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

↑ 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)