Sejarah matematika: Perbedaan revisi

55 bita ditambahkan ,  10 tahun yang lalu
Matematika India, masih dilanjut
(Matematika India, masih dilanjut)
(Matematika India, masih dilanjut)
| doi=10.1023/A:1017506118885
}}</ref> Notasi yang dia gunakan sama dengan notasi matematika modern, dan menggunakan aturan-aturan meta, [[transformasi (geometri)|transformasi]], dan [[rekursi]]. [[Pingala]] (kira-kira abad ke-3 sampai abad pertama SM) di dalam risalahnya [[Prosody (puisi)|prosody]] menggunakan alat yang bersesuaian dengan [[sistem bilangan biner]]. Pembahasannya tentang [[kombinatorika]] [[meter (musik)|meter]] bersesuaian dengan versi dasar dari [[teorema binomial]]. Karya Pingala juga berisi gagasan dasar tentang [[bilangan Fibonacci]] (yang disebut ''mātrāmeru'').<ref>Rachel W. Hall. [http://www.sju.edu/~rhall/mathforpoets.pdf Matematika bagi pujangga dan penabuh drum]. ''Math Horizons'' '''15''' (2008) 10-11.</ref>
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The ''[[Surya Siddhanta]]'' (c. 400) introduced the [[trigonometric functions]] of [[sine]], [[cosine]], and inverse sine, and laid down rules to determine the true motions of the luminaries, which conforms to their actual positions in the sky.<ref>http://www.westgatehouse.com/cycles.html Exegesis of Hindu Cosmological Time Cycles</ref> The cosmological time cycles explained in the text, which was copied from an earlier work, correspond to an average [[sidereal year]] of 365.2563627 days, which is only 1.4 seconds longer than the modern value of 365.25636305 days. This work was translated into to Arabic and Latin during the Middle Ages.
 
''[[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.
 
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