mahaveera (ganithashaasthranjan)

onpathaam noottaandil indiayile mysooril janicha oru jaina ganithashaasthranjanaayirunnu mahaveera (athawa mahaveerachaarya, "mahaveera guru"). addeham eiii. dii. 850-ll ganithashaasthrathinte saaramshathekkurichulla "gaanita-saara-samghra" ("gaanita saara samghra") allengil samahaaram rachichu. raashtrakooda rajaavaaya amoghavarsha addehathe samrakshichu. addeham jyothishathe ganithathil ninnu verthirichu. poornnamaayum ganithashaasthrathinaayi samarppichirikkunna aadyakaala indian grandhamaanithu. aryabhattanum brahmaguptan vaadicha athe vishayangalekkurich addeham vishadeekarichuvenkilum avaa kooduthal vyakthamaayi prakadippichu. beejaganithathodulla valare samanvayippicha sameepanamaan addehathinte kruthi, addehathinte vaachakathil bhooribhaagavum oonnal nalkunnathu beejaganita prasnangal pariharikkunnathin aavashyamaaya saankethikavidyakal vikasippikkunnathilaan. samabahu, samadvibahu trikonam, rombus, vritham, ardhavritham thudangiya aashayangalkk padavali sthaapichathinaal addeham indian ganithashaasthranjarkkidayil valareyadhikam bahumaanikkappedunnu. mahaaveerante shreshtatha dakshinenthyayiludaneelam vyaapichu, addehathinte pusthakangal dakshinenthyayile mattu ganithashaasthranjarkku prachodanamaayi. pavuluri mallana ithu telung bhaashayilekku "saara sanghraha gaanitamu" ennu vivarthanam cheythu.
a" 3 = "a" ("a" + "b") ("a" − "b") + "b" 2 ("a" − "b") + "b" 3 polulla beejaganita identittikal addeham kandethi. "n" c "r" ennathinte soothravaakyam ["n" ("n" −1) ("n" −2) ennum addeham kandethi... ("n" − "r" + 1)]/["r" ("r" −1) ("r" −2)... 2 * 1]. deerghavrithangalude vistheernavum chuttalavum ekadeshamaayi kanakkaakkunna oru soothravaakyam addeham aavishkarikkukayum oru samkhyayude chathuravum oru samkhyayude ghanamoolangalum kanakkakkaanulla reethikal kandethukayum cheythu. oru negatteevu samkhyayude varggamoolamillennu addeham urappichu paranju.
bhinnasamkhyakal vighadippikkunnathinulla niyamangal.
mahaaveerante 'gaanita-saara-samgha' thil oru bhinnasamkhyaye ekasamkhya bhinnasamkhyakalude aakethukayaayi prakadippikkunnathinula chittayaya niyamangal nalkiyittundu. vaidika kaalaghattatthil indian ganithashaasthrathil yoonit bhinnasamkhyakalude upayogavum soothravaakyam _ 1 nuu thulyamaaya ekadesha kanakk nalkunna sulba soothrangalum pinthudarunnu.
ganitha-chaara-samgharshathil (jii. ezz. ezz), ganithashaasthrathekkurishulla adhyaayathinte randaam bhaagathinu "kalaa-savarna-vyavahara" (littu. "bhinnasamkhyakalude kuravinte pravartthanam"). ithil, "bhagajathi" vibhaagam (vaakyangal 55-98) inipparayunna niyamangal nalkunnu
pathinalam noottaandil naaraayanante "gaanita-kaumudi" yill chila niyamangal koodi nalkiyittundu.

