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Porism
A porism is a mathematical proposition or corollary. It has been used to refer to a direct consequence of a proof, analogous to how a corollary refers to a direct consequence of a theorem. In modern usage, it is a relationship that holds for an infinite range of values but only if a certain condition is assumed, such as Steiner's porism. The term originates from three books of Euclid that have been lost. A proposition may not have been proven, so a porism may not be a theorem or true. Origins The book that talks about porisms first is Euclid's ''Porisms''. What is known of it is in Pappus of Alexandria's ''Collection'', who mentions it along with other geometrical treatises, and gives several lemmas necessary for understanding it. Pappus states: :The porisms of all classes are neither theorems nor problems, but occupy a position intermediate between the two, so that their enunciations can be stated either as theorems or problems, and consequently some geometers think that they ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poncelet's Porism
In geometry, Poncelet's closure theorem, also known as Poncelet's porism, states that whenever a polygon is inscribed in one conic section and circumscribes another one, the polygon must be part of an infinite family of polygons that are all inscribed in and circumscribe the same two conics. It is named after French engineer and mathematician Jean-Victor Poncelet, who wrote about it in 1822; however, the triangular case was discovered significantly earlier, in 1746 by William Chapple. Poncelet's porism can be proved by an argument using an elliptic curve, whose points represent a combination of a line tangent to one conic and a crossing point of that line with the other conic. Statement Let ''C'' and ''D'' be two plane conics. If it is possible to find, for a given ''n'' > 2, one ''n''-sided polygon that is simultaneously inscribed in ''C'' (meaning that all of its vertices lie on ''C'') and circumscribed around ''D'' (meaning that all of its edges are tangent to ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pappus Of Alexandria
Pappus of Alexandria (; ; AD) was a Greek mathematics, Greek mathematician of late antiquity known for his ''Synagoge'' (Συναγωγή) or ''Collection'' (), and for Pappus's hexagon theorem in projective geometry. Almost nothing is known about his life except for what can be found in his own writings, many of which are lost. Pappus apparently lived in Alexandria, where he worked as a Mathematics education, mathematics teacher to higher level students, one of whom was named Hermodorus.Pierre Dedron, J. Itard (1959) ''Mathematics And Mathematicians'', Vol. 1, p. 149 (trans. Judith V. Field) (Transworld Student Library, 1974) The ''Collection'', his best-known work, is a compendium of mathematics in eight volumes, the bulk of which survives. It covers a wide range of topics that were part of the ancient mathematics curriculum, including geometry, astronomy, and mechanics. Pappus was active in a period generally considered one of stagnation in mathematical studies, where, to s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclid
Euclid (; ; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics. Very little is known of Euclid's life, and most information comes from the scholars Proclus and Pappus of Alexandria many centuries later. Medieval Islamic mathematicians invented a fanciful biography, and medieval Byzantine and early Renaissance scholars mistook him for the earlier philo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Simson
Robert Simson (14 October 1687 – 1 October 1768) was a Scottish mathematician and professor of mathematics at the University of Glasgow. The Simson line is named after him.Robert Simson University of Glasgow (multi-tab page) Biography Robert Simson was born on 14 October 1687, probably the eldest of the seventeen children, all male, of John Simson, a Glasgow merchant, and Agnes, daughter of Patrick Simpson, minister of Renfrew; only six of them reached adulthood. Simson matriculated at the in 1701, intending to enter the Church. He followed the course in the faculty of arts (Latin, Greek, logic, natural phil ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michel Chasles
Michel Floréal Chasles (; 15 November 1793 – 18 December 1880) was a French mathematician. Biography He was born at Épernon in France and studied at the École Polytechnique in Paris under Siméon Denis Poisson. In the War of the Sixth Coalition he was drafted to fight in the defence of Paris in 1814. After the war, he gave up on a career as an engineer or stockbroker in order to pursue his mathematical studies. In 1837 he published the book ''Aperçu historique sur l'origine et le développement des méthodes en géométrie'' ("Historical view of the origin and development of methods in geometry"), a study of the method of reciprocal polars in projective geometry. The work gained him considerable fame and respect and he was appointed Professor at the École Polytechnique in 1841, then he was awarded a chair at the Sorbonne in 1846. A second edition of this book was published in 1875. In 1839, Ludwig Adolph Sohncke (the father of Leonhard Sohncke) translated the original ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lemma (mathematics)
In mathematics and other fields, a lemma (: lemmas or lemmata) is a generally minor, proven Theorem#Terminology, proposition which is used to prove a larger statement. For that reason, it is also known as a "helping theorem" or an "auxiliary theorem". In many cases, a lemma derives its importance from the theorem it aims to mathematical proof, prove; however, a lemma can also turn out to be more important than originally thought. Etymology From the Ancient Greek λῆμμα, (perfect passive εἴλημμαι) something received or taken. Thus something taken for granted in an argument. Comparison with theorem There is no formal distinction between a lemma and a theorem, only one of intention (see Theorem#Terminology, Theorem terminology). However, a lemma can be considered a minor result whose sole purpose is to help prove a more substantial theorem – a step in the direction of proof. Well-known lemmas Some powerful results in mathematics are known as lemmas, first named for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Corollary
In mathematics and logic, a corollary ( , ) is a theorem of less importance which can be readily deduced from a previous, more notable statement. A corollary could, for instance, be a proposition which is incidentally proved while proving another proposition; it might also be used more casually to refer to something which naturally or incidentally accompanies something else. Overview In mathematics, a corollary is a theorem connected by a short proof to an existing theorem. The use of the term ''corollary'', rather than ''proposition'' or ''theorem'', is intrinsically subjective. More formally, proposition ''B'' is a corollary of proposition ''A'', if ''B'' can be readily deduced from ''A'' or is self-evident from its proof. In many cases, a corollary corresponds to a special case of a larger theorem, which makes the theorem easier to use and apply, even though its importance is generally considered to be secondary to that of the theorem. In particular, ''B'' is unlikely to be te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proposition
A proposition is a statement that can be either true or false. It is a central concept in the philosophy of language, semantics, logic, and related fields. Propositions are the object s denoted by declarative sentences; for example, "The sky is blue" expresses the proposition that the sky is blue. Unlike sentences, propositions are not linguistic expressions, so the English sentence "Snow is white" and the German "Schnee ist weiß" denote the same proposition. Propositions also serve as the objects of belief and other propositional attitudes, such as when someone believes that the sky is blue. Formally, propositions are often modeled as functions which map a possible world to a truth value. For instance, the proposition that the sky is blue can be modeled as a function which would return the truth value T if given the actual world as input, but would return F if given some alternate world where the sky is green. However, a number of alternative formalizations have be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pforta
Schulpforta, otherwise known as Pforta, is a school located in Pforta monastery, a former Cistercian monastery (1137–1540). The school is located near Naumburg on the Saale River in the German state of Saxony-Anhalt. The site has been a school since the 16th century. Notable alumni include mathematician August Ferdinand Möbius, historian Leopold von Ranke, and philosopher Friedrich Nietzsche. Today, it is a notable public boarding school for academically gifted children, otherwise called Landesschule Pforta. It is coeducational and teaches around 300 high school students. Pforta was proposed for inscription in the World Heritage List as one component of the German nomination Naumburg Cathedral and the High Medieval Cultural Landscape of the Rivers Saale and Unstrut. History Monastery The abbey was at first situated in Schmölln on the Sprotta, near Altenburg. In 1127, Count Bruno of Pleissengau founded a Benedictine monastery there and endowed it with 1,100 hides o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessment to form Cambridge University Press and Assessment under Queen Elizabeth II's approval in August 2021. With a global sales presence, publishing hubs, and offices in more than 40 countries, it published over 50,000 titles by authors from over 100 countries. Its publications include more than 420 academic journals, monographs, reference works, school and university textbooks, and English language teaching and learning publications. It also published Bibles, runs a bookshop in Cambridge, sells through Amazon, and has a conference venues business in Cambridge at the Pitt Building and the Sir Geoffrey Cass Sports and Social Centre. It also served as the King's Printer. Cambridge University Press, as part of the University of Cambridge, was a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philology
Philology () is the study of language in Oral tradition, oral and writing, written historical sources. It is the intersection of textual criticism, literary criticism, history, and linguistics with strong ties to etymology. Philology is also defined as the study of literary texts and oral and written records, the establishment of their authentication, authenticity and their original form, and the determination of their meaning. A person who pursues this kind of study is known as a philologist. In older usage, especially British, philology is more general, covering comparative linguistics, comparative and historical linguistics. Classical philology studies classical languages. Classical philology principally originated from the Library of Pergamum and the Library of Alexandria around the fourth century BC, continued by Greeks and Romans throughout the Roman Empire, Roman and Byzantine Empire. It was eventually resumed by European scholars of the Renaissance humanism, Renaissance, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
