Page 5 - Bigyan Katha Mar 21

Z‡e ‡Kej MwYZ bq weÁv‡bi Avi GKwU kvLvi m‡1⁄2 GB ‡cÖwm‡W‡›Ui bvg wKQyUv c‡ivÿfv‡e Rwo‡q i‡q‡Q| cÂvk eQi eqmx weskwZZg gvwK©b ‡cÖwm‡W›U Mviwdì 1881 mv‡j Zvi Kvh©fvi MÖnY Kivi gvÎ cvuP gvm c‡i AvZZvqxi e›`y‡Ki ¸wj‡Z ¸iæZifv‡e AvnZ nb| Zvi kix‡i ¯’vb K‡i ‡bIqv `ywU ey‡j‡Ui g‡a¨ GKwU wPwKrm‡Kiv Lye ZvovZvwo evi Ki‡Z cvi‡jI Ab¨wUi mwVK Ae¯’vb wbY©q Kiv m¤¢e nq wb| cÖvq `ygvm a‡i GB bvbv cÖ‡Póv Pvwj‡qI mdj nbwb Wv3v‡iiv| Gi c‡i ‡cÖwm‡W‡›Ui Ae¯’v μgk Lvivc n‡Z _v‡K Ges ¸wjwe× nIqvi `ygvm ev‡` wZwb cÖqvZ nb|
‡Rgm Aveavnvg Mviwd‡ìi kix‡i IB ey‡j‡Ui Ae¯’vb wbY©q KivB wQj wPwKrmK‡`i Kv‡Q wQj hv‡K ejv hvq
P¨v‡jÄ| g‡b ivL‡Z n‡e, mgqUv Dbwesk kZvãxi Av‡Ui `kK Ges G· iwk¥i Avwe®‹vi ZLbI fwel¨‡Zi M‡f©| ZvB GKUv mg‡q ‡cÖwm‡W‡›Ui kix‡ii ey‡j‡Ui Ae¯’vb wbY©‡qi Rb¨ WvK coj Ggb GKR‡bi whwb wPwKrmK bb eis Zvi
wKQyUv cwiwPwZ i‡q‡Q GKRb cÖhyw3we` I Avwe®‹Z©v wn‡m‡e| ‡kvbv ‡Mj wZwb ZLb GKwU hš¿ DTM¢vebv K‡i‡Qb ‡h h‡š¿i mvnv‡h¨ ‡Kv‡bviKg KvuUv‡Qov bv K‡iI kix‡ii g‡a¨ emZ Kiv avZe e¯Íyi mwVK Ae¯’vb wbY©q Kiv m¤¢e| cï‡`i kix‡i bvbv Kvi‡Y avZzLÛ cÖ‡ek K‡i Ae¯’vb K‡i| GB hš¿ Zv ai‡Z mÿg n‡q‡Q|
Av‡j·RvÛviMvÖnvg‡ejZLbm`¨ Avwe®‹vi K‡i‡Qb ‡Uwj‡dvb ev AvR‡Ki cwifvlvq j¨vÛjvBb| GKB bxwZi Ici wfwË K‡i GK ‡gUvj wW‡U±vi wWRvBb K‡i wZwb
gv©P 2021 5 ZLb ‡Póv Ki‡Qb Zv‡K AviI KvhK© ix K‡i
‡Zvjvi| GB hš¿wU‡Z wQj `wy U Zv‡ii KÛz jx ev K‡qj| GKwU K‡q‡ji g‡a¨ w`‡q we`¨ry ceÖ vn Pj‡Z _vK‡j Aci K‡q‡j jvMv‡bv ‡nW‡dv‡b ZLbB ‡Kv‡bv kã aiv co‡e hLb c_Ö g K‡q‡ji g‡a¨ we`¨ry ceÖ v‡ni cwieZb© NU‡e| GB cwieZb© NU‡Z cv‡i hw` K‡q‡ji ga¨eZx© A‡j Dcw¯’Z Dcv`vb e`‡j
hvq, ‡hgb ‡mLv‡b kix‡ii Askwe‡k‡li RvqMvq G‡m hw` ‡mLv‡b nvwRi nq ‡Kv‡bv avZiy UKz ‡iv|‡hbxwZiIciwfwËK‡i hš¿wU‡K wWRvBb Kiv n‡qwQj Zv‡K AvR‡Ki cwifvlvq BbWvKkvb e¨v‡jÝ ejv hvq| GLb Avgiv Rvwb ‡h c‡y iv e¨vcviUv `vwu o‡q Av‡Q `wyUK‡q‡jig‡a¨‡PŠ¤K^ dv¬‡·i‡gje܇bi Ici| Avi gv‡S ‡Kv‡bv avZLz Û P‡j G‡j e¨vNvZ NU‡e ‡mB ‡gje܇bi, ‰Zwi n‡e
mßg c„ôvq `Öóe¨|
Z„Zxq c„ôvi ci...
wZb As‡Ki PviwU ¯^KvgR msL¨v 153, 370, 371, 407-Gi m‡1⁄2 Avgv‡`i cwiPq n‡q ‡M‡Q|
Pvi As‡Ki ¯^KvgR msL¨vi msL¨v wZb|
1634 = 1 + 1296 + 81 + 256 = 14 + 64 + 34 + 44 8208 = 4096 + 16 + 0 + 4096 = 84 + 24 + 04 + 84 9474 = 6561 + 256 + 2401 + 256 = 94 + 44 + 74 + 44 cvuP As‡Ki ¯^KvgR msL¨v wZbwUÑ 54748, 92727, 93084
ÑDrmvnx cvVK wbðq ciL K‡i ‡b‡eb|
Gfv‡e ‡`Lv hv‡e `k-g~‡ji ‡gvU 88wU ¯^KvgR msL¨v Av‡Q|
e„nËg msL¨vwU 39 As‡KiÑ 115,132,219,018,736,992,565,095,597,973,971,522,401 1 ‡_‡K 39-Gi g‡a¨ me As‡Ki ¯^KvgR msL¨v ‡bB| ‡hgb, Ô2Õ,
Ô12Õ, Ô13Õ, Ô15Õ, Ô18Õ, Ô22Õ, Ô26Õ, Ô28Õ, Ô30Õ, Ô36Õ As‡Ki ‡Kv‡bv ¯^KvgR msL¨v ‡bB| Gevi ‡Kv‡bv ‡Kv‡bv As‡Ki GKvwaK ¯^KvgR msL¨v i‡q‡Q| Gi g‡a¨ D‡jøL‡hvM¨ n‡jv Ô23Õ, Ô25Õ Ges Ô27Õ| wZb‡U ‡ÿ‡ÎB cvuPwU K‡i ¯^KvgR msL¨v Av‡Q|
Ô23Õ -As‡Ki ¯^KvgR msL¨v: 218,876,968,411,229,162,888,58 278,796,948,930,540,744,714,05 279,078,650,099,770,525,678,14 283,612,813,213,192,294,633,98 354,525,901,040,316,919,359,43 Ô25Õ-As‡Ki ¯^KvgR msL¨v: 155,047,533,421,450,153,908,889,4 155,324,216,289,377,185,066,937,8 370,690,799,595,547,598,864,438,0 370,690,799,595,547,598,864,438,1 442,209,511,809,589,961,945,793,8 Ô27Õ-As‡Ki ¯^KvgR msL¨v: 121,204,998,563,613,372,405,438,066 121,270,696,006,801,314,328,439,376 128,851,798,696,487,777,842,012,787
174,650,464,499,531,377,631,639,254 177,265,453,171,792,792,366,489,765
¯^KvgR msL¨vi wel‡q we‡klfv‡e D‡jøL‡hvM¨ n‡jv ‡h‡Kv‡bv
GKwU As‡Ki GKwU ¯^KvgR msL¨v 0 w`‡q ‡kl n‡j Zvi c‡ii msL¨vwUI ¯^KvgR n‡e| ‡hgb wZb As‡Ki ‡ÿ‡Î Ô370Õ I Ô371Õ| Gi KviY wbZvšÍB my¯úó| Ô1Õ-‡K ‡h‡Kv‡bv Nv‡Z DbœxZ Ki‡j djvdj Ô1Õ-B nq| GB cÖm‡1⁄2 Ô25Õ As‡Ki Z...Zxq I PZy_© msL¨v`ywU jÿYxq| GQvov Ô39Õ As‡Ki e„nËg ¯^KvgR msL¨vi ‡kl AsK Ô1Õ, AZGe Zvi wVK Av‡Mi msL¨vwU, hvi ‡kl AsK Ô0Õ, ¯^KvgR|
‡kl Kivi Av‡M K‡qKwU g‡bviÄK msL¨vNwUZ AcwieZ©bkxj (Digital Invariant)-Gi D`vniY ‡ck KiwQ| msL¨v¸wj wbixÿY Ki‡j ‡evSv hv‡e, Giv ¯^KvgR cwiev‡ii AšÍf©yw3i `vwe iv‡LÑ
729 = 93 = (7 + 2)√9
512 = 83 = (5 + 1 + 2)6/2 = (5 + 1 + 2)(5+1)/2
144 = 9 × 16 = (1 + 4 + 4) (1 × 4 × 4) 4096 = 212 = (21/8)12 × 8 = (21/8)96
4
‡MŠwbK wPý e¨envi K‡i GiKg Av‡iv `wy U msL¨v cvIqv ‡h‡Z cv‡i| 145 = 1 + 24 + 120
= 1 + 4.3.2.1 + 5.4.3.2.1
= 1! + 4! + 5!
Ges
40585 = 24 + 0 + 120 + 40320 + 120
= 4.3.2.1 + 1 + 5.4.3.2.1 + 8.7.6.5.4.3.2.1 + 5.4.3.2.1 = 4! + 0! + 5! + 8! + 5! (g‡b ivL‡Z n‡e, 0! = 1) •
‡jLK wewkó ‡jvKweÁvb MšÖ ’ I ceÖ Ü iPwqZv| B-‡gj: contactckg@gmail.com
GLb 21/8 ‡K cÖKvk Kiv ‡h‡Z cv‡i (21/2)1/4 = √2 21/8 = √√√2
= 4 + 0 √√√√
96
AZGe, 4096 = √√√√4 + 0