mechanics of the Provençal mill from southern France. Although the turbine of his design was not constructed until 1838, he envisioned such

265-587: A design twelve years previous to that. In 1835, he left École d'Application, and in December 1837 became a tenured professor at Sorbonne (the University of Paris ), where a 'Chaire de mécanique physique et expérimentale' was specially created for him with the support of Louis Jacques Thénard . In 1848, Poncelet became the Commanding General of his alma mater , the École Polytechnique. He held

318-516: A letter dated "12/22 Dec. 1635". In his biography of John Dee , The Queen's Conjurer , Benjamin Woolley surmises that because Dee fought unsuccessfully for England to embrace the 1583/84 date set for the change, "England remained outside the Gregorian system for a further 170 years, communications during that period customarily carrying two dates". In contrast, Thomas Jefferson , who lived while

371-413: A significant contribution to Feuerbach's theorem . He also made discoveries about projective harmonic conjugates ; relating these to the poles and polar lines associated with conic sections . He developed the concept of parallel lines meeting at a point at infinity and defined the circular points at infinity that are on every circle of the plane. These discoveries led to the principle of duality , and

424-911: A start-of-year adjustment works well with little confusion for events before the introduction of the Gregorian calendar. For example, the Battle of Agincourt is well known to have been fought on 25 October 1415, which is Saint Crispin's Day . However, for the period between the first introduction of the Gregorian calendar on 15 October 1582 and its introduction in Britain on 14 September 1752, there can be considerable confusion between events in Continental Western Europe and in British domains. Events in Continental Western Europe are usually reported in English-language histories by using

477-472: A stick and so his parents abandoned the idea of his becoming an officer in the family tradition. His disability prevented his playing many children's games and he devoted himself instead to mathematics. In 1832, the family moved to Moscow , mainly to attend to the education of their eldest sons (Pafnuty and Pavel, who would become lawyers). Education continued at home and his parents engaged teachers of excellent reputation, including (for mathematics and physics)

530-479: A work he is famous for, and improved the design of turbines and water wheels . In 1837, a tenured 'Chaire de mécanique physique et expérimentale' was specially created for him at the Sorbonne (the University of Paris ). In 1848, he became the commanding general of his alma mater , the École Polytechnique . He is honoured by having his name listed among notable French engineers and scientists displayed around

583-595: Is Čebyšëv . The American Mathematical Society adopted the transcription Chebyshev in its Mathematical Reviews . His first name comes from the Greek Paphnutius (Παφνούτιος), which in turn takes its origin in the Coptic Paphnuty (Ⲡⲁⲫⲛⲟⲩϯ), meaning "that who belongs to God" or simply "the man of God". One of nine children, Chebyshev was born in the village of Okatovo in the district of Borovsk , province of Kaluga . His father, Lev Pavlovich,

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636-536: Is 9 February 1649, the date by which his contemporaries in some parts of continental Europe would have recorded his execution. The O.S./N.S. designation is particularly relevant for dates which fall between the start of the "historical year" (1 January) and the legal start date, where different. This was 25 March in England, Wales, Ireland and the colonies until 1752, and until 1600 in Scotland. In Britain, 1 January

689-451: Is considered a reviver of projective geometry , and his work Traité des propriétés projectives des figures is considered the first definitive text on the subject since Gérard Desargues ' work on it in the 17th century. He later wrote an introduction to it: Applications d'analyse et de géométrie . As a mathematician, his most notable work was in projective geometry , although an early collaboration with Charles Julien Brianchon provided

742-516: Is considered to be a founding father of Russian mathematics. Among his well-known students were the mathematicians Dmitry Grave , Aleksandr Korkin , Aleksandr Lyapunov , and Andrei Markov . According to the Mathematics Genealogy Project , Chebyshev has 17,467 mathematical "descendants" as of February 2024. The lunar crater Chebyshev and the asteroid 2010 Chebyshev were named to honor his major achievements in

795-703: The École Polytechnique , a prestigious school in Paris , from 1808 to 1810, though he fell behind in his studies in his third year due to poor health. After graduation, he joined the Corps of Military Engineers . He attended the École d'application in his hometown during this time, and achieved the rank of lieutenant in the French Army the same year he graduated. Poncelet took part in Napoleon 's invasion of Russia in 1812. His biographer Didion writes that he

848-574: The Chebyshev inequality (which can be used to prove the weak law of large numbers ), the Bertrand–Chebyshev theorem , Chebyshev polynomials , Chebyshev linkage , and Chebyshev bias . The surname Chebyshev has been transliterated in several different ways, like Tchebichef, Tchebychev, Tchebycheff, Tschebyschev, Tschebyschef, Tschebyscheff, Čebyčev, Čebyšev, Chebysheff, Chebychov, Chebyshov (according to native Russian speakers, this one provides

901-672: The Imperial Academy of Sciences . In the same year he became an honorary member of Moscow University . He accepted other honorary appointments and was decorated several times. In 1856, Chebyshev became a member of the scientific committee of the ministry of national education. In 1859, he became an ordinary member of the ordnance department of the academy with the adoption of the headship of the commission for mathematical questions according to ordnance and experiments related to ballistics. The Paris academy elected him corresponding member in 1860 and full foreign member in 1874. In 1893, he

954-609: The Russian Empire and the very beginning of Soviet Russia . For example, in the article "The October (November) Revolution", the Encyclopædia Britannica uses the format of "25 October (7 November, New Style)" to describe the date of the start of the revolution. The Latin equivalents, which are used in many languages, are, on the one hand, stili veteris (genitive) or stilo vetere (ablative), abbreviated st.v. , and meaning "(of/in) old style" ; and, on

1007-419: The principle of continuity and also aided in the development of complex numbers . As a military engineer, he served in Napoleon 's campaign against the Russian Empire in 1812, in which he was captured and held prisoner until 1814. Later, he served as a professor of mechanics at the École d'application in his home town of Metz , during which time he published Introduction à la mécanique industrielle ,

1060-408: The 19th century, a practice that the author Karen Bellenir considered to reveal a deep emotional resistance to calendar reform. Jean-Victor Poncelet Jean-Victor Poncelet ( French pronunciation: [ʒɑ̃ viktɔʁ pɔ̃slɛ] ; 1 July 1788 – 22 December 1867) was a French engineer and mathematician who served most notably as the Commanding General of the École Polytechnique . He

1113-539: The 4th century , had drifted from reality . The Gregorian calendar reform also dealt with the accumulated difference between these figures, between the years 325 and 1582, by skipping 10 days to set the ecclesiastical date of the equinox to be 21 March, the median date of its occurrence at the time of the First Council of Nicea in 325. Countries that adopted the Gregorian calendar after 1699 needed to skip an additional day for each subsequent new century that

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1166-583: The Boyne was commemorated with smaller parades on 1 July. However, both events were combined in the late 18th century, and continue to be celebrated as " The Twelfth ". Because of the differences, British writers and their correspondents often employed two dates, a practice called dual dating , more or less automatically. Letters concerning diplomacy and international trade thus sometimes bore both Julian and Gregorian dates to prevent confusion. For example, Sir William Boswell wrote to Sir John Coke from The Hague

1219-515: The British Isles and colonies converted to the Gregorian calendar, instructed that his tombstone bear his date of birth by using the Julian calendar (notated O.S. for Old Style) and his date of death by using the Gregorian calendar. At Jefferson's birth, the difference was eleven days between the Julian and Gregorian calendars and so his birthday of 2 April in the Julian calendar is 13 April in

1272-410: The British colonies, changed the start of the year from 25 March to 1 January, with effect from "the day after 31 December 1751". (Scotland had already made this aspect of the changes, on 1 January 1600.) The second (in effect ) adopted the Gregorian calendar in place of the Julian calendar. Thus "New Style" can refer to the start-of-year adjustment , to the adoption of the Gregorian calendar , or to

1325-585: The Elementary Analysis of the Theory of Probability." His biographer Prudnikov suggests that Chebyshev was directed to this subject after learning of recently published books on probability theory or on the revenue of the Russian insurance industry. In 1847, Chebyshev promoted his thesis pro venia legendi "On integration with the help of logarithms" at St Petersburg University and thus obtained

1378-623: The Gregorian calendar. For example, the Battle of Blenheim is always given as 13 August 1704. However, confusion occurs when an event involves both. For example, William III of England arrived at Brixham in England on 5 November (Julian calendar), after he had set sail from the Netherlands on 11 November (Gregorian calendar) 1688. The Battle of the Boyne in Ireland took place a few months later on 1 July 1690 (Julian calendar). That maps to 11 July (Gregorian calendar), conveniently close to

1431-466: The Gregorian calendar. Similarly, George Washington is now officially reported as having been born on 22 February 1732, rather than on 11 February 1731/32 (Julian calendar). The philosopher Jeremy Bentham , born on 4 February 1747/8 (Julian calendar), in later life celebrated his birthday on 15 February. There is some evidence that the calendar change was not easily accepted. Many British people continued to celebrate their holidays "Old Style" well into

1484-430: The Julian and Gregorian dating systems respectively. The need to correct the calendar arose from the realisation that the correct figure for the number of days in a year is not 365.25 (365 days 6 hours) as assumed by the Julian calendar but slightly less (c. 365.242 days). The Julian calendar therefore has too many leap years . The consequence was that the basis for the calculation of the date of Easter , as decided in

1537-581: The Julian calendar had added since then. When the British Empire did so in 1752, the gap had grown to eleven days; when Russia did so (as its civil calendar ) in 1918, thirteen days needed to be skipped. In the Kingdom of Great Britain and its possessions, the Calendar (New Style) Act 1750 introduced two concurrent changes to the calendar. The first, which applied to England, Wales, Ireland and

1590-517: The Julian date of the subsequent (and more decisive) Battle of Aughrim on 12 July 1691 (Julian). The latter battle was commemorated annually throughout the 18th century on 12 July, following the usual historical convention of commemorating events of that period within Great Britain and Ireland by mapping the Julian date directly onto the modern Gregorian calendar date (as happens, for example, with Guy Fawkes Night on 5 November). The Battle of

1643-497: The celebrated prime number theorem was proved, independently, by Jacques Hadamard and Charles Jean de la Vallée Poussin : using ideas introduced by Bernhard Riemann . Chebyshev is also known for the Chebyshev polynomials and the Chebyshev bias – the difference between the number of primes that are congruent to 3 (modulo 4) and 1 (modulo 4). Chebyshev was the first person to think systematically in terms of random variables and their moments and expectations . Chebyshev

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1696-550: The closest pronunciation in English to the correct pronunciation in old Russian), and Chebychev, a mixture between English and French transliterations considered erroneous. It is one of the most well known data-retrieval nightmares in mathematical literature. Currently, the English transliteration Chebyshev has gained widespread acceptance, except by the French, who prefer Tchebychev. The correct transliteration according to ISO 9

1749-492: The combination of the two. It was through their use in the Calendar Act that the notations "Old Style" and "New Style" came into common usage. When recording British history, it is usual to quote the date as originally recorded at the time of the event, but with the year number adjusted to start on 1 January. The latter adjustment may be needed because the start of the civil calendar year had not always been 1 January and

1802-543: The end of the following December, 1661/62 , a form of dual dating to indicate that in the following twelve weeks or so, the year was 1661 Old Style but 1662 New Style. Some more modern sources, often more academic ones (e.g. the History of Parliament ) also use the 1661/62 style for the period between 1 January and 24 March for years before the introduction of the New Style calendar in England. The Gregorian calendar

1855-663: The first stage of the Eiffel tower . Poncelet was born in Metz , France, on 1 July 1788, the illegitimate then legitimated son of Claude Poncelet, a lawyer of the Parliament of Metz and wealthy landowner. His mother, Anne-Marie Perrein, had a more modest background. At a young age, he was sent to live with the Olier family at Saint-Avold . He returned to Metz for his secondary education, at Lycée Fabert . After this, he attended

1908-422: The greatest influence on Chebyshev. Brashman instructed him in practical mechanics and probably showed him the work of French engineer J.V. Poncelet . In 1841 Chebyshev was awarded the silver medal for his work "calculation of the roots of equations" which he had finished in 1838. In this, Chebyshev derived an approximating algorithm for the solution of algebraic equations of n degree based on Newton's method . In

1961-590: The mathematical realm. Old Style and New Style dates Old Style ( O.S. ) and New Style ( N.S. ) indicate dating systems before and after a calendar change, respectively. Usually, they refer to the change from the Julian calendar to the Gregorian calendar as enacted in various European countries between 1582 and 1923. In England , Wales , Ireland and Britain's American colonies , there were two calendar changes, both in 1752. The first adjusted

2014-456: The other, stili novi or stilo novo , abbreviated st.n. and meaning "(of/in) new style". The Latin abbreviations may be capitalised differently by different users, e.g., St.n. or St.N. for stili novi . There are equivalents for these terms in other languages as well, such as the German a.St. (" alter Stil " for O.S.). Usually, the mapping of New Style dates onto Old Style dates with

2067-564: The position until 1850, when he retired. During this time, he wrote Applications d'analyse et de géométrie , which served as an introduction to his earlier work Traité des propriétés projectives des figures . It was published in two volumes in 1862 and 1864. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1865. Poncelet discovered the following theorem in 1822: Euclidean compass and straightedge constructions can be carried out using only

2120-501: The probability that the outcome of X {\displaystyle X} is no less than a σ {\displaystyle a\sigma } away from its mean is no more than 1 / a 2 {\displaystyle 1/a^{2}} : The Chebyshev inequality is used to prove the weak law of large numbers . The Bertrand–Chebyshev theorem (1845, 1852) states that for any n > 3 {\displaystyle n>3} , there exists

2173-604: The right to teach there as a lecturer. At that time some of Leonhard Euler 's works were rediscovered by P. N. Fuss and were being edited by Viktor Bunyakovsky , who encouraged Chebyshev to study them. This would come to influence Chebyshev's work. In 1848, he submitted his work The Theory of Congruences for a doctorate, which he defended in May 1849. He was elected an extraordinary professor at St Petersburg University in 1850, ordinary professor in 1860 and, after 25 years of lectureship, he became merited professor in 1872. In 1882 he left

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2226-589: The same year, he finished his studies as "most outstanding candidate". In 1841, Chebyshev's financial situation changed drastically. There was famine in Russia, and his parents were forced to leave Moscow. Although they could no longer support their son, he decided to continue his mathematical studies and prepared for the master examinations, which lasted six months. Chebyshev passed the final examination in October 1843 and, in 1846, defended his master thesis "An Essay on

2279-512: The senior Moscow University teacher Platon Pogorelsky  [ ru ] , who had taught, among others, the future writer Ivan Turgenev . In summer 1837, Chebyshev passed the registration examinations and, in September of that year, began his mathematical studies at the second philosophical department of Moscow University. His teachers included N.D. Brashman , N.E. Zernov and D.M. Perevoshchikov of whom it seems clear that Brashman had

2332-644: The start of a new year from 25 March ( Lady Day , the Feast of the Annunciation ) to 1 January, a change which Scotland had made in 1600. The second discarded the Julian calendar in favour of the Gregorian calendar, skipping 11 days in the month of September to do so. To accommodate the two calendar changes, writers used dual dating to identify a given day by giving its date according to both styles of dating. For countries such as Russia where no start-of-year adjustment took place, O.S. and N.S. simply indicate

2385-553: The university and devoted his life to research. During his lectureship at the university (1852–1858), Chebyshev also taught practical mechanics at the Alexander Lyceum in Tsarskoe Selo (now Pushkin), a southern suburb of St Petersburg . His scientific achievements were the reason for his election as junior academician (adjunkt) in 1856. Later, he became an extraordinary (1856) and in 1858 an ordinary member of

2438-465: The years 1812–1814, he wrote his most notable work, Traité des propriétés projectives des figures , which outlined the foundations of projective geometry, as well as some new results. Poncelet, however, could not publish it until after his release in 1814. In 1815, the year after his release, Poncelet was employed a military engineer at his hometown of Metz. In 1822, while at this position, he published Traité des propriétés projectives des figures . This

2491-642: Was a Russian nobleman and wealthy landowner. Pafnuty Lvovich was first educated at home by his mother Agrafena Ivanovna Pozniakova (in reading and writing) and by his cousin Avdotya Kvintillianovna Sukhareva (in French and arithmetic ). Chebyshev mentioned that his music teacher also played an important role in his education, for she "raised his mind to exactness and analysis". Trendelenburg's gait affected Chebyshev's adolescence and development. From childhood, he limped and walked with

2544-421: Was altered at different times in different countries. From 1155 to 1752, the civil or legal year in England began on 25 March ( Lady Day ); so for example, the execution of Charles I was recorded at the time in Parliament as happening on 30 January 164 8 (Old Style). In newer English-language texts, this date is usually shown as "30 January 164 9 " (New Style). The corresponding date in the Gregorian calendar

2597-596: Was celebrated as the New Year festival from as early as the 13th century, despite the recorded (civil) year not incrementing until 25 March, but the "year starting 25th March was called the Civil or Legal Year, although the phrase Old Style was more commonly used". To reduce misunderstandings about the date, it was normal even in semi-official documents such as parish registers to place a statutory new-year heading after 24 March (for example "1661") and another heading from

2650-551: Was elected honorable member of the St. Petersburg Mathematical Society , which had been founded three years earlier. Chebyshev died in St Petersburg on 8 December 1894. Chebyshev is known for his work in the fields of probability , statistics , mechanics , and number theory . The Chebyshev inequality states that if X {\displaystyle X} is a random variable with standard deviation σ > 0, then

2703-496: Was implemented in Russia on 14 February 1918 by dropping the Julian dates of 1–13 February 1918 , pursuant to a Sovnarkom decree signed 24 January 1918 (Julian) by Vladimir Lenin . The decree required that the Julian date was to be written in parentheses after the Gregorian date, until 1 July 1918. It is common in English-language publications to use the familiar Old Style or New Style terms to discuss events and personalities in other countries, especially with reference to

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2756-481: Was part of the group which was cut from Marshal Michel Ney 's army at the Battle of Krasnoi and was forced to capitulate to the Russians, though other sources say that he was left for dead. Upon capture, he was interrogated by General Mikhail Andreyevich Miloradovich , but he did not disclose any information. The Russians held him as a prisoner of war and confined him at Saratov . During his imprisonment, in

2809-586: Was the first major work to discuss projective geometry since Desargues', though Gaspard Monge had written a few minor works about it previously. It is considered the founding work of modern projective geometry. Joseph Diaz Gergonne also wrote about this branch of geometry at approximately the same time, beginning in 1810. Poncelet published several papers about the subject in Annales de Gergonne (officially known as Annales de mathématiques pures et appliquées ). However, Poncelet and Gergonne ultimately engaged in

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