Perbezaan antara semakan "Aryabhata"

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=== Algebra ===
InDalam ''Aryabhatiya'' Aryabhata providedmemberikan eleganthasil resultsyang forelegan theuntuk summation ofpenjumlahan [[seriesurutan (mathematicsmatematik)|seriesurutan]] of squareskotak anddan cubeskubus:<ref>{{cite book|first=Carl B.| last=Boyer |authorlink=Carl Benjamin Boyer |title=A History of Mathematics |edition=Second |publisher=John Wiley & Sons, Inc. |year=1991 |isbn=0471543977 |page = 207 |chapter = The Mathematics of the Hindus |quote= "HeDia gavememberikan moreperaturan elegantyang ruleslebih forelegan theuntuk sumjumlah ofpetak thedan squareskubus andsegmen cubesawal ofbilangan anbulat initial segment of the positive integerspositif. TheBahagian sixthkeenam produk partdari oftiga thekuantiti productyang ofterdiri threedaripada quantitiesjumlah consisting of the number of termsistilah, thebilangan numberistilah of terms plusditambah onesatu, anddan twicedua thekali numberjumlah ofistilah termsditambah plussatu oneadalah isjumlah the sum of the squarespetak. TheKuadrat squaredari ofjumlah thesiri sumadalah of the series is the sum of thejumlah cubeskubus."}}</ref>
:<math>1^2 + 2^2 + \cdots + n^2 = {n(n + 1)(2n + 1) \over 6}</math>
dan
and
:<math>1^3 + 2^3 + \cdots + n^3 = (1 + 2 + \cdots + n)^2</math>
 
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