aaryabhat ki jya saarani
aaryabhat dvaara rachit aaryabhateeya mein diye gaye 24 sankhyaaon ka samuchchaya aaryabhat ki jya-saarani (Āaaryabhaṭaaa's sine table) kahalaata hai. aadhunik arth mein yeh koi ganiteeya saarani (tebul) naheen hai jismein sankhyaaeain pankti va stambh ke roop mein vinyast (arranged) hon.[1][2]
paramparaagat arthon mein yeh trikonamiti mein prayukt jya falan (sine function) ke maanon ki soochi bhi naheen hai balki yeh jya falan ke maanon ke pratham antar (first differences) hai. isi liye ise 'aaryabhat ki jya-antar saarani (Āaaryabhaṭaaa's table of sine-differences) bhi kaha jaata hai.[3][4]
aaryabhat ki yeh saarani, ganit ke itihaas mein, vishv ki sabse pehle rachit jya-saarani hai.[5]
anukram
shlok ke roop mein jya-saarani
mool saarani
aaryabhateeya ka nimnaankit shlok hi aaryabhat ki jya-saarani ko niroopit karta hai:
makhi bhakhi fakhi dhakhi nakhi nyaakhi ङaakhi hasjh skaki kishg shghaki kighv .
ghlaki kigr hakya dhaki kich sg jhash ङav kl pt f chh kala-ardh-jyaas .
aadhunik niroopan
uparokt shlok koot roop mein hai. aaryabhateeya mein hi iski sahaayata se jya-maan nikaalne ki vidhi bhi bataayi gayi hai. is vidhi ka upayog karke jo maan praapt hote hain ve neeche ki saarani mein diye gaye hain.
kramaank | kon (A) (degree, aarkamint mein) |
aaryabhat ke sankhyaatmak niroopan ke roop mein maan |
aaryabhat ke sankhyaatmak niroopan ka (ISO 15919 lipyantaran) |
sankhya ke roop mein maan | jya (A) ka aaryabhat dvaara diya maan |
jya (A) ka aadhunik maan (3438 × sin (A) |
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2 |
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3 |
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5 |
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6 |
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7 |
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8 |
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9 |
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10 |
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11 |
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12 |
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13 |
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14 |
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15 |
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16 |
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17 |
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18 |
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19 |
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20 |
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21 |
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22 |
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23 |
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24 |
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aaryabhat ki ganana-vidhi
aaryabhateeya ke 'ganitpaad' naamak adhyaaya mein jya-saarani ki ganana ki vidhi bataayi gayi hai.
sandarbh
- ↑ Selin, Helaine, san (2008). Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures (2 san॰). Springer. pp. 986–988. aai॰aऍsa॰abee॰aऍna॰ 978-1-4020-4425-0.
- ↑ Eugene Clark (1930). The Āaryabhaṭaiya of Āaaryabhaṭaaa: An ancient Indian work on mathematics and astronomy. Chicago: The University of Chicago Press.
- ↑ Takao Hayashi, T (November 1997). "Āaaryabhaṭaaa's rule and table for sine-differences". Historia Mathematica 24 (4): 396–406. doi:10.1006/hmat.1997.2160.
- ↑ B. L. van der Waerden, B. L. (March 1988). "Reconstruction of a Greek table of chords". Archive for History of Exact Sciences (Berlin: Springer) 38 (1): 23–38. doi:10.1007/BF00329978.
- ↑ J J O'Connor and E F Robertson (June 1996). "The trigonometric functions". http://www-history.mcs.st-andrews.ac.uk/HistTopics/Trigonometric_functions.html. abhigman tithi: 4 March 2010.
inhein bhi dekhe
- maadhavaachaarya ki jya saarani
- bhaaskar pratham ka jya sanniktan sootr (Bhaskar I's Sine approximation formula)