brahmagupt

brahmagupt

janm 598 CE
mrutyoo c.670 CE
kshetr ganitjnya,
prasiddh kaarya shoonya
brahmagupt ka prameya, iske anusaar AF = FD.

brahmagupt (598-668) prasiddh bhaarateeya ganitjnya the. ve tatkaaleen gurjar pradesh (bheenamaal) ke antargat aane vaale prakhyaat shahar ujjain (vartamaan madhya pradesh) ki antariksh prayogashaala ke pramukh the aur is dauraan unhone do vishesh granth likhe: braahmasfutasiddhaant (san 628 mein) aur khandakhaadyak ya khandakhaadyapaddhati (san 665 E mein).

ye achhe vedhakarta the aur inhonne vedhon ke anukool bhaganon ki kalpana ki hai. prasiddh ganitjnya jyotishi, bhaaskaraachaarya, ne apne siddhaant ko aadhaar maana hai aur bahut sthaanon par inki vidvatta ki prashansa ki hai. madhyakaaleen yaatri alabarooni ne bhi brahmagupt ka ullekh kiya hai.

anukram

jeevan parichay

brahmagupt Abu parvat tatha luni nadi ke beech sthit, bheenamaal naamak gram ke nivaasi the. inke pita ka naam jishnu tha. inka janm shak sanvat 520 mein hua tha. inhonne praacheen brahmapitaamahasiddhaant ke aadhaar par braahmasfutasiddhaant tatha khandakhaadyak naamak karan granth likhe, jinka anuvaad arabi bhaasha mein, anumaanat: khaleefa mansoor ke samay, sindahind aur al akarand ke naam se hua. inka ek anya granth 'dhyaanagrahopadesh' naam ka bhi hai. in granthon ke kuchh parinaamon ka vishvaganit mein apoorv sthaan hai.

aachaarya brahmagupt ka janm Rajasthan raajya ke bheenamaal shahar me isvi san 598 me hua tha. isi kaaran unhein ' bhillamaalaaaachaarya ' ke naam se bhi kai jagah ullekhit kiya gaya hai. yeh shahar tatkaaleen Gujarat pradesh ki rajdhani tatha harshavardhan saamraajya ke raaja vyaaghramukh ke samakaaleen maana jaata hai.

ganiteeya kaarya

'brahmasfutasiddhaant' unka sabse pehla granth maana jaata hai jismein shoonya ka ek alag ank ke roop mein ullekh kiya gaya hai. yahi naheen, balki is granth mein rinaatmak (negative) ankon aur shoonya par ganit karne ke sabhi niyamon ka varnan bhi kiya gaya hai. ye niyam aaj ki samajh ke bahut kareeb hain. haaain, ek antar avashya hai ki brahmagupt shoonya se bhaag karne ka niyam sahi naheen de paaye: 0/0 = 0.

"brahmasfutasiddhaant" ke saadhe chaar adhyaaya moolabhoot ganit ko samarpit hain. 12vaan adhyaaya, ganit, ankaganiteeya shrunkhalaaon tatha jyaamiti ke baare mein hai. 18vein adhyaaya, kuttak (beejaganit) mein aaryabhatt ke raikhik anirdhaarya sameekaran (linear indeterminate equation, equations of the form ax − by = c) ke hal ki vidhi ki charcha hai. (beejaganit ke jis prakaran mein anirdhaarya sameekaranon ka adhyayan kiya jaata hai, usaka puraana naam 'kuttak' hai. brahmagupt ne ukt prakaran ke naam par hi is vigyaan ka naam san 628 E. mein 'kuttak ganit' rakha.)[1] brahmagupt ne dvighaateeya anirdhaarya sameekaranon (Nx2 + 1 = y2) ke hal ki vidhi bhi khoj nikaali. inki vidhi ka naam chakravaal vidhi hai. ganit ke siddhaanton ka jyotish mein prayog karne wala vah pratham vyakti tha. unke braahmasfutasiddhaant ke dvaara hi arabon ko bhaarateeya jyotish ka pata laga. abbaasid khleefa al-mansoor (712-775 isvi) ne bagdaad ki sthaapana ki aur ise shiksha ke kendra ke roop mein viksit kiya. usane ujjain ke kank: ko aamantrit kiya jisne braahmasfutasiddhaant ke sahaare bhaarateeya jyotish ki vyaakhya ki. abbaasid ke aadesh par al-fjri ne iska arabi bhaasha mein anuvaad kiya.

brahmagupt ne kisi vrutt ke kshetrafal ko uske samaan kshetrafal vaale varg se sthaanaantarit karne ka bhi yatn kiya.

brahmagupt ne pruthvi ki paridhi gyaat ki thi, jo aadhunik maan ke nikat hai.

brahmagupt pai (pi) (3.14159265) ka maan 10 ke vargamool (3.16227766) ke baraabar maana.

brahmagupt anaavart vitt bhinnon ke siddhaant se parichit the. inhonne ek ghaateeya anirdhaarya sameekaran ka poornaakon mein vyaapak hal diya, jo aadhunik pustakon mein isi roop mein paaya jaata hai aur anirdhaarya varg sameekaran, K y2 + 1 = x2, ko bhi hal karne ka prayatn kiya.

brahmagupt ka sootr

sandarbh ke liye chitr

brahmagupt ka sabse mahatvapoorn yogadaan chakreeya chaturbhuj par hai. unhone bataaya ki chakreeya chaturbhuj ke vikrn paraspar lambavat hote hain. brahmagupt ne chakreeya chaturbhuj ke kshetrafal nikaalne ka sannikt sootr (approximate formula) tatha yathaatath sootr (exact formula) bhi diya hai.

chakreeya chaturbhuj ke kshetrafal ka sannikt sootr:


chakreeya chaturbhuj ke kshetrafal ka yathaatath sootr:

jahaaain t = chakreeya chaturbhuj ka ardhaparimaap tatha p, q, r, s usaki bhujaaon ki naap hai. heron ka sootr, jo ek tribhuj ke kshetrafal nikaalne ka sootr hai, iska ek vishisht roop hai.

yeh bhi dekhein

baahari kadiyaaain

sandarbh

  1. "vaidik beejaganit" (peeechapi). bhaarateeya saahitya sangrah. http://pustak.org/bs/home.php?bookid=2558. abhigman tithi: 2008.