Perbezaan antara semakan "Aryabhata"

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=== Pi sebagai tidak rasional ===
 
Aryabhata workedmengerjakan onpendekatan the approximation foruntuk [[Pi]] (<math>\pi</math>), anddan maymungkin havesampai comepada tokesimpulan the conclusion thatbahawa <math>\pi</math> istidak irrationalrasional. InDi thebahagian second part of thekedua ''Aryabhatiyam'' ({{IAST|gaṇitapāda}} 10), hedia writesmenulis:
<blockquote>
''{{IAST|chaturadhikam śatamaśṭaguṇam dvāśaśṭistathā sahasrāṇām}} <br />
''{{IAST|Ayutadvayaviśkambhasyāsanno vrîttapariṇahaḥ.''}}<br />
"AddTambahkan fourempat tohingga 100, multiplykalikan bydengan eightlapan, anddan thenkemudian addtambah 62,000. ByDengan thisperaturan ruleini, thelilitan circumferencebulatan of a circle with adengan diameter of 20,000 can bedapat approacheddidekati."
</blockquote>
ThisIni impliesmenunjukkan thatbahawa thenisbah ratiolilitan of the circumference to theke diameter isadalah (([4+100)]×8+62000)/20000 = 3.1416, which isyang accuratetepat tountuk fivelima [[significantangka figurespenting]].
 
ItDiperkirakan is speculated thatbahwa Aryabhata used themenggunakan wordkata ''āsanna'' (approachingmendekati), tountuk meanbermaksud thatbahwa notini onlybukan ishanya thispendekatan antetapi approximationjuga butnilainya thattidak thedapat value is incommensurabledibandingkan (oratau [[irrationaltidak rasional]]). IfSekiranya thisini is correctbetul, itini isadalah quitewawasan ayang sophisticatedcukup insightcanggih, because the irrationalitykerana ofrasionalitas pi wasdibuktikan proveddi inEropah Europehanya onlypada intahun 1761 byoleh [[Johann Heinrich Lambert|Lambert]]).<ref>
{{cite book
| author = S. Balachandra Rao
}}</ref>
 
AfterSelepas Aryabhatiya wasditerjemahkan translatedke intodalam [[Arabicbahasa language|ArabicArab]] (ca.sekitar 820 CEM)
thispendekatan approximationini wasdisebut mentioneddalam inbuku [[Al-Khwarizmi]]'s bookmengenai on algebraaljabar.<ref name = Ansari/>
 
=== Mensurasi dan trigonometri ===
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