bhaaskar pratham ka jya sanniktan sootr

yeh lekh ek aadhaar hai. aap ise badhaakar vikipeediya ki sahaayata kar sakte hain. the va b

Bhaarat ke mahaan ganitjnya bhaaskar pratham ne apne 'mahaabhaaskareeya' naamak granth mein trikonamiteeya falan jya ya (Sin x) ka maan nikaalne ka ek parimeya vyanjak diya hai. yeh pata naheen hai ki bhaaskar ne yeh sanniktan sootr kaise nikaala hoga. kintu ganit ke anekon itihaasakaaron ne apne-apne anumaan lagaaye hain ki bhaaskar ne yeh sootr kis prakaar nikaala hoga. yeh sootr sundar evam sahaj hai tatha iske dvaara Sin x ka paryaapt shuddh maan praapt hota hai.

mahaabhaaskareeya mein aath adhyaaya hain. saatavein adhyaaya mein bhaaskar ne Sin x ka sannikt maan (approximate value) nikaalne ka nimnalikhit sootr diya hai-

${\displaystyle \sin x\approx {\frac {16x(\pi -x)}{5\pi ^{2}-4x(\pi -x)}},\qquad (0\leq x\leq {\frac {\pi }{2}})}$

is sootr ko unhone aaryabhatt dvaara diya hua bataaya hai. is sootr se praapt jya ya ke maanon ka aapekshik truti 1.9% se kam hai. (adhiktam vichlan ${\displaystyle {\frac {16}{5\pi }}-1\approx 1.859\%}$ jo ${\displaystyle x=0}$ par hota hai.)

• aaryabhat ki jya saarani
• maadhav ki jya saarani