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]

vrutt mein chaap (Arc) tatha jeeva (chord)

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)
1
03° 45′
makhi
makhi
225
225′
224.8560
2
07° 30′
bhakhi
bhakhi
224
449′
448.7490
3
11° 15′
fakhi
phakhi
222
671′
670.7205
4
15° 00′
dhakhi
dhakhi
219
890′
889.8199
5
18° 45′
nakhi
ṇaaakhi
215
1105′
1105.1089
6
22° 30′
nyaakhi
ñaakhi
210
1315′
1315.6656
7
26° 15′
ङaakhi
ṅaakhi
205
1520′
1520.5885
8
30° 00′
hasjh
hasjha
199
1719′
1719.0000
9
33° 45′
skaki
skaki
191
1910′
1910.0505
10
37° 30′
kishg
kiṣaaga
183
2093′
2092.9218
11
41° 15′
shghaki
śaaghaki
174
2267′
2266.8309
12
45° 00′
kighv
kighva
164
2431′
2431.0331
13
48° 45′
ghlaki
ghlaki
154
2585′
2584.8253
14
52° 30′
kigr
kigra
143
2728′
2727.5488
15
56° 15′
hakya
hakya
131
2859′
2858.5925
16
60° 00′
dhaki
dhaki
119
2978′
2977.3953
17
63° 45′
kich
kica
106
3084′
3083.4485
18
67° 30′
sg
sga
93
3177′
3176.2978
19
71° 15′
jhash
jhaśaaa
79
3256′
3255.5458
20
75° 00′
ङav
ṅaava
65
3321′
3320.8530
21
78° 45′
kl
kla
51
3372′
3371.9398
22
82° 30′
pt
pta
37
3409′
3408.5874
23
86° 15′
f
pha
22
3431′
3430.6390
24
90° 00′
chh
cha
7
3438′
3438.0000

aaryabhat ki ganana-vidhi

aaryabhateeya ke 'ganitpaad' naamak adhyaaya mein jya-saarani ki ganana ki vidhi bataayi gayi hai.

sandarbh

  1. 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.
  2. Eugene Clark (1930). The Āaryabhaṭaiya of Āaaryabhaṭaaa: An ancient Indian work on mathematics and astronomy. Chicago: The University of Chicago Press.
  3. 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.
  4. 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.
  5. 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