Page 4 - Bigyan Katha Mar 21

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gv©P 2021
wc_v‡Mvivm, Av‡j·RvÛvi MÖvnvg ‡ej
Ges GK gvwK©b ‡cÖwm‡W›U
f~cwZ PμeZ©x
G‡Kev‡i we`¨vjq ¯Í‡ii Qv·`i Kv‡Q MxÖKMwYZÁwc_v‡Mvivm(Avbgy vwbK 570 Ló„ ce~ v©ã Ñ 495 Ló„ ce~ v©ã) cwiwPZ
Zvi weL¨vZ Dccv‡`¨i Rb¨| GKwU mg‡KvYx wÎf‡y Ri AwZf‡y Ri eM,© Zvi evwK `wy U evûi IciKvie‡Mi© mgwóimgvb;GBDccv‡`¨i weew„ ZwU GKw`‡K ‡hgb eoB ‡Pbv Ab¨w`‡K Zvi c‡Ö qvMI jÿ Kiv hvq ev¯Íe Rxe‡b| BwZnvmMZ fv‡e Avgiv Rvwb ‡h wc_v‡Mvivm GB Dccv`¨ c¯Ö Íve Kivi Av‡M ‡_‡KB e¨vwej‡bi evwm›`viv Zvi c‡Ö qvM Rvb‡Zb Ges wgk‡ii wcivwgW M‡o Zjz ‡Z mvnvh¨ ‡bIqv n‡qwQj GB Dccv‡`¨ ewYZ© wÎf‡y Ri| Z‡e GUv ¯x^ KZ... n‡q‡Q ‡h wc_v‡MvivmB mg‡KvYx wÎf‡y Ri GB we‡kl agw© U G‡Kev‡i R¨vwgwZi wbqg ‡g‡b c_Ö g cwÖ Zôv K‡ib| cieZx© Kv‡j ‡`Lv ‡Mj ‡h Dccv`¨wU cgÖ v‡Yi Rb¨ wc_v‡Mviv‡mi c×wZB GKgvÎ c_ bq| D‡V Avm‡Z jvM‡jv bvbv weKí cgÖ vY| jÿ Kiv ‡Mj ‡h GB bZby cgÖ vY¸‡”Qi A‡bK¸wjB mswÿß Ges R¨vwgwZK hwy 3web¨v‡m AZ¨šÍ FRy I mvejxj|
eZg© v‡b wewfbœ Dcv‡q wc_v‡Mviv‡mi Dccv`¨ cgÖ v‡Yi msL¨v cvÖ q ‡cŠ‡Y PviÕk
ev 375 Q‡uy q‡Q| GB cgÖ vY¸wji g‡a¨ wKQy G‡Kev‡i ïiæ ‡_‡K ‡kl chš© Í P‡j‡Q wbR¯^ iv¯Ívq Avi wKQy cgÖ vY GKwU RvqMv ‡_‡K hvÎv ïiæ K‡i LvwbKUv c_ ¯v^ axb fv‡e AwZμg
K i v i c ‡ i A b ¨ ‡ K v ‡ b v c gÖ v ‡ Y i c _ a ‡ i MšÍ‡e¨ ‡cŠ‡u Q‡Q| fviZxq MwYZwe‡`iv GB wel‡q Zv‡`i cÁÖ vi Qvc ‡i‡L‡Qb| Avgiv eis c_Ö ‡g GKevi ‡`‡L wbB Kxfv‡e AšÍZ GKwU cgÖ vY fviZel© ‡_‡K cvIqv wM‡qwQj|
fviZe‡l© MwYZwe` wn‡m‡e `yÕRb fv¯‹ivPv‡h©i bvg cvIqv hvq| cÖ_gRb wQ‡jb Lax÷xq mßg kZvãxi gvbyl, Bwb fv¯‹ivPvh©-GK (I) bv‡g cwiwPZ| Ab¨Rb fv¯‹ivPvh©-`yB (II) Øv`k kZvãx‡Z wc_v‡Mviv‡mi Dccv‡`¨i GKwU Lye mnR I PgrKvi GKwU cÖgvY Dc¯’vcbv K‡ib| cÖgvYwU GB Kvi‡Y Abb¨ ‡h R¨vwgwZi cÖvq ‡Kv‡bv we‡kl Ávb QvovB cÖgvYwU ‡evSv m¤¢e| fv¯‹ivPvh©-`yB (II) GB cÖgv‡Yi Rb¨ c‡ii Kjv‡gi wPÎwUi mvnvh¨ wb‡qwQ‡jb|
GB wP‡Î ‡`Lv hv‡”Q ‡h PviwU mem© g
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IB eMv© Kvi AÂjwUi cwÖ ZwU evû (b Ñ a) i mgvb| Gi A_© n‡”Q
gvSLv‡bi XvKv bv cov
AÂjwU ‡Kej eMv© Kw... ZB bq,
Z v i c w Ö Z w U e v û ( b Ñ a ) | AZGe GB ‡QvU eM‡© ÿÎwUi ‡ÿÎdj (b Ñ a)2 ev (b2 + a2 Ñ 2ab)|
‡h PviwU me©mg wÎfyR
ILv‡b i‡q‡Q Zv‡`i
cÖ‡Z¨‡Ki evû`ywU n‡”Q a
Ges b Avi c n‡”Q cÖ‡Z¨K
wÎfy‡Ri AwZfyR| ZvB
cÖwZwU wÎfy‡Ri ‡ÿÎdj
`vuov‡e [1/2 (a.b)]; Avi
Zvn‡j PviwU wÎfy‡Ri ‡gvU ‡ÿÎdj nj 4. [1/2 (a.b)] = 2 a.b| AZGe
c2 = (b Ñ a)2 + 4[1/2 (a.b)] = (b2 + a2 Ñ 2ab) + 2a.b = a2 + b2
Gfv‡e wc_v‡Mviv‡mi Dccv`¨wU cgÖ vY K‡ib fv¯‹ivPvh-© `By (II)| GB cgÖ vYwU‡K
A‡b‡K `w„ óMvÖ n¨ cgÖ vY wn‡m‡e wPwýZ K‡ib KviY ‡KejgvÎ ‡Pv‡L ‡`‡LB GwU ‡evSv m¤¢e|
Ab¨w`‡K `w... ó ‡divB| `:y ‡Li K_v, wewfbœ mg‡qgvwKb© h3y iv‡óia PviRb‡cwÖm‡W›U ÿgZvq _vKvKvjxb AvZZvqxi e‡y j‡U cvÖ Y nvivb| Dbwesk kZ‡K Aveva nvg wjsKb I wesk kZvãx‡Z Rb Gd ‡K‡bwW GB ZvwjKvq ‡ewk cwiwPZ bvg| G Qvov `fy v© M¨RbK GBZvjKvqi‡q‡Qb‡cwÖm‡W›UDBwjqvg g¨vKwKb‡jI‡cwÖm‡W›U‡RgmAvevanvg Mviwdì|AviGB‡cwÖm‡W›UMviwd‡ìibvg m¤¢eZ mvaviY gvwKb© bvMwi‡Ki ‡_‡K A‡bK ‡ewk g‡b ‡i‡L‡Qb MwYZ I weÁv‡bi Qv‡Îiv, hw`I wZwb wQ‡jb gj~ Z AvBb we‡klÁ|
‡cÖwm‡W›U Mviwdì wc_v‡Mviv‡mi Dccv‡`¨i GKwU m¤ú~Y© ¯^vaxb cÖgvY Dc¯’vcbv K‡ib 1876 mv‡j| wZwb Aek¨ ZLb ‡cÖwm‡W›U bb; wZwb Inv‡qv ‡_‡K wbe©vwPZ GK Ks‡MÖmg¨vb| IB eQi Ô`¨ wbD Bsj¨vÛ Rvb©vj Ae GWy‡KkvbÕ bv‡gi mycwiwPZ M‡elYv cwÎKvq cÖKvwkZ wbe‡Ü wZwb GB cÖgvYwU Dc¯’vcbv K‡ib| eZ©gv‡b IB M‡elYv cwÎKvi bvg ms‡ÿwcZ n‡q `vuwo‡q‡Q ÔRvb©vj Ae& GWy‡KkvbÕ| bx‡Pi wP‡Î GB cÖgvY mswÿß AvKv‡i ‡`Iqv nj| Aek¨ cÖgvYwU Ggwb‡ZB Lye ‡QvÆ|
e¯ÍyZ ‡cÖwm‡W›U Mviwdì AvR ch©šÍ GKgvÎ gvwK©b ivóacwZ whwb ‡Kv‡bv MvwYwZK wel‡q M‡elYvcÎ cÖKvk K‡i‡Qb| Avi wc_v‡Mviv‡mi Dccv‡`¨i GB cÖgvYwU wPwýZ n‡q Av‡Q Zvi bv‡g Mviwd‡ìi cÖgvY ev ‡cÖwm‡W‡›Ui cÖgvY bv‡g|