આયુ .રાજેશ સુમેરા અને ગણિત
Ul6T
ÒJGDF\ Ul6T
Ul6T HLJG ;FY[ HM0FI[,]\ K[P 5]:TSDF\ ZC[, X{1Fl6S 5|lS|IFVMG[ ;FY[ HM0JL H~ZL K[ U6TZL SZJFDF\ H ZC[J]\ GlC Ul6TGM VeIF; ,F\AF ;DI ;]WL ;TT RF,[ K[P Ul6TG]\ SFI" 5|lS|IF 5Z YFI K[P 5lZ6FD 5Z GCLP 5lZ6FD 5|lS|IFG]\ VFBZL V\U K[P VFDF\ VFJJF HJFYL AF/SM 5MTFG]\ D}<IF\SG HFT[ SZL XS[ K[P 5|lS|IF JUZ 5lZ6FD CMT]\ GYLP Ul6TG]\ lX1F6 5|lS|IF VFWFlZT CMJ]\ HM.V[P VF5[ 5]:TSGL V\NZ GYLP X{1Fl6S 5|lS|IFVMG[ T[GL ;FY[ HM0JL 56 H~ZL K[P U6TZL SZJFDF\ H ZC[J]\ GlCPV[8,F DF8[ VeIF; ,F\AF ;DI ;]WL ;TT RF,[ K[P Ul6TG]\ SFI" 5|lS|IF 5Z YFI K[P 5lZ6FD 5Z GCLP 5lZ6FD 5|lS|IFG]\ VFBZL V\U K[P VFDF\ VFJJF HJFYL AF/SM 5MTFG]\ D}<IF\SG HFT[ SZL XS[ K[ 5|lS|IF JUZ 5lZ6FD CMT]\ GYLP Ul6TG]\ lX1F6 5|lS|IF VFWFિZT CMJ]\ HM.V[P
VF56[ 5MTFGL ZLT[ lX1F6 SZTF CM.V[ KLV[PT[ VFU/GL Z6GLlT GSSL SZJFDF\ DNN ~5 YFI K[P HIFZ[ 5lZ6FD VFWFlZT 5|lS|IF AF\WL N[ K[P 5|lS|IF VFWFlZTDF\ B]<,F56]\ HMJF D/[ K[P
Ul6TG[ V[S U\ELZ lJQFI DFGJFDF\ VFJ[ K[P X]\ VF SYG 5FK/ SM. ;rRF. K[ m SM. 56 lJQFI U\ELZ GYL CMTM 56 VF56L DFgITF T[ lJQFIG[ ;C[,M VYJF U\ELZ AGFJL N[ K[P ;DFHDF\ Ul6T lJX[ VFJL lJ5], 5|DF6DF\ WFZ6FVM 5|Rl,T K[P Ul6T AWFGF JXG]\ GYLP Ul6T DC[GTGM lJQFI K[P PPP VFJL WFZ6FVMV[ H Ul6TG[ V3ZM AGFjIM K[P BZ[BZ TM Ul6TG[ HLJG ;FY[ µ\0M ;\A\W K[P VF56[ µ\3TF4 HFUTF4 ;\bIFVM4 VF\S0FVMYL ZDTF ZCLV[ KLV[ Ul6T tIFZ[ U\ELZ VG[ V~lRSZ AGL HFI HIFZ[ JUM"DF\ lGZ; ZLTMYL V\SM VG[ WFZ6FVMG[ UMBFJFDF\ VFJ[ K[P HLJG H~ZL J:T]YL GCÄ 5Z\T] 5ZL1FF 5F; SZJF DF8[ Ul6TG]\ lX1F6 SZJFDF\ VFJ[ K[P
KMSZLVM VG[ Ul6T
KMSZLVM Ul6TDF\ GA/L K[ T[GL 5FK/ SM. lGl`RT SFZ6 GYLP VF V[S 5}J"U|C VYJF DFgITF K[ VF56[ C\D[XF\ KMSZLVMG[ Ul6TDF\ Z; 50JF N[TF GYL VG[ T[G[ Ul6TDF\ GA/L CMJFGL EFJGF 5[NF SZLV[ KLV[P JUM"DF\ VG[ ;DFHDF\ 56 KMSZLVMG[ ;DFG TS GYL D/TLP KMSZLVM Ul6T E6LG[ X]\ SZX[ m Ul6T T[GM lJQFI GYLP VFJF 5|SFZGL DFgITFVMV[ KMSZLVMG[ Ul6TYL N}Z ZFBL K[P
XF/FV[ VFJTF 5C[,F AF/SMGF UFl6lTS VG]EJ VG[ VG]EJG]\ 1F[+ o
XF/FV[ VFJTF\ 5C[,F\ Ul6T ;FY[ ;\A\lWT VG[S VG]EJM AF/SM 5F;[ CMI K[P AF/SM ;\bIFVMG[ AM,L ,[ K[ AF/SMGL TDFD ZDTM V[JL CMI K[ S[ H[DF\ V[S0FYL ,.G[ CHFZ ;]WLGM lC;FA ZFB[ K[P VMK]\vJWFZ[4 N}Z v GHLS4 H}Y AGFJJ]\ lNJ;4 ;DI4 C,S]\4 EFZ[4 ,\AF.4 v 5CM/F.4 VFSFZ4 JHGG]\ 7FG AF/SMDF\ CMI K[P T[VM 5MTFGL ZDTMDF\ J:T]VMGM AZFAZ EFU 5F0L ,[ K[ 5MTFGL J:T]VMGM lC;FA ZFB[ K[P GFG]\ DM8]\ VMK]\ JWFZ[4 VFU/v5FK/4 p5ZvGLR[ H}Y AGFJJ]\ T],GF SZJL4 U6TZL SZJL4 lRCGGL VM/B4 N}Z V\TZG]\ VG]DFG4 38J]\v JWJ] H[JL TDFD WFZ6FVMYL AF/SM 5lZlRT CMI K[P VF56[ AF/SMG[ 5|TLS H XLBJLV[ KLV[P V[DGF VG]EJMG[ 5|TLS ;FY[ HM0J]\ DCÀJ5}6" K[P
Ul6T XF DF8[ m
Ul6T XLBJ]\ VUtIG]\ K[P jIFJCFlZS HLJGGL DM8F EFUGL lS|IFVMDF\ Ul6TGL H~Z 50[ K[P Ul6TYL AF/SMDF\ S[8,LS 1FDTFVMGM lJSF; YFI K[P AF/SMDF\ S|DAwWTF4 lGIlDTTF JW[ K[P TS" VG[ lR\TG XlST JW[ K[P lG6"I ,[JFGL 1FDTF JW[ K[P AF/SM ;\`,[QF6v lJ`,[QF6 VG[ TFZ6M SF-TF XLB[ K[ TyI 5|F%T SZ[ K[ VG[ ZH} SZTF\ XLB[ K[P UFl6lTS EFQFF ;DH[ K[P VFJL ZLT[ Ul6T lJRFZJFGM ãlQ8SM6 VF5[ K[ H[DF\ AF/S 5MTFGF JFTFJZ6G[ ;DHTF\4 N{lGS HLJGGL ;D:IFVM C, SZJFGL 1FDTF 5|F%T SZ[ K[P
Z;5|N K[ Ul6T o
Ul6T Z;5|N lJQFI K[P T[G[ VFGFYL 56 JWFZ[ Z;5|N AGFJJFGL VFJxISTF K[P Ul6T ~lRSZ G ,FUJFG]\ SFZ6 lX1FS Ul6T E6FJTL JBT[ DM8[ EFU[ OST a,[S AM0"GM H p5IMU SZ[ K[ T[ K[P VF SFZ6YL Ul6TGL WFZ6FVM AF/SMDF\ :5Q8 YTL GYLP Ul6TGL WFZ6FVMGL ZH}VFTDF\ ;FDU|L4 JFTFJZ6 VG[ 5|J'l¿VMGM p5IMU SZJFDF\ VFJ[ TM Ul6T Z;5|N AGL XS[ K[P JWFZ[ Z;5|N AFJJF DF8[ Ul6TDF\ GSSZ ;FDU|L4 SMI0F4 5|NX"G4 JU[Z[GM p5IMU YJM HM.V[ ZH} SZ[,F ;JF,MDF\ 38GF DF8[ ;FY"S TS" CMJM H~ZL K[P VFJL l:YlTDF\ AF/SM Z; ,[ K[P XLB[ K[ VG[ Ul6T Z;5|N ,FU[ K[P
GSSZ q D}T" J:T]VMGM p5IMU DCÀJ5}6"
Ul6T D}T"G[ VD}T" ;FY[ HM0JFGM VG[ ;\A\W AF\WJFGM 5|IF; K[P WFZ6FVM VD}T" CMI K[P lJQFI SM.56 CMI 56 Ul6TGL WFZ6FVMYL VF56G[ JWFZ[ 0Z S[D ,FU[ K[ m Ul6T G[ DF8[ JFZ\JFZ SC[JFDF\ VFJ[ K[ S[ VF VD}T" lJQFI K[P V[GL ;\S<5GF D}/E}T ZLT[ VD}T" K[P 5Z\T] VD}T"GM VY" ;DHDF\ G VFJ[ T[ GYLP UFl6lTS VD}T"TFG[ D}T" q GSSZ RLHMGL DNNYL ;Z/ AGFJL XSFI K[ HIFZ[ D}T"G[ VD}T" ;FY[ HM0JFDF\ VFJ[ K[ tIFZ[ VD}T"GM VY" :5Q8 YFI K[P ZH}VFTGL ZLTMYL 56 36LJFZ Ul6T VD}T" K[ T[J\] 5|TLT YFI K[P
D}T" J:T]VMGL E}lDSF BZ[BZ DCÀJGL CMI K[P VF p\DZDF\ AF/SM :JFEFlJS ZLT[ H]NL H]NL J:T]VMYL ZD[ K[4 T[GM ;\U|C SZ[ K[4 AUF0[ K[ VG[ OZLYL E[UL SZ[ K[ VF 5|lS|IFDF\ T[VMGL AWL H .lg§IM ;\lRT CMI K[ VG[ T[GF VFWFZ[ 5|DF6G[[ XMW[ K[ VG[ ;DH[ K[PVCÄYL X~ YFI K[ s5|DF6f Ul6T XLBJFGL X~VFTP
Ul6T XLBJFGM V[S lGl`RT S|D K[P 5C[,F D}T" J:T]VMGL ;FY[ SFD VG[ 5KL ;\S[TM TYF 5|TLSMGL ;FY[ SFD SZJ]\ VFJxIS K[P
v VG]EJ o D}T" J:T]VM ;FY[ VG]EJ SZJMP lJlJW 5|SFZGL J:T]VM ;FY[ JFZ\JFZ VeIF;
v EFQFF o J:T]VMGL ;FY[ lS|IF SZTF\ SZTF\ N{lGS HLJG ;FY[ HM0FI[,L EFQFFGM 5|IMUP
v lR+ o 5|TLSM VG[ lR+MGL T],GF4 lJlJW 5|SFZGF lR+M VG[ lJlJW ZLTMYL T],GF SZJLP
v 5|TLS o 5|TLSMGL ;FY[ VeIF;4 lR+FtDS VG[ lS|IFtDS VJWFZ6FVMGL ;FY[
VF AW]\ BF; SZLG[ GFGF AF/SMGF ;\NE"DF\ lJX[QF p5IMUL K[P D}T" J:T]VMYL ;\S<5GFVMG[ TFZJJFDF\ DNN D/L ZC[ K[P AF/S HFT[ SFI" SZLG[ VG]EJ SZ[ K[ AF/SMG[ AWL .lg§IMGF 5|IMUGL TS D/[ K[P AF/SMG[ HIFZ[ 5MTFGF VG]EJ VG[ JU"GF VG]EJDF\ lJZMWFEF; YFI K[ TM T[G[ VD}T" lJRFZU|C6 SZJFDF\ D]xS[,L YFI K[P
UMBJ]\ GCLqDCFJZM SZJM o
Ul6T XLBJFDF\ ;DHJ]\ H~ZL K[P ;DHJFYL WFZ6FGL ;DH D/[ K[ 56 T[ ;DHG[ :YFIL AGFJJF DF8[ DCFJZM SZJM 50[ K[4 VeIF;4 SF{X,G[ JWFZ[ K[P VeIF;DF\ GJLGTF4 lS|IF SZJFGL ;FY"STF4 ;lS|ITF4 ;DH VG[ TS"GL ;FY[ SFD SZJFGL H~Z CMI K[P VeIF;G]\ V[S ;FZ]\ 5F;]\ V[ K[ S[ T[DF\ AF/SMGL E}lDSF CMI K[P AF/S SM. ,1IGL 5|Fl%T DF8[ :JI\ 5|ItG SZ[ K[P
JUM"DF\ 3l0IF4 lUGTL H[JL VJWFZ6F DF8[ ;DHFJJF G[ AN,[ UMBFJFI K[P UMBJ]\ V[S DXLGL 5|lS|IF K[P H[DF\ SM. JFTG[ ;DHIF JUZ JFZ\JFZ JF5ZJFDF\ VFJ[ K[P HIFZ[ lX1FS AF/SMGL ;FD[ D}T" J:T]VMGL ;FY[ ;\A\W AF\WLG[ VJWFZ6FVMG[ 5|:T]T GYL SZTF tIFZ[ AF/SM UMBJF DF8[ 5|[ZFI K[P H~ZL K[ S[ JUM"DF\ UFl6lTS VJWFZ6FGL ;DH DF8[ lX1FS £FZF ;FY"S ;\NE" AGFJJFDF\ VFJ[P AF/SMG[ VeIF;GL TS D/[ tIFZ[ H AF/SMDF\ UFl6lTS VJWFZ6FVMGL ;DH AGX[ VG[ VF ;DH lJlEgG VG]EJM q VeIF;MDF\YL 5;FZ Y.G[ :YFIL AGX[P
;FRF p¿Z SZTF\ ;FRL 5|lS|IF H~ZL K[
Ul6T lX1F6DF\ 5|lS|IFG]\ DCÀJ5}6" :YFG K[P V[S H JU"DF\ V,U V,U :TZGF\ AF/SM CMI K[ T[GFDF\ lJlEgGTF CMI K[P Ul6TDF\ ;DH 5Z EFZ CMI K[ VFYL Ul6TGM VY" v V[S lS|IFG[ V,U V,U 5wWlTYL 5|IMU SZJM T[ YFIP AF/SM 5MTFGL ZLTMYL ;JF,MGF HJFA D[/JL XS[ K[P JU"DF\ lX1FS SM. lS|IF V[S 5wWlT ZH} SZL XS[ K[ 56 AF/SM p5Z SM. V[S 5wWlT G ,FNL XSFIP AF/SMG[ V[JL TS VF5JL HM.V[ S[ ;JF,MG[ C, SZJFDF\ 5MTFGL ZLT JF5ZL XS[P AF/SMDF\ V[ 1FDTF lJS;JL HM.V[ S[ T[ p5IMUL ;\NE"DF\ V,U V,U 5wWlTGM 5|IMU SZL XS[ AF/SMG[ T[GL 5wWlT 5;\N SZJFGL :JT\+TF CMJL HM.V[P lX1FS DF+ 5|`GGM p¿Z G HMTF\ V[ 56 H]V[ S[ AF/SMV[ 5|`GGM HJFA S. ZLTYL D[/jIM K[P AF/SMG[ a,[S AM0" p5Z 5|`GMGM pS[, SZFJLG[ T[GL ZLTM G[ ;DHL XSFIP Ul6TDF\ ;DH H~ZL K[ VFYL JU"DF\ p¿Z SZTF\ 5|lS|IFG[ JW] DCÀJ VF5J]\ HM.V[P
DF{lBS Ul6T DF{lBS Ul6T AF/SM DF8[ B}AH p5IMUL K[P T[ AF/SMGL lJRFZJFGL 5|lS|IFG[ J[U VF5[ K[ 5Z\T] T[GL 5|J'l¿VM NZdIFG V[ wIFG ZFBJ]\ H~ZL K[ S[ DF{lBS Ul6TGF ;JF, 5lZJ[X ;FY[ HM0FI[,F CMIPV[8,[ S[ AF/SM T[GM jIFJCFlZS VY" SF-L XS[ ;JF,DF\ VF5JDF\ VFJ[, 38GFVMGF\ SFZ6M TYF T[GF\ 4 5lZ6FDM lJX[ 56 AF/SM lJRFZ[ K[P SFZ6M VG[ 5lZ6FDMGL VCÄ T[GL T],GF SZ[ K[4 VCÄ 36LJFZ lX1FSG]\ ,1I DF+ Ul6T CMI K[ ;JF,GL 5FK/GF SFZ6M lJX[ GYL lJRFZTFP HIFZ[ AF/SMG]\ wIFG 5C[,F SFZ6 p5Z H HFI K[P T[YL V[ ;\NE[" 5|J'l¿VM UM9JJL HM.V[P
