Page 8 - Bigyan Katha June 2021

8
Ryb 2021
wc_v‡Mvixq Îqx:
GKwUcwiμgv(w`Z¦ xqfvM)
f~cwZ PμeZ©x
msL¨v| MvwYwZKfv‡e Aek¨B ‡Kv‡bv mgm¨v ‡bB, Z‡e ‡gŠwjK wc_v‡Mvixq Îqx‡K ‡Zv Gfv‡e cv‡ev bv, KviY Avgiv e‡jwQ ‡h Zv‡`i m`m¨‡`i g‡a¨ ‡Kv‡bv mvaviY Drcv`K _vK‡e bv| A_P mK‡jB ‡Rvo msL¨v n‡q ‡M‡j Kgc‡ÿ 2 ‡Zv mvaviY Drcv`K wn‡m‡e Zv‡`i g‡a¨ ‡_‡K hv‡e| Avi ‡mRb¨B m`m¨‡`i ‡_‡K `wy U K‡i ‡Rvov wn‡m‡e ‡e‡Q wb‡j ‡mB msL¨v¸wj‡ZI cvIqv hv‡e mvaviY Drcv`K Ges Zviv ci¯ú‡ii mv‡c‡ÿ ‡gŠwjK _vK‡e bv| ZvB Gfv‡e mvaviY wc_v‡Mvixq Îqx wbðqB cvIqv ‡h‡Z cv‡i, ‡gŠwjK Îqx bq| Avgiv GB Av‡jvPbvq c‡i we¯ÍZ... fv‡e Avm‡ev|
GKUzjÿKi‡j‡`Lvhv‡e‡h,Zjz bvq ‡QvU ALÛ msL¨v w`‡q ‰Zwi ‡hme ‡gŠwjK wc_v‡Mvixq Îqxi m‡1⁄2 Avgiv ‡ewk cwiwPZ Zv‡`i m`m¨‡`i hw` ‡Rvo ev we‡Rvo ‡h ‡Kv‡bv msL¨v w`‡q ¸Y Kwi Zvn‡j Avgiv wZbwU bZbz msL¨v ‡c‡q hve, hviv wc_v‡Mvixq Îqx MVb Ki‡e| welqUv GKUv D`vni‡Yi mvnv‡h¨ ‡evSvi ‡Póv Kiv hvK| Avgiv ‡`‡LwQ (3, 4, 5) GKwU ‡gŠwjK wc_v‡Mvixq Îqx| Gi cwÖ ZwU m`m¨‡K hw` 10 (`k) w`‡q ¸Y Kiv hvq Zvn‡j Kx cvIqv hv‡e? Avgiv cv‡ev (30, 40, 50) GiKg wZbwU ALÛ msL¨v| G‡`i wb‡q GKwU mg‡KvYx wÎfRz Aek¨B MVb Kiv m¤¢e| Zvn‡j (30, 40, 50) Gi GB `jwU‡K
mv
aviYfv‡e ‡gŠwjK wc_v‡Mvixq Îqx‡`i ‰ewkó¨ wb‡q K_v
ejvi Rb¨ Avgiv wd‡i hv‡ev wc_v‡Mvixq m¤úK© A_©vr a2 + b2 = c2 Gi Kv‡Q| GB m¤úK©wUi g‡a¨ w`‡q hy3 a, b
Ges c i cÖwZwU‡K hLb ALÛ msL¨v wn‡m‡e ‡c‡Z PvBwQ ZLb K‡qKwU wel‡qi w`‡K `„wó w`‡Z n‡e|
cÖ_gZ, a, b Ges c Gi cÖ‡Z¨KwU msL¨v we‡Rvo n‡Z cv‡i bv| KviY, ‡m‡ÿ‡Î a2 Ges b2 Df‡qB we‡Rvo n‡e Ges Zv‡`i mgwó, A_©vr (a2 + b2) n‡e ‡Rvo msL¨v| wKš‘ c hw` we‡Rvo nq Zvn‡j c2 I n‡e we‡Rvo| Zvn‡j wK `vuov‡jv? wc_v‡Mvixq m¤ú‡K©i evu w`K n‡q ‡M‡jv ‡Rvo msL¨v Avi Wvbw`K n‡q ‡M‡jv we‡Rvo msL¨v! Avgiv Rvwb GKwU mgvb wP‡ýi `ycv‡k _vKv msL¨v‡`i ‡ÿ‡Î GgbUv nIqv m¤¢e bq| ZvB mg‡KvYx wÎfz‡Ri wZbwU evû hLb ALÛ ivwk w`‡q cÖKvwkZ n‡”Q ZLb Zvi cÖ‡Z¨KwU A_©vr a, b Ges c Gi mK‡jB we‡Rvo ivwk n‡Z cv‡i bv|
wØZxqZ, a, b Ges c Gi c‡Ö Z¨KwU wK ‡Rvo msL¨v n‡Z cv‡i? n¨vu GUv m¤¢e| KviY, ‡hhwy3iwfwˇZ‡_‡KAvgivwZbwUevû we‡Rvo nIqvi m¤¢vebv LvwiR K‡i w`‡qwQ ZvGLv‡bLvU‡Qbv|ZvBa,bGescGi mK‡jB ‡Rvo msL¨v n‡j a2 Ges b2 Df‡qB n‡e ‡Rvo msL¨v Ges Zv‡`i mgwó, A_v© r
(a2 + b2) I n‡e ‡Rvo msL¨v| Avi c ‡Rvo msL¨v nIqvi mey v‡` c2 I n‡e ‡Rvo| mZy ivs G‡ÿ‡Î mgvb wP‡ýi `Õy cv‡kB _vK‡e ‡Rvo
Avgiv Aek¨B wc_v‡Mvixq Îqx ej‡Z cvwi, Z‡e Zv ‡gŠwjK Îqx n‡”Q bv|
Avgiv Ic‡ii D`vni‡Y ‡Rvo msL¨v w`‡q ¸Y K‡iwQ wVKB, wKš‘ GKwU wc_v‡Mvixq Îqxi meKÕwU m`m¨‡K ‡Kv‡bv we‡Rvo msL¨v w`‡q ¸Y Ki‡j GKB AwfÁZv Avgv‡`i n‡e| A_©vr IB (3, 4, 5) Îqx‡K aiv hvK, 9 w`‡q ¸Y Kiv n‡jv, cvIqv ‡Mj GK bZzb Îqx; (27, 36, 45)| GLv‡b cÖwZwU m`m¨ wKš‘ ‡Rvo msL¨v nÕj bv| Zey GB bZzb Îqx wK (3, 4, 5)-Gi gZ GKB ‡kÖwYi? bv bq; KviY (30, 40, 50) ev (27, 36, 45) Gi Df‡qi m`m¨‡`i g‡a¨ i‡q‡Q mvaviY Drcv`K (hv Aek¨B 1 Gi
m`„k wÎfzR D ABC Ges D DEF
m`„k mg‡KvYx wÎfzR D PQR Ges D LMN