January 2007; DOI: 10.1007/978-0-387-30400-7_9088. 4. (fl. Mathematicians have the envious job of creating new patterns from nothingness. ." Campanus of Novara Leon wurde im letzten Jahrzehnt des 8. Mit Flexionstabellen der verschiedenen Fälle und Zeiten Aussprache und … Starting late did not have much of a negative effect on Pascal’s skills as a mathematician since he would go on to great fame as a legendary math trailblazer. In the 15th and 16th century mathematicians were also painters. The Byzantine emperor Theophilus (829-842), learning of this invitation, responded by charging Leo with … [2] He was archbishop of Thessalonica and later became the head of the Magnaura School of philosophy in Constantinople,[3] where he taught Aristotelian logic. Byzantine philosopher, mathematician and logician. Hertlein, ed., in Hermes, 8 (1874), 173-176; cf. Mathematician definition, an expert or specialist in mathematics. Fibonacci (/ˌfɪbəˈnɑːtʃi/; also US: /ˌfiːb-/, Italian:; c. 1170 – c. 1240–50), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'), was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages". He returned to Dearborn after college and lived there until the middle 1960s (in a different middle-class neighborhood than his childhood) even as other Ford executives moved out to fancier zip codes. He not only made formative contributions to the subjects of geometry, calculus, mechanics, and number theory but also developed methods for solving problems in astronomy and demonstrated practical applications of mathematics. He also introduced a … Enjoy a range of facts and information about brilliant mathematicians such as Pythagoras, Euclid, Pierre Fermat, Blaise Pascal, Leonhard Euler, Carl Friedrich Gauss, Alan Turing and more. 790; d. Important thinkers throughout history like Archimedes, Pythagoras, and Benjamin Banneker have helped us understand our world through mathematics and numbers. Then, copy and paste the text into your bibliography or works cited list. 25-29. MARSILIUS OF INGHEN (OR INGUEM OR DE NOVIMAGIO) Had it not been for famous mathematicians and their contributions, some of those concepts may not be around today. Today these vintage consumer goods are prized by antique dealers and collectors. Alexandria [and Athens? Leon der Mathematiker war ein bedeutender byzantinischer Gelehrter, Mathematiker und Philosoph des 9. [18] Leo also invented several automata, such as trees with moving birds, roaring lions, and a levitating imperial throne. Datasets available include LCSH, BIBFRAME, LC Name Authorities, LC Classification, MARC codes, PREMIS vocabularies, ISO language codes, and more. Create a WebQuest: Simple. 148-176 ; Lemerle gives references to almost all the pp. Newton’s Early Years. Main navigation. See more. It remains, then, that Leo was important for his role in the transmission of Greek scientific literature and in the restoration of Byzantine learning after a long period of decline. Task. From the Cambridge English Corpus This is because … [11], In the version of the story recorded by Theophanes Continuatus, the caliph, upon receiving Leo's letter of refusal, sent a letter requesting answers to some difficult questions of geometry and astrology, which Leo obliged. 19-21) and from Hephaestio I 21, 12-32 (Pingree, pp. Leo X, originally Giovanni de’ Medici, (born December 11, 1475, Florence [Italy]—died December 1, 1521, Rome), one of the leading Renaissance popes (reigned 1513–21). His only preserved writings are some notes contained in manuscripts of Plato's dialogues. Mathematicians analyze data, study patterns and develop mathematical models that not only help to further human knowledge, but are also utilized for solving problems in various fields. Create models to resolve practical problems in fields such as business, government, engineering, and the sciences; Develop computational methods and computer codes; Compare inferences derived from models with observations or experiments ; Mathematicians work in government and in private science and engineering research. He was archbishop of Thess… He was probably at least in part of Armenian descent. This includes data values and the controlled vocabularies that house them. A self-taught genius Indian mathematician, Srinivasa Ramanujan is known for his contributions to mathematical analysis, number theory and continued fractions. In book: The Biographical Encyclopedia of Astronomers; Authors: Leonard B. Abbey. “How to Know the Lengths of the Reigns of Kings and Rulers, and What Happens in Their Reigns” and “On the Appearance of the Ruler,” F. Cumont, ed., in CCAG, IV (Brussels, 1903), 92—93; it has been noted previously that these are taken from Ahmad. It contained the following recreational problem: “How many pairs of rabbits can be produced from a single pair in one year if it is assumed that every month each pair begets a new… His efforts to standardize these and other symbols (including πand the trigonometric functions) helped to internationalize mathematics and to encourage collaboration on problems. In the 820’s Leo began to give private instruction at Constantinople; one of the students who had read Euclid’s Elements with him was captured by the Arab army in 830 or 831, and his enthusiastic report of his master’s accomplishments caused the caliph alMa’mûn (813-833) to invite Leo to Baghdad. Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. 1-2 of A 56 sup. Science History Institute/Gregory Tobias A … Jahrhunderts. Secondary Literature. Finally, from some of his poems preserved in thePalatine Anthology, it is known that he possessed copies of the Mechanics of Cyrinus and Marcellus, theConics of Apollonius, the Introduction of the astrologer Paul of Alexandria, the romance of Achilles Tatius, as well as works of Theon on astronomy and Proclus on geometry. Learn about the famous mathematicians whose incredible work has helped change both the field of mathematics and the world we live in today. The best source is now P. Lemerle, Le premier humanisme byzantin (Paris, 1971), pp. Cite this article Pick a style below, and copy the text for your bibliography. "Leo the Mathematician A poem edited by P. Matranga, Anecdota graeca, II (Rome, 1850), 559, is sometimes–and probably erroneously–ascribed to Leo; it follows some pieces by Leo’s student Constantine, attacking him for studying pagan science, ibid., 555-559. Quick. theology, science, scientific and academic administration and organization. “Earthquake Omens,” A. Delatte, ed., CCAG, X (Brussels, 1924), 132-135, is attributed to the Emperor Leo (Leo VI the Wise); but the attribution could possibly be a mistake for Leo the Mathematician. Make that: the multiverse of every possible universe of patterns. With noun/verb tables for the different cases and tenses links to audio pronunciation and relevant forum discussions free vocabulary trainer He is sometimes called “the father of algebra”, and wrote an influential series of books called the “Arithmetica”, a collection of algebraic problems which greatly influenced the subsequent development of number theory. Famous Mathematicians Learn about the famous mathematicians whose incredible work has helped change both the field of mathematics and the world we live in today. Leonhard Euler, Swiss mathematician and physicist, one of the founders of pure mathematics. "Leo the Mathematician Starting late did not have much of a negative effect on Pascal’s skills as a mathematician since he would go on to great fame as a legendary math trailblazer. ], ca. His collection included the works of Archimedes, Apollonius of Perga, Proclus, Ptolemy, and Theon of Alexandria. Er spielte eine nicht unbedeutende Rolle bei der verstärkten Beschäftigung mit griechischem Wissen in Byzanz im Rahmen der sogenannten makedonischen Renaissance . It is at present impossible to judge the authenticity of the other brief tracts on divination by thunder, earthquakes, the lords of the weekdays, and the gospels and psalms that are found in Byzantine manuscripts, but skepticism seems to be called for. “Gnomic Sayings,” M. A. Šangin, ed., in CCAG, XII (Brussels, 1936), 105. Философская Энциклопедия [ред. Like the Bernoulli’s, he was born in Basel, Switzerland, and he studied for a while under Johann Bernoulli at Basel University. Times, Sunday Times ( 2010 ) The wealthiest people in Britain have worked out that if you employ an accountant then both the mathematician and the philosopher can be made redundant . He introduced the world to such wide-ranging mathematical concepts as what is now known as the Arabic numbering system, the concept of square roots, number sequencing, and even math word problems. In particular, he would study geometry. There is a discrepancy in this account, however, in that the caliph died in 833. In fact, Pascal would study math on his own in secret. They begin with the parentage, religion, and geographic origin of the mathematician, and such biographical dates as could be established. In fact, Pascal would study math on his own in secret. 3. ]; d. Athens, 485) 14. Dictionaries thesauruses pictures and press releases, Complete Dictionary of Scientific Biography. Girolamo Cardano, Girolamo also spelled Gerolamo, English Jerome Cardan, (born September 24, 1501, Pavia, duchy of Milan [Italy]—died September 21, 1576, Rome), Italian physician, mathematician, and astrologer who gave the first clinical description of typhus fever and whose book Ars magna (The Great Art; or, The Rules of Algebra) is one of the cornerstones in the … mathematics. “Divination From the Holy Gospel and Psalter,” on fols. The following are of doubtful authenticity: 6-7. The story goes that when one of his students[9] was captured during the Byzantine–Arab Wars, the Caliph al-Mamun was so impressed by his knowledge of mathematics that he offered Leo great riches to come to Baghdad. He made Rome a cultural centre and a political power, but he depleted the papal treasury, and, by failing to take the developing Reformation seriously, he contributed to the dissolution of the … Most people don’t even know there are mathematicians out there creating new math. Later Byzantine scholars sometimes confused Leo with the scholar Leo Choirosphaktes and the emperor Leo VI the Wise, and ascribe to him oracles. His “Scholia on the Hourly Motion,” which claims to correct an error in an example given in Porphyrius’ commentary on Ptolemy’s Apotelesmatics, in fact refers to one in Pancharius’ commentary on Ptolemy III 11, 8-11, as cited by Hephaestio of Thebes, ApotelesmaticsII 11, 39-40 (Pingree, p. 124); his solution is absurdly taken from an entirely different example in the anonymous commentary on Ptolemy III 11, 10 (Wolf, p.114). natural philosophy. Boethius, Anicius Manlius Severinus We get to see the nuts and bolts of how the universe of patterns works. Ф. В. Константинова], According to the Pseudo-Symeon, this student was Boïditzes, who. I. 12. Constantinople[? 13. Among the Hindu mathematicians, Aryabhata was known as Arjehir by Arabs, may be most famous. 284v–285v of codex 3632 of the University Library, Bologna. His own surving scientific works are astrological. The rather conflicting sources attest that Leo obtained a rudimentary In the 820’s Leo began to give private instruction at Constantinople; one of the students who had read Euclid’s Elements with him was captured by the Arab army in 830 or 831, and his enthusiastic report of his master’s accomplishments caused the caliph alMa’mûn (813-833) to invite Leo to Baghdad. 28v–30 of Laurentianus graecus 86, 14, Florence. Free. ... that Leo the Mathematician, called by some the cleverest man in 9th century Byzantium, invented a system of beacons to warn of Arab raids and a fabled levitating throne for the emperor?" This latter option squares with the account of Symeon the Logothete, who makes Leo teach at the Magnaura from late 838 to early 840 and was paid handsomely. Leo the Mathematician: | |Leo the Mathematician| or |the Philosopher| (|Aristotelian logic|. education in rhetoric, philosophy, and arithmetic from a scholar on the island of Andros but that his more advanced knowledge of these subjects, and of geometry, astronomy, and astrology was gained through his own researches among the manuscripts that he found in monastic libraries. Flourished: Constantinople, (Istanbul, Turkey), 850. View WebQuests; About; Log in; Famous Mathematician. 5. (b. Byzantium, 410 [412? Leo has been credited with a system of beacons (an optical telegraph) stretching across Asia Minor from Cilicia to Constantinople, which gave advance warning of Arab raids, as well as diplomatic communication. Treadgold, "Chronological Accuracy ", 172. But, partly due to the overwhelming dominance of the Bernoulli family in Swiss mathematics, and the difficulty of finding a good position and recognition in his hometown, he spent most of his … His father died before Newton was born and his mother remarried. Brahmagupta used a special sign for negatives and stated the rules for dealing with positive … Leo did not come from wealth, was raised in a working-class neighborhood and clearly was born to a rural, farming family. The Byzantine emperor Theophilus (829-842), learning of this invitation, responded by charging Leo with the task of providing public education at the Church of the Forty Martyrs in Constantinople. II. Leo the Mathematician or the Philosopher (Greek: Λέων ὁ Μαθηματικός or ὁ Φιλόσοφος, Léōn ho Mathēmatikós or ho Philósophos; c. 790 – after 869) was a Byzantine philosopher and logician associated with the Macedonian Renaissance and the end of Iconoclasm. [10] Leo took the letter from the caliph to the Byzantine emperor Theophilos, who, impressed by his international repute, conferred on him a school (ekpaideutērion) in either the Magnaura or the church of the Forty Martyrs. ☰ Menu. 480; d. near Pavia, Italy, 524/525) Lernen Sie die Übersetzung für 'mathematician' in LEOs Englisch ⇔ Deutsch Wörterbuch. Mathematician definition is - a specialist or expert in mathematics. Teacher and scholar; also called Leo the Philosopher. Encyclopedia.com. In 1202 the mathematician Leonardo of Pisa, also called Fibonacci, published an influential treatise, Liber abaci. Learn the translation for ‘mathematician’ in LEO’s English ⇔ German dictionary. These scientists work in the fields of pure and applied mathematics. Listen to the audio pronunciation of Leo the Mathematician on pronouncekiwi Felix Klein; Klein (German mathematician who created the Klein bottle (1849-1925)) ... Could a linguist, could a grammarian, could even a mathematician have seen what she did, have witnessed their appearance together, and heard their history of it, without feeling that circumstances had been at work to make them peculiarly interesting to each other? The last notice of him is in a chronicle recording an astrological prediction that he made in Constantinople in 869. . [12], Leo, an iconoclast sometimes accused of paganism, lost his metropolitancy with the end of the Iconoclasm in 843. In particular, he would study geometry. — Dan Rockmore, The New Yorker, "Three Mathematicians We Lost in 2020," 31 Dec. 2020 Kra, 54, has grown from an uncertain graduate student into a mathematician at the top of her field. 10. Supposedly, Leo was so famous an astronomer, mathematician, and physician that the Caliph asked the Roman emperor to loan Leo to him. Almost no…, Euclid His treatise “On the Solar Eclipse in the Royal Triplicity” is lifted from Lydus’On Omens 9 (Wachsmuth, pp. mathematics, astro…, Proclus Known for his discovery of gravity, Newton remains to this day a very influential figure from the Age of Enlightenment. He […] Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA). The emperor then honoured Leo by having John the Grammarian consecrate him metropolitan of Thessalonica, which post he held from the spring of 840 to 843. (January 14, 2021). Most of Leo's writings have been lost. ], ca. The short works on political astrology attributed to him in some manuscripts seem to be derived from the eleventh-century Byzantine translation of an Arabic astrological compendium of one Ahmad, in which they are II 123-125. Leonardo made a living with what would nowadays be the work of a mathematician, painter, architect and engineer. [4][5][6][7] In his youth he was educated at Constantinople, but he travelled to the monasteries of Andros, where he could obtain rare manuscripts and was taught mathematics by an old monk. (b. Rome [? Leonardo Pisano Fibonacci (1170–1240 or 1250) was an Italian number theorist. The following article is in two parts: Life and Works; Transmission of the Elements.…, Boethius, Anicius Manlius Severinus Pick a style below, and copy the text for your bibliography. In any case, he was connected with the transcription of at least some of the Tetralogies of Plato’s works, of the larger part of the corpus of Archimedes’ works, and of Ptolemy’s Almagest; it is likely that he was also concerned with the collection of mathematical and astronomical writings known as the Little Astronomy. A work on astrological predictions from the lords of the weekdays, accompanied by a “portrait” of Leo, on fols. (Paris, 1864-1877). Diophantus was a Hellenistic Greek (or possibly Egyptian, Jewish or even Chaldean) mathematician who lived in Alexandria during the 3rd Century CE. He was a nephew (or cousin) of John VII Grammatikos and metropolitan of Thessalonike (qq.v.) ." Among them, worthy of special mention are some centos preserved in the Palatine Anthology, see Prieto Domínguez, Óscar (2011), "Leone il Matematico, un anello mancante nella storia della scienza", https://en.wikipedia.org/w/index.php?title=Leo_the_Mathematician&oldid=993119594, Articles containing Ancient Greek (to 1453)-language text, Wikipedia articles with SUDOC identifiers, Wikipedia articles with WORLDCATID identifiers, Creative Commons Attribution-ShareAlike License. [8] He composed his own medical encyclopaedia. Original Works. Famous Mathematicians. Katerina Ierodiakonou and Börje Bydén (2008), This page was last edited on 8 December 2020, at 22:04. [8] He originally taught privately in obscurity in Constantinople. His library can at least partially be reconstructed: Archimedes, Euclid, Plato, Paul of Alexandria, Theon of Alexandria, Proclus, Porphyry, Apollonius of Perga, the lost Mechanics of Quirinus and Marcellus, and possibly Thucydides. Leonardo da Vinci lived around 1500 in Italy. in the Ambrosian Library, Milan. From ninth-century manuscripts Leo is known to have been involved in the process of transcribing texts written in majuscule script into minuscule; this activity may well have included some editorial work, although its nature and extent are uncertain. At the age of 12, he made the discovery that two right angles are the sum of a triangle. Complete Dictionary of Scientific Biography. He was a skilled mathematician and engineer, and in his long career he invented many of the basic practices of computer science. PROCLUS It has been suggested that either the connection between the caliph's final letter and Leo's appointment as metropolitan is in error, or the caliph in question was actually al-Mutasim. Much of the notation used by mathematicians today – including e, i, f(x), ∑, and the use of a, b and c as constants and x, y and z as unknowns – was either created, popularized or standardized by Euler. However, your hard work will pay off if you stick with it. It would have been impossible to make as many scientific discoveries that we have till now without the generous contribution of Einstein to science through mathematics and physics. The globally renowned physicist and mathematician who discovered the mass-energy formula E = mc2 was Albert Einstein, who revolutionized the technological advancement. [1] The throne was in operation a century later, when Liutprand of Cremona witnessed it during his visit to Constantinople.[19][20]. A record of the entry may be seen at Wikipedia:Recent additions/2008/November . Leopold Kronecker (German: [ˈkʁoːnɛkɐ]; 7 December 1823 – 29 December 1891) was a German mathematician who worked on number theory, algebra and logic.He criticized Georg Cantor's work on set theory, and was quoted by Weber (1893) as having said, "Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk" ("God made the integers, all else is the work of man"). He wrote book-length works, poems, and many epigrams,[21] and was also a compiler, who brought together a wide range of philosophical, medical, and astronomic texts. He has been called a "true Renaissance man" [1] and "the cleverest man in Byzantium in the 9th century". He has been called a "true Renaissance man"[1] and "the cleverest man in Byzantium in the 9th century". Born into a humble family, the celebrated mathematician struggled with poverty but still managed to publish first of his papers in the Journal of the Indian Mathematical Society. Retrieved January 14, 2021 from Encyclopedia.com: https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/leo-mathematician. © 2019 Encyclopedia.com | All rights reserved. His only preserved writings are some notes contained in manuscripts of Plato's dialogues. from 840 843. 11. Supposedly, Leo was so famous an astronomer, mathematician, and physician that the Caliph asked the Roman emperor to loan Leo to him. Wilkins’s career coincides with the most even…, Leo, Leonardo (actually, Lionardo Ortensio Salvatore de), https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/leo-mathematician. Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. 2. What do famous Mathematicians have to do with the math we learn today? His only preserved writings are some notes contained in manuscripts of Plato's dialogues. (b. [13] Despite this, he delivered a sermon favourable of icons within months of Theophilos' death. From the spring of 840 until the spring of 843 Leo served as archbishop of Thessalonica, a post he received presumably because of his political influence rather than his holiness. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list. Isaac Newton is one of the most celebrated and recognized mathematicians and physicists in world history. This webquest is going to help answer questions like these. This proves that his technical mastery of astrology was very shaky indeed. Proclus’ parents, Patricius and Marcella, were wellbor…, Wilkins, John How do you say Leo the Mathematician? Born: March 31, 1596, in La Haye en Touraine, Kingdom of France Died: Feb 11, 1650 (at age 53), in Stockholm, Swedish Empire Nationality: French Famous For: Developing the Cartesian coordinate system René Descartes was a French mathematician, philosopher, and writer that spent nearly all of his adult life living in the Dutch Republic. He painted many beautiful and peaceful pictures, and at the same time he designed war machines. Where did math come from? He was promptly deposed when the iconodule Methodius I succeeded his iconoclast cousin John as patriarch in 843. The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. He made few, if any, original contributions to science. [probably] Novara, Italy, first quarter of thirteenth century; d. Viterbo, Italy, 1296), A message could be transmitted over these stations in less than an hour; by establishing theoretically synchronized chronometers at either end, Leo was able to provide for the transmission of twelve different messages depending on the hour at which the first fire was lit. [16][17] Cyril was his student. 14 Jan. 2021 . Philosophy, mathematics, astronomy. Constantinople[? The name he is commonly called, Fibonacci, was made up in 1838 by the Franco … Symeon says the Magnaura, Continuatus the Forty Martyrs (Treadgold, "Chronological Accuracy ", 186). “On the Solar Eclipse in the Royal Triplicity,” F.C. 54-62). [15] He was renowned for his philosophical, mathematical, medical, scientific, literary, philological, astronomic, and astrological learning, and was patronised by Theoktistos and befriended by Photios I of Constantinople. 8. He even managed to combine several of these together in an amazing feat of mathematical alchemy to produce one of the most beau… Encyclopedia.com. His collection included the works of Archimedes, Apollonius of Perga, Proclus, Ptolemy, and Theon of Alexandria.. A homily delivered at Thessalonica on 25 March 842, is in V. Laurent, ed., Mélanges Eugène Tisserant,II (Vatican City, 1964), 281-302. WILKINS, JOHN In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Isaac Newton was born in Lincolnshire on Christmas Day of 1642. A group of poems was attributed to Leo and edited by J. F. Boissonade, in Anecdota graeca, II (Paris, 1830), 469 ff. “On a Sick Man,” a treatise on medical astrology preserved on fols. Colorful objects made of Bakelite—jewelry, telephones, radios, and billiard balls, to name just a few—brightened everyday life in the first half of the 20th century. Leonhard Euler was one of the giants of 18th Century mathematics. Arethas’ copy of Euclid’s Elements contains, at VI.5, a “school note” by Leo on the addition and subtraction of fractions, in which he uses the Greek alphabetical symbols for numbers as the denominators. The Linked Data Service provides access to commonly found standards and vocabularies promulgated by the Library of Congress. [14] Around 855, Leo was appointed at the head of a newly established Magnaura School by Bardas. ], ca. Leo the Mathematician or the Philosopher (Greek: Λέων ὁ Μαθηματικός or ὁ Φιλόσοφος, Léōn ho Mathēmatikós or ho Philósophos; c. 790 – after 869) was a Byzantine philosopher and logician associated with the Macedonian Renaissance and the end of the Second Byzantine Iconoclasm. Leo revived Byzantine interest in old books by copying them into new script. Who invented math? 845-850’ d. after 919), belonged to a prominent Byzantine family, as is indicated by the fact that his cousin, John VII Morocharzianus the Grammarian, had been patriarch (837-843). (b. near Nijmegen, Netherlands; d. Heidelberg, Germany, 20 August 1396) The index to CCAG, III (Brussels, 1901), incorrectly ascribes to Leo that text edited by A. Martini and D. Bassi on pp. , your hard work will pay off if you stick with it if any, original contributions mathematical... Of how the universe of patterns works, architect and engineer ’ on Omens 9 Wachsmuth... A “ portrait ” of Leo ’ s astrological tracts today these vintage consumer goods prized... Discovery that two right angles are the sum of a triangle in chronicle!, 2021 from Encyclopedia.com: https: //www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/leo-mathematician Royal Triplicity, ” a on... Katerina Ierodiakonou and Börje Bydén ( 2008 ), 173-176 ; cf technical... 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