Sejarah matematika: Perbedaan revisi

13 bita dihapus ,  10 tahun yang lalu
Matematika India, belum beres
(Matematika India, masih dilanjut)
(Matematika India, belum beres)
 
''[[Surya Siddhanta]]'' (kira-kira 400) memperkenalkan [[fungsi trigonometri]] [[sinus]], [[kosinus]], dan balikan sinus, dan meletakkan aturan-aturan yang menentukan gerak sejati benda-benda langit, yang bersesuaian dengan posisi mereka sebenarnya di langit.<ref>http://www.westgatehouse.com/cycles.html Exegesis of Hindu Cosmological Time Cycles</ref> Daur waktu kosmologi dijelaskan di dalam tulisan itu, yang merupakan salinan dari karya terdahulu, bersesuaian dengan rata-rata [[tahun siderik]] 365,2563627 hari, yang hanya 1,4 detik lebih panjang daripada nilai modern sebesar 365,25636305 hari. Karya ini diterjemahkan ke dalam [[bahasa Arab]] dan [[bahasa Latin]] pada [[Zaman Pertengahan]].
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[[Aryabhata]], in 499, introduced the [[versine]] function, produced the first Indian [[trigonometry|trigonometric]] tables of sine, developed techniques and [[algorithm]]s of [[algebra]], [[infinitesimal]]s, and [[differential equation]]s, and obtained whole number solutions to linear equations by a method equivalent to modern methods, along with accurate [[astronomy|astronomical]] calculations based on a [[heliocentrism|heliocentric]] system of [[gravity|gravitation]].<ref name="sarma">{{citation | author=[[K. V. Sarma]] | journal=Indian Journal of History of Science | year=2001 | pages=105–115 | title=Āryabhaṭa: His name, time and provenance |volume=36 |issue=4 | url=http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005b67_105.pdf}}</ref> An [[Arabic]] translation of his ''Aryabhatiya'' was available from the 8th century, followed by a Latin translation in the 13th century. He also gave a value of π corresponding to 62832/20000 = 3.1416. In the 14th century, [[Madhava of Sangamagrama]] found the [[Leibniz formula for pi|Madhava–Leibniz series]], and, using 21 terms, computed the value of π as 3.14159265359.
 
[[Aryabhata]], inpada tahun 499, introducedmemperkenalkan thefungsi [[versineversinus]] function, producedmenghasilkan the first Indiantabel [[trigonometry|trigonometrictrigonometri]] tablesIndia ofpertama tentang sinesinus, developedmengembangkan techniquesteknik-teknik anddan [[algorithmalgoritma]]s of [[algebraaljabar]], [[infinitesimal]]s, anddan [[differentialpersamaan equationdiferensial]]s, anddan obtainedmemperoleh wholesolusi numberseluruh solutionsbilangan tountuk persamaan linear equationsoleh bysebuah ametode methodyang equivalentsetara todengan modernmetode methodsmodern, alongbersama-sama withdengan accurateperhitungan [[astronomy|astronomical]astronomi] calculationsyang basedakurat onberdasarkan asistem [[heliocentrism|heliocentricheliosentris]] system of [[gravity|gravitationgravitasi]].<ref name="sarma">{{citation | author=[[K. V. Sarma]] | journal=Indian Journal of History of Science | year=2001 | pages=105–115 | title=Āryabhaṭa: His name, time and provenance |volume=36 |issue=4 | url=http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005b67_105.pdf}}</ref> AnSebuah terjemahan [[Arabicbahasa Arab]] translation ofdari hiskaryanya ''Aryabhatiya'' wastersedia availablesejak fromabad theke-8, 8thdiikuti century,oleh followedterjemahan by abahasa Latin translationpada in the 13thabad centuryke-13. HeDia alsojuga gavememberikan anilai valueπ ofyang π correspondingbersesuaian todengan 62832/20000 = 3.,1416. InPada theabad 14th centuryke-14, [[Madhava ofdari Sangamagrama]] found themenemukan [[rumus Leibniz formula foruntuk pi|Madhava–Leibniz series]], anddan, usingmenggunakan 21 termssuku, computeduntuk themenghitung value ofnilai π assebagai 3.,14159265359.
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In the 7th century, [[Brahmagupta]] identified the [[Brahmagupta theorem]], [[Brahmagupta's identity]] and [[Brahmagupta's formula]], and for the first time, in ''[[Brahmasphutasiddhanta|Brahma-sphuta-siddhanta]]'', he lucidly explained the use of [[0 (number)|zero]] as both a [[placeholder]] and [[decimal digit]], and explained the [[Hindu-Arabic numeral system]].<ref name="Boyer Siddhanta">{{cite book|last=Boyer|authorlink=Carl Benjamin Boyer|title=|year=1991|chapter=The Arabic Hegemony|pages=226|quote=By 766 we learn that an astronomical-mathematical work, known to the Arabs as the ''Sindhind'', was brought to Baghdad from India. It is generally thought that this was the ''Brahmasphuta Siddhanta'', although it may have been the ''Surya Siddhanata''. A few years later, perhaps about 775, this ''Siddhanata'' was translated into Arabic, and it was not long afterwards (ca. 780) that Ptolemy's astrological ''Tetrabiblos'' was translated into Arabic from the Greek.}}</ref> It was from a translation of this Indian text on mathematics (c. 770) that Islamic mathematicians were introduced to this numeral system, which they adapted as [[Arabic numerals]]. Islamic scholars carried knowledge of this number system to Europe by the 12th century, and it has now displaced all older number systems throughout the world. In the 10th century, [[Halayudha]]'s commentary on [[Pingala]]'s work contains a study of the [[Fibonacci sequence]] and [[Pascal's triangle]], and describes the formation of a [[matrix (mathematics)|matrix]].
 
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