Difference between revisions 4795150 and 4795153 on mswiki

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[[Fail:2064 aryabhata-crp.jpg|thumb|300px|Arca Aryabhata di tapak [[Inter-University Centre for Astronomy and Astrophysics|IUCAA]], [[Pune]]. Dengan tiadanya maklumat diketahui mengenai rupawannya, apa-apa imej Aryabhata berasal dari konsepsi artis.]]
(contracted; show full)

A third text, which may have survived in the [[Arabic language|Arabic]] translation, is ''Al ntf'' or ''Al-nanf''. It claims that it is a translation by Aryabhata, but the Sanskrit name of this work is not known.   
Probably dating from the 9th century, it is mentioned by the Persian scholar and chronicler of India, [[Abū Rayhān al-Bīrūnī]].<ref name = Ansari/>

=== Aryabhatiya ===


Direct details of Aryabhata's work are therefore known only from the ''[[Aryabhatiya]]''.  
The name "Aryabhatiya" is due to later commentators. Aryabhata himself may not have given it a name. His disciple [[Bhaskara I]] calls it ''Ashmakatantra'' (or the treatise from the Ashmaka). It is also occasionally referred to as ''Arya-shatas-aShTa'' (literally, Aryabhata's 108), because there are 108 verses in the text. It is written in the very terse style typical of [[sutra]] literature, in which each line is an aid to memory for a complex system. Thus, the explication of meaning is due to commentators. The text consists of the 108 verses and 13 introductory verses, and is divided into four ''pāda''s or chapters: 

# ''Gitikapada'': (13 verses): large units of time—''kalpa'', ''manvantra'', and ''yuga''—which  present a cosmology different from earlier texts such as Lagadha's ''[[Vedanga Jyotisha]]''(ca. 1st century BCE). There is also a table of sines (''jya''), given in a single verse. The duration of the planetary revolutions during a ''mahayuga'' is given as 4.32 million years.
# ''Ganitapada'' (33 verses): covering mensuration (''kṣetra vyāvahāra''), arithmetic and geometric progressions, [[gnomon]] / shadows (''shanku''-''chhAyA''), simple, [[quadratic equations|quadratic]], [[simultaneous equations|simultaneous]], and [[diophantine equations|indeterminate]] equations (''kuTTaka'')
# ''Kalakriyapada'' (25 verses): different units of time and a method for  determining the positions of planets for a given day, calculations concerning the intercalary month (''adhikamAsa''), ''kShaya-tithi''s, and a seven-day week with names for the days of week. 
# ''Golapada'' (50 verses): Geometric/[[trigonometric]] aspects of the [[celestial sphere]], features of the [[ecliptic]], [[celestial equator]], node, shape of the earth, cause of day and night, rising of [[zodiacal sign]]s on horizon, etc. In addition, some versions cite a few [[colophon (publishing)|colophons]] added at the end, extolling the virtues of the work, etc. 

The Aryabhatiya presented a number of innovations in mathematics and astronomy in verse form, which were influential for many centuries. The extreme brevity of the text was elaborated in commentaries by his disciple [[Bhaskara I]] (''Bhashya'', ca. 600 CE) and by [[Nilakantha Somayaji]] in his ''Aryabhatiya Bhasya,'' (1465 CEOleh itu, perincian langsung karya Aryabhata hanya diketahui dari ''[[Aryabhatiya]]''.
Nama "Aryabhatiya" adalah kerana pengulas kemudian. Aryabhata sendiri mungkin tidak memberikan namanya. Muridnya [[Bhaskara I]] menyebutnya ''Ashmakatantra'' (atau risalah dari Ashmaka). Kadang-kadang juga disebut sebagai ''Arya-shatas-aShTa'' (secara harfiah, 108 Aryabhata), kerana ada 108 ayat dalam teks. Ini ditulis dalam gaya yang sangat tipikal khas dari sastra [[sutra]], di mana setiap baris adalah bantuan ingatan untuk sistem yang kompleks. Oleh itu, penjelasan makna adalah disebabkan oleh pengulas. Teks ini terdiri dari 108 ayat dan 13 ayat pengantar, dan dibahagikan kepada empat ''pāda'' atau bab:

# ''Gitikapada'': (13 ayat): unit waktu yang besar—''kalpa'', ''manvantra'', dan ''yuga''—yang menyajikan kosmologi yang berbeza dari teks sebelumnya seperti ''[[Vedanga Jyotisha]]'' Lagadha (sekitar abad ke-1 SM). Ada juga tabel sinus (''jya''), yang diberikan dalam satu ayat. Tempoh revolusi planet semasa ''mahayuga'' adalah 4.32 juta tahun.
# ''Ganitapada'' (33 ayat): meliputi mensurasi (''kṣetra vyāvahāra''), kemajuan aritmetik dan geometri, [[gnomon]] / bayang-bayang (''shanku''-''chhAyA''), sederhana, [[persamaan kuadratik|kuadratik]], [[persamaan serentak|serentak]], dan [[persamaan diophantine|tidak tentu]] persamaan (''kuTTaka'')
# ''Kalakriyapada'' (25 ayat): unit waktu dan kaedah yang berbeza untuk menentukan kedudukan planet untuk hari tertentu, perhitungan mengenai bulan interkala (''adhikamAsa''), ''kShaya-tithi'', dan seminggu tujuh hari dengan nama untuk hari dalam seminggu.
# ''Golapada'' (50 ayat): Aspek geometri / [[trigonometri]] dari [[cakerawala]], ciri-ciri [[ekliptik]], [[khatulistiwa cakerawala]], simpul, bentuk bumi, penyebab siang dan malam, kenaikan [[tanda zodiak]] di cakrawala, dll. Selain itu, beberapa versi memetik beberapa [[kolofon (penerbitan)|kolofon]] yang ditambahkan pada akhir, memuji kebajikan karya, dan lain-lain.

Aryabhatiya menyampaikan sejumlah inovasi dalam matematik dan astronomi dalam bentuk ayat, yang berpengaruh selama berabad-abad. Ringkas teks ini dijelaskan dalam ulasan oleh muridnya [[Bhaskara I]] (''Bhashya'', sekitar 600 M) dan oleh [[Nilakantha Somayaji]] dalam bukunya ''Aryabhatiya Bhasya,'' (1465 M).

== Matematik ==
=== Menempatkan sistem nilai dan kosong ===
Sistem [[place-value]], pertama kali dilihat pada abad ke-3 [[Manuskrip Bakhshali]], jelas terdapat dalam karyanya.<ref>P. Z. Ingerman, "Panini-Backus form," Communications of the ACM 10 (3)(1967), ms.137</ref> ; dia pasti tidak menggunakan simbol, tetapi ahli matematik Perancis [[Georges Ifrah]] berpendapat bahawa pengetahuan tentang sifar tersirat dalam sistem nilai tempat Aryabhata sebagai pemegang tempat untuk kekuatan(contracted; show full)
[[Kategori:Kelahiran 476]]
[[Kategori:Kematian 550]]
[[Kategori:Ahli matematik abad ke-5]]
[[Kategori:Ahli matematik abad ke-6]]
[[Kategori:Ahli astronomi India]]
[[Kategori:Ahli matematik India silam]]
[[Kategori:Ahli astronomi zaman pertengahan]]