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Subject Item: dbr:Kerala_school_of_astronomy_and_mathematics
rdf:type: owl:Thing wikidata:Q43229 wikidata:Q24229398 wikidata:Q2385804 wikidata:Q3914 dbo:Organisation schema:School schema:Organization dbo:EducationalInstitution dbo:Agent n30:SocialPerson n30:Agent schema:EducationalOrganization dbo:School
rdfs:label: Керальська школа з Астрономії і Математики Escuela de Kerala Escola de Querala de Astronomia e Matemática Mazhab astronomi dan matematika Kerala ケーララ学派 케랄라 학파 مدرسة كيرلا لعلم الفلك والرياضيات École du Kerala Керальская школа астрономии и математики Kerala school of astronomy and mathematics Scuola del Kerala
rdfs:comment: Керальська школа з Астрономії і Математики була школою з і астрономії основаною у Кералі що в Індії, серед учасників якої були: , , , , і . Школа набула розвитку між 14-им і 16-им століттями, а оригінальні відкриття школи схоже закінчилися після Нараяни Бхаттатірі (1559–1632). При намаганні вирішити астрономічні задачі, Керальська школа незалежно від інших створила ряд важливих математичних понять. Їхнім найважливішим результатом є розкладання в ряди тригонометричних функцій, описане на санскриті в книзі Нілаканти, що називалася Тантрасанграга (англ. ), і в коментарях до цієї роботи, що називалися Тантрасанграга-вах'я, авторство яких не відомо. Теореми описувалися без доведення, але докази для рядів синуса, косинуса і оберненого тангенса були приведені століттям пізніше у роботі (близь La Escuela de Kerala fue una escuela de matemática y astronomía fundada por Madhava en Kherala (sur de la India) que incluía como miembros destacados a Paramésuara, , Jyeshtadeva, , y . Floreció entre los siglos XIV y XVI y las raíces intelectuales se remontan al s. V d. C., con los trabajos de Aryabhatta. Esta Escuela tiene una evolución rastreable hasta nuestros días, aunque los métodos de investigación finalizaron con . Estos astrónomos, al intentar resolver algunos problemas, desarrollaron un notable número de ideas, que incluyen: ケーララ学派（ケーララがくは、英語：Kerala school of astronomy and mathematics）は、インドのケーララ地方で活動した数学と天文学の学派。サンガマグラーマのマーダヴァが始祖とされ、主に14世紀から17世紀にかけて活動した。マーダヴァ学派とも呼ばれる。 케랄라 학파(Kerala school)는 중세 말기 인도의 케랄라 사람 가 창시한 수학 및 천문학 학파다. 주요 소속 학자로 , 닐라칸타 소마야지, 제하데바, , 등이 있다. 케랄라 학파는 14세기에서 16세기 사이에 번창하다가, 17세기의 나라야나 바타티리 이후로는 독창적 발견이 끊어졌다. 케랄라 학파는 천문학 문제들을 해결하기 위해 시도하는 과정에서 삼각함수의 급수전개를 비롯한 여러 가지 중요한 수학 개념들을 독립적으로 발견했다. 이런 내용들은 산스크리트어로 쓰인 『』(1501년경)에 처음 언급되지만 이 책에는 증명이 없었다. 증명은 제하데바가 말레이어로 쓴 『』(1530년경)에서 제시되었다. 서양에서 미적분학이 발명되기 두 세기 전에 이루어진 케랄라 학파의 작업은 수학사상 최초로 멱급수를 사용한 사례로 인정되고 있다.:173 그러나 케랄라 학파는 미분과 적분의 체계적 이론으로까지는 나아가지 못했고, 그들의 업적이 케랄라 바깥에 전파되어 유의미한 영향을 남겼다는 증거도 없다.:12:293:562:173–174 Кера́льская школа астрономии и математики — научная школа, которая существовала в Индии в XIV—XVII веках и внесла заметный вклад в астрономию и математику. مدرسة كيرلا لعلم الفلك والرياضيات كانت مدرسة للرياضيات وعلم الفلك في كيرلا في الهند. A Escola de Querala de Astronomia e Matemática foi uma escola de matemática e astronomia indiana fundada por Madhava de Sangamagrama na Costa do Malabar, Querala, no sul da Índia. Dentre seu membros constam: Parameshvara, Nilakantha Somayaji, , , e . A escola foi ativa entre os séculos XIV e XVI e as descobertas originas da escola parecem ter terminado com (1559–1632). Na tentativa de resolver problemas de astronomia, a escola de Querala independentemente criou um número significativo de conceitos matemáticos. Seus resultados mais importantes foram as séries de expansão para funções trigonométricas, descritas em versos em sânscrito em um livro de Neelakanta chamado Tantrasangraha, e novamente comentado no trabalho Tantrasangraha-vakhya de autoria desconhecida. Os teoremas foram enunciado Mazhab astronomi dan matematika Kerala adalah mazhab matematika dan astronomi yang didirikan oleh Madhava dari Sangamagrama di Kerala, India Selatan; yang para anggotanya termasuk antara lain , , , , , dan . Mazhab ini berkembang antara abad ke-14 dan ke-16 masehi, dan penemuan orisinil terakhir mazhab ini tampaknya terdapat pada (1559-1632). Dalam upaya untuk memecahkan masalah-masalah astronomi, mazhab Kerala secara mandiri menciptakan beberapa konsep-konsep penting matematika. Hasil terpenting mereka, yaitu ekspansi untuk fungsi trigonometri, digambarkan dalam syair bahasa Sanskerta dalam sebuah buku karangan Neelakanta yang bernama Tantrasangraha, serta dalam komentar tentang karya ini yang disebut Tantrasangraha-vakhya, yang tidak diketahui penulisnya. Teorema-teorema yang ada dinya La Scuola del Kerala è stata un'importante scuola di matematici e astronomi ivi fiorita tra il XIV e il XVI secolo. Fu fondata da Madhava di Sangamagrama (ca. 1350 - ca. 1425) e tra i suoi membri vanno ricordati: Narayana Pandit, , Nilakantha Somayaji, , , e Achyuta Panikkar. Si ritiene che le scoperte originali della scuola siano terminate con (1559-1632). The Kerala school of astronomy and mathematics or the Kerala school was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Tirur, Malappuram, Kerala, India, which included among its members: Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar. The school flourished between the 14th and 16th centuries and the original discoveries of the school seems to have ended with Narayana Bhattathiri (1559–1632). In attempting to solve astronomical problems, the Kerala school independently discovered a number of important mathematical concepts. Their most important results—series expansion for trigonometric functions—were described in Sanskrit verse in a book by Neelakanta called Tantrasangraha, and again in a c L’école du Kerala est une école de mathématiques et d'astronomie fondée par Madhava de Sangamagrama dans la province du Kerala en Inde, et ayant eu entre autres pour membres (en) et Nilakantha Somayaji. Elle prospéra entre le XIVe et le XVIe siècle, s'achevant avec les travaux de Melpathur Narayana Bhattathiri. Les découvertes mathématiques de l'école anticipent de deux siècles certains des résultats du calcul infinitésimal de Newton et Leibniz (mais non leurs techniques), obtenant par exemple le développement en série entière des fonctions trigonométriques, mais il n'y a pas de preuve que ces découvertes se soient diffusées en dehors du Kerala.
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dbo:thumbnail: n25:Kerala_school_chain_of_teachers.jpg?width=300
dbp:caption: Chain of teachers of the Kerala school
dbp:country: India
dbp:founder: dbr:Madhava_of_Sangamagrama
dbp:location: Central and North Kerala
dbp:type: dbr:Astronomy dbr:Mathematics dbr:Science
dbo:abstract: ケーララ学派（ケーララがくは、英語：Kerala school of astronomy and mathematics）は、インドのケーララ地方で活動した数学と天文学の学派。サンガマグラーマのマーダヴァが始祖とされ、主に14世紀から17世紀にかけて活動した。マーダヴァ学派とも呼ばれる。 L’école du Kerala est une école de mathématiques et d'astronomie fondée par Madhava de Sangamagrama dans la province du Kerala en Inde, et ayant eu entre autres pour membres (en) et Nilakantha Somayaji. Elle prospéra entre le XIVe et le XVIe siècle, s'achevant avec les travaux de Melpathur Narayana Bhattathiri. Les découvertes mathématiques de l'école anticipent de deux siècles certains des résultats du calcul infinitésimal de Newton et Leibniz (mais non leurs techniques), obtenant par exemple le développement en série entière des fonctions trigonométriques, mais il n'y a pas de preuve que ces découvertes se soient diffusées en dehors du Kerala. Керальська школа з Астрономії і Математики була школою з і астрономії основаною у Кералі що в Індії, серед учасників якої були: , , , , і . Школа набула розвитку між 14-им і 16-им століттями, а оригінальні відкриття школи схоже закінчилися після Нараяни Бхаттатірі (1559–1632). При намаганні вирішити астрономічні задачі, Керальська школа незалежно від інших створила ряд важливих математичних понять. Їхнім найважливішим результатом є розкладання в ряди тригонометричних функцій, описане на санскриті в книзі Нілаканти, що називалася Тантрасанграга (англ. ), і в коментарях до цієї роботи, що називалися Тантрасанграга-вах'я, авторство яких не відомо. Теореми описувалися без доведення, але докази для рядів синуса, косинуса і оберненого тангенса були приведені століттям пізніше у роботі (близько 1500 - 1610), написаній мовою Малаялам, математиком Юєштадева, а також у коментарях до Тантрасанграга. La Scuola del Kerala è stata un'importante scuola di matematici e astronomi ivi fiorita tra il XIV e il XVI secolo. Fu fondata da Madhava di Sangamagrama (ca. 1350 - ca. 1425) e tra i suoi membri vanno ricordati: Narayana Pandit, , Nilakantha Somayaji, , , e Achyuta Panikkar. Si ritiene che le scoperte originali della scuola siano terminate con (1559-1632). Nel tentativo di risolvere problemi astronomici, la scuola del Kerala sviluppò autonomamente un gran numero di importanti concetti matematici. I loro risultati più importanti, gli sviluppi in serie di funzioni trigonometriche, sono stati descritti mediante versi in sanscrito in un libro di Neelakanta chiamato Tantrasangraha, e anche in un commentario su questo lavoro, chiamato Tantrasangraha-vakhya, di autore ignoto. I teoremi vennero enunciati senza dimostrazione, ma le dimostrazioni relative alle serie per seno, coseno e tangente furono fornite un secolo più tardi nel lavoro Yuktibhasa (c.1500-c.1610), scritto in malayalam da Jyesthadeva, e anche in un commentario su Tantrasangraha. La loro scoperta di queste tre importanti sviluppi in serie — molti secoli prima che fossero sviluppati in Europa da Leibniz e Newton — fu una pietra miliare per la matematica. Non si può comunque dire che la scuola del Kerala abbia inventato il calcolo infinitesimale in quanto, mentre i matematici del Kerala erano in grado di sviluppare in serie di Taylor le funzioni trigonometriche, non svilupparono una teoria globale del calcolo differenziale o integrale, né svilupparono i teoremi fondamentali dell'analisi. Mazhab astronomi dan matematika Kerala adalah mazhab matematika dan astronomi yang didirikan oleh Madhava dari Sangamagrama di Kerala, India Selatan; yang para anggotanya termasuk antara lain , , , , , dan . Mazhab ini berkembang antara abad ke-14 dan ke-16 masehi, dan penemuan orisinil terakhir mazhab ini tampaknya terdapat pada (1559-1632). Dalam upaya untuk memecahkan masalah-masalah astronomi, mazhab Kerala secara mandiri menciptakan beberapa konsep-konsep penting matematika. Hasil terpenting mereka, yaitu ekspansi untuk fungsi trigonometri, digambarkan dalam syair bahasa Sanskerta dalam sebuah buku karangan Neelakanta yang bernama Tantrasangraha, serta dalam komentar tentang karya ini yang disebut Tantrasangraha-vakhya, yang tidak diketahui penulisnya. Teorema-teorema yang ada dinyatakan tanpa bukti, tetapi bukti-bukti untuk deret sinus, kosinus, dan tangen terbalik diberikan satu abad kemudian dalam karya Yuktibhasa (k. 1500 - k. 1610), yang ditulis dalam bahasa Malayalam oleh Jyesthadeva, dan juga dalam komentar tentang Tantrasangraha. Karya mereka, yang diselesaikan dua abad sebelum penemuan kalkulus di Eropa, memberikan gambaran tentang apa yang sekarang disebut sebagai contoh pertama suatu deret pangkat (berbeda dengan deret geometri). Namun mereka tidak merumuskan teori diferensial dan integral secara sistematis, serta tidak terdapat bukti yang jelas bahwa hasil karya mereka pernah dikabarkan di luar wilayah Kerala. A Escola de Querala de Astronomia e Matemática foi uma escola de matemática e astronomia indiana fundada por Madhava de Sangamagrama na Costa do Malabar, Querala, no sul da Índia. Dentre seu membros constam: Parameshvara, Nilakantha Somayaji, , , e . A escola foi ativa entre os séculos XIV e XVI e as descobertas originas da escola parecem ter terminado com (1559–1632). Na tentativa de resolver problemas de astronomia, a escola de Querala independentemente criou um número significativo de conceitos matemáticos. Seus resultados mais importantes foram as séries de expansão para funções trigonométricas, descritas em versos em sânscrito em um livro de Neelakanta chamado Tantrasangraha, e novamente comentado no trabalho Tantrasangraha-vakhya de autoria desconhecida. Os teoremas foram enunciados sem provas, mas estas foram publicadas um século depois para as séries do seno, cosseno e o inverso da tangente no trabalho (ca. 1500 – ca. 1610), escrito em por Jyesthadeva e também comentado no Tantrasangraha. مدرسة كيرلا لعلم الفلك والرياضيات كانت مدرسة للرياضيات وعلم الفلك في كيرلا في الهند. The Kerala school of astronomy and mathematics or the Kerala school was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Tirur, Malappuram, Kerala, India, which included among its members: Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar. The school flourished between the 14th and 16th centuries and the original discoveries of the school seems to have ended with Narayana Bhattathiri (1559–1632). In attempting to solve astronomical problems, the Kerala school independently discovered a number of important mathematical concepts. Their most important results—series expansion for trigonometric functions—were described in Sanskrit verse in a book by Neelakanta called Tantrasangraha, and again in a commentary on this work, called Tantrasangraha-vakhya, of unknown authorship. The theorems were stated without proof, but proofs for the series for sine, cosine, and inverse tangent were provided a century later in the work Yuktibhasa (c. 1530), written in Malayalam, by Jyesthadeva, and also in a commentary on Tantrasangraha. Their work, completed two centuries before the invention of calculus in Europe, provided what is now considered the first example of a power series (apart from geometric series). 케랄라 학파(Kerala school)는 중세 말기 인도의 케랄라 사람 가 창시한 수학 및 천문학 학파다. 주요 소속 학자로 , 닐라칸타 소마야지, 제하데바, , 등이 있다. 케랄라 학파는 14세기에서 16세기 사이에 번창하다가, 17세기의 나라야나 바타티리 이후로는 독창적 발견이 끊어졌다. 케랄라 학파는 천문학 문제들을 해결하기 위해 시도하는 과정에서 삼각함수의 급수전개를 비롯한 여러 가지 중요한 수학 개념들을 독립적으로 발견했다. 이런 내용들은 산스크리트어로 쓰인 『』(1501년경)에 처음 언급되지만 이 책에는 증명이 없었다. 증명은 제하데바가 말레이어로 쓴 『』(1530년경)에서 제시되었다. 서양에서 미적분학이 발명되기 두 세기 전에 이루어진 케랄라 학파의 작업은 수학사상 최초로 멱급수를 사용한 사례로 인정되고 있다.:173 그러나 케랄라 학파는 미분과 적분의 체계적 이론으로까지는 나아가지 못했고, 그들의 업적이 케랄라 바깥에 전파되어 유의미한 영향을 남겼다는 증거도 없다.:12:293:562:173–174 Кера́льская школа астрономии и математики — научная школа, которая существовала в Индии в XIV—XVII веках и внесла заметный вклад в астрономию и математику. La Escuela de Kerala fue una escuela de matemática y astronomía fundada por Madhava en Kherala (sur de la India) que incluía como miembros destacados a Paramésuara, , Jyeshtadeva, , y . Floreció entre los siglos XIV y XVI y las raíces intelectuales se remontan al s. V d. C., con los trabajos de Aryabhatta. Esta Escuela tiene una evolución rastreable hasta nuestros días, aunque los métodos de investigación finalizaron con . Estos astrónomos, al intentar resolver algunos problemas, desarrollaron un notable número de ideas, que incluyen: * Ideas revolucionarias de cálculo. * Teoría de series infinitas. * Series de potencias. * Series de Taylor. * Pruebas de convergencia (usualmente atribuidas a Cauchy). * Diferenciación. * Integración término a término. * Integración numérica en términos de series infinitas. * La teoría que indica que el área bajo la curva es la integral de esta. * Métodos iterativos para solucionar ecuaciones no lineales. * Puntos decimales en coma flotante, sistema que permitió investigar y racionalizar la convergencia de series. Esta escuela matemática logró estos resultados siglos antes que los matemáticos europeos. Jyeshtadeva consolidó los descubrimientos de la Escuela de Kerala en el Yuktibhasa, el primer libro de cálculo en la historia. La Escuela de Kerala también hizo contribuciones en el campo de la lingüística. Las tradiciones poéticas de Kerala fueron fundadas por esta Escuela. El poema Narayaneeyam, fue escrito por .
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