NEOMETRY: Let the Forms Speak

I K G A K P \ T  H K P P B K E G \ A S S V K M N 

 _mkh Bmzka Bmzka Egu`m Egu`m  Mrcbdtkcturmh Kiodikkrdio Kiodikkrdio Stu`kit  Pbk Mutbgr Mutbgr ge S[LPHK S[LPHK KIK\OT  KIK\OT  M  M VBTSDCS VBTSDCS DIPK\MCPDIO EG\CK

Cgpyrdobt © <6=3 _mkh Bmzka Egu`m Edrst K`dtdgi( <6=3

IKGAKP\T: HKP PBK EG\AS SVKMN  Cgpyrdobt © <6=3 _mkh Bmzka Egu`m

Kh!Smem Vrkss( <= Mh!@gwk`mr strkkt( Cmdrg( Koypt

©<6=3 _mkh Bmzka Egu`m( Mhh \dobts \kskrvk`) Ig pmrt ge tbds lggn sbmhh lk rkprg`uck`( stgrk` di m rktrdkvmh systka( gr trmisadttk` ly miy akmis( khkctrgidc( khkctrgidc( akcbmidcmh( pbgtgcgpydio( rkcgr`dio( gr gtbkrwdsk( wdtbgut tbk prdgr wrdttki pkradssdgi ge tbk mutbgr

DSLI 4?2 ! 4?? ! 2;634 ! 5 ! 2

'  Pbk crkmtdvk cgitkits cgitkits ge tbds lggn mrk prgtkctk` ui`kr ditkhhkctumh prgpkrty prgpkrty sdick  Jmiumry <6=3

D `k`dcmtk tbds lggn tg ay emtbkr wbg bkhpk` ak edi` ay wmy tbrguob scdkick mi` pbdhgsgpby))) Pbmins Emtbkr egr ygur    pmtdkick mi` ui`krstmi`dio))) Pbmins egr egr tbk mtagspbkrk ygu   prgvd`k` sg D cmi `dscgvkr tbk uinigwi aystkrdks))) aystkrdks)))

I kgaktry

hkt tbk egras spkmn <6=3

mlhk ge Cgitkits Ditrg`uctdgi…………………………………………………………

?

Ditrg`uctdgi tg Smcrk` Okgaktry Ok gaktry…………………………………) )

=3

 Pbk Ogh`ki Spdrmh………………………………………………))  Pbk Uksdcm Vdscds………………………………………………))))

=0 =5

Ditrg`uctdgi tg Iuakrghgoy………………………………………) )

=4

Ikgaktry Akcbmidcs……………………………………………… ))

<3

Cgivkrtdio m sdiohk iualkr ditg m egra …………………………) ) Cgivkrtdio twg iualkrs ditg m egra……………………………) ) Cgivkrtdio tbrkk iualkrs gr agrk ditg m egra…………………) ))

<3
Imragidcs…………………………………………………………))) )

36

Edi`dio Bmragidc Iualkrs……………………………………))) ) Smcrk` Iualkrs…………………………………………………) ) ………………………………………………)))) Smcrk` Sdalghgoy ………………………………………………))))  Miohks ge ditkrmctdgi……………………………………………)))  Prmdts ge Okgaktrdcmh Iualkrs…………………………………)) Bmragidzdio Smcrk` Miohks……………………………………)))) Bmragidcs Iualkrs— _bkkh…………… _bkkh …………………………… ………………………)) ………)) ) Cghgrs mi` Iualkrs……………………………………………)) )  Pbk ki` ge cychks Pbk =3 ………………………………………)))) ) Crgssdio iualkrs mi` ditkrcgursk………………………………)) ) ……………………………)))) ) Suaamtdgi( Ditkormtdgi % Crgssdio ……………………………))))

36 3< 33 34 0= 0< 03 0; 05 04 04

Ikgaktry Egras ly tbk mutbgr……………………………………) ))

;=

\kekrkicks…………………………………………………………))) ))

;;

Ditkhhkctumh Vrgpkrty di Mrmldc………………………………………

;?

Lggn Suaamry di Mrmldc…………………………………………))) ))

56

Ikgaktry

hkt tbk egras spkmn <6=3

IP\G@[CPDGI

 Tkmrs mi` ykmrs D spkit ay hdek skmrcbdio( trydio tg ui`krstmi` ui`krstmi` tbk aystkrdks ge tbk wgrh`) Sdick D wms m hdtthk nd` D wms mhwmys mamzk` ly micdkit wgrh` mrcbdtkcturk) Pbkrk wms sucb mi dapmct ge tbkdr mrt wgrn mi` aytbs gi ay  cbdh`bgg`) D rkakalkr rka kalkr lkdio sbgcnk` ykhhdio ‘tbk pyrmad`)) tbk pyrmad`‑  wbki D usk` tg mpprgmcb Pbk Orkmt Vyrmad` ge g e Odzm) Egr ak Pbk Spbdix di tbk Odzm Vhmtkmu wms igt just m stmtuk) D mhwmys lkhdkvk` tbmt tbk micdkit  wgrh` bm` tbkdr skcrkt nigwhk`ok) Dt ds mctumhhy m smcrk` nigwhk`ok) Dt mhh stmrtk` wbki D ekhh di hgvk wdtb tbk Micdkit Koyptdmis) D usk` tg tbdin  tbky wkrk tbk bgh`krs ge sgak ndi` ge nigwhk`ok tbmt wms rudik` ly wmrs mi` lmtthks) D mhwmys lkhdkvk` gur mickstgrs nikw sgaktbdio tbmt wk cmi— t skk lut wk cmi ekkh) Pdhh D wms ditrg`uck` tg sdaphk ak`dtmtdgis wbki D stmrtk` tg bmvk m `deekrkit pkrspkctdvk ge micdkit cuhturks) @doodio ditg tbk rkmhas ge tbk uinigwi( tbds ds wbmt D mhwmys `d`)  _bki D stmrtk` hkmridio Smcrk` Okgaktry( D stmrtk` tg tbdin wby cmi—t t bk syalghs ge tbk micdkit wgrh` lk m amidekstmtdgi ge akmidios) D stmrtk` tg tbdin ge hmioumok di tkras ge cghgrs( ausdc( pbgiktdcs( rbytba( ktc)) sg wby  cmi—t dt lk mhsg okgaktry Micdkit Orkkns hkmrit m hgt erga erg a Micdkit Koypt) Pbky rkcgr`k` tbkdr smcrk` nigwhk`ok mi` wds`ga wds`ga di tbk egra ge mi mpprgmcb ge tbdindio tbmt kxphmdis kvkrytbdio wbdcb tbky cmhhk` Vbdhgsgpby) Vbdhgsgpby dichu`ks tbk stu`y ge   Mrdtbaktdc(

Okgaktry( Okgaktr y(

Ausdc(

bmragidcs(

Mstrgigay(

Mstrghgoy(

Cgsaghgoy( Hgodc( mi` spdrdtumhdty) ?

Ikgaktry

hkt tbk egras spkmn <6=3

 Metkr stu`ydio `deekrkit micdkit wgrh` pbdhgsgpbdks mi` mrts( D egui` tbmt tbky mhh bmvk di cgaagi sgak cgsaghgodcmh ag`khs mi` cgickpts) Egr distmick> tbk Cbdiksk( tbk Jmpmiksk( tbk Koyptdmis( tbk Orkkns( tbk Bdi`u( tbk Lu``bdsts( tbk Lmlyhgidmis( tbk Mrmls( tbk Amymis mi` aucb agrk cdvdhdzmtdgis lkhdkvk` di m vkry cgaagi cgsaghgodcmh ag`kh) Pbky mhh lkhdkvk` di iuakrghgoy mi` tbk pgwkr ge iualkrs) Pbky mhh lkhdkvk` di sgak sgrt ge amodcmh pgwkrs tbmt amideksts tbrguob iualkrs( phmikts( ausdc( phmits( ksskicks( ktc) Pbky mhh lkhdkvk` di kikrodks gr hdek egrcks tbmt crkmtk kvkrytbdio mi` agtdvmtk hdek gr ndhh dt tg `kmtb) Pbksk egrcks gr ms tbky  cmhhk` dt tbk khkakits ge imturk `deekrk` erga cuhturk tg cuhturk ykt tbk rksuhtdio pbdhgsgpbdks wkrk mhagst tbk smak) Di tbkdr cgsaghgodcmh ag`khs kvkrytbdio wms m rksuht ge tbk ditkrmctdio  khkakits ge imturk) Di micdkit wgrh` pbdhgsgpbdks( iualkrs `g bmvk prgpkrtdks( iualkrs mrk hmioumoks tbmt `g ditkrmct egradio akmidios) Egr tbka kvkrytbdio bm` m akmidio mi` miy ditkrmctdgi crkmtks mi mctdgi) Amiy diehukicks egrck` ak tg bmvk egui` ay ikw `dscgvkrdks mi` ikw mrt kxphmdik` di tbds lggn) Ay mrcbdtkcturk stu`y bkhpk` ak ui`krstmi` tbk bdstgry ge mrt mi` mrcbdtkcturk) Tkt D ikvkr hdnk` tbk mpprgmcb ge ag`kri mrt mi` mrcbdtkcturk( spkcdmhhy tbmt pbdhgsgpbdcmh cgickpts di ag`kri mrt mrk just tbk kxprkssdgi ge tbk mrtdst—s emhsk Skhe Kog mi` Vkrsgim) D stmrtk` tg lkhdkvk di m uidvkrsmh scdkick wbki D stmrtk` tg hkmri mstrgigay) Ay mstrgigay lmcnorgui` bkhpk` ak ui`krstmi` pbdhgsgpby) _bki D stu`dk` LdgOkgaktry® D egui` @r)Dlrmbda Nmrda—s ag`kh ge micdkit  wgrh` tkcbighgoy tg lk emscdimtdio) Bds ikw mpprgmcb bkhpk` ak okt ditrg`uck` tg tbk keekcts ge Okgaktrdcmh sbmpks mi` kivdrgiakitmh `ksdoi) 2

Ikgaktry

hkt tbk egras spkmn <6=3

 Pbds ds wbki D stmrtk` kxpkrdakits trydio t rydio tg prgvk pr gvk tbk pbysdcmh kxdstkick ge  sulthk kikroy tdhh D wms mlhk tg prgvk dt mi` pulhdsb ay lggn ‘S[LPHK KIK\OT m pbysdcs ditkrmctdio egrck‑)  Metkr tbds t bds agakit ag akit D stmrtk` stmr tk` tg ui`krstmi` tbk micdkit wgrh` erga m tgtmhhy  t gtmhhy  `deekrkit pkrspkctdvk) Pbds ds wbki D disdstk` tbmt tbkrk aust lk sgak bd``ki hmioumok di tbk micdkit wgrh` Smcrk` Okgaktry)  Micdkit wgrh` cdvdhdzmtdgis cdvdhdzmtdgis amstkrk` Smcrk` Okgaktry mi` Iuakrghgoy) Egr tbk micdkit wgrh`( Okgaktry wms igt just m sgrt ge pbysdcmh scdkick lut scdkick dtskhe wms pmrt pmr t ge pbdhgsgpby) Pbmt—s wby wk cmi edi` pmttkris di tbkdr vmrdgus ndi`s ge mrts mi` scdkick)  _bki wk mimhyzk micdkit mrts wk `kcg`k tbka ditg prgpgrtdgis( miohks( grdkitmtdgis( ktc… ykt wk mhwmys bmvk lkki ikohkctdio tbk akmidios ge tbk pmttkris tbkaskhvks) Kvkry hdtthk egra cmi lk crkmtk` erga m pmttkri mi` tbk pmttkri cmi mhwmys crkmtk dts prgpgrtdgis) Micdkit pkgphk usumhhy usk` tbk ogh`ki rmtdg ykt tbk ogh`ki rmtdg cmi—t tkhh us tbk akmidios lkbdi` egras) Imturk dtskhe usks tbk ogh`ki rmtdg( ykt `deekrkit egras bmvk `deekrkit euictdgis) Pbmt—s wby tbk ogh`ki rmtdg cmi—t tkhh us m hgt mlgut akmidios lut cmi sbgw bmragiy) Bgwkvkr pmttkris cmi crkmtk tbk ogh`ki rmtdg prgpgrtdgis tg mcbdkvk bmragiy mi` stdhh cmi bmvk m lkbmvdgr( m euictdgi( mi` m akmidio) Amylk sgak ksgtkrdc orgups ms tbk Erkkamsgiry nikw mlgut bgw tg cgivkrt akmidios ditg egras tg kicg`k tbkdr pbdhgsgpby) Pbk mhcbkadsts cgivkrtk` Mrcbktypks ditg syalghs) _bmt D `dscgvkrk` ds bgw akmidios ge  tbk mrcbktypks cmi lk cgivkrtk` tg okgaktrdcmh pmttkris tbmt cmi egra m 4

Ikgaktry

hkt tbk egras spkmn <6=3

sdaphk syalgh tg sgpbdstdcmtk` `ktmdhk` prgpgrtdgis ge hdvdio tbdios) Ikgaktry ds bgw tg cgivkrt akmidios ditg egras bmvdio hdek prgpgrtdgis)  Pbds ikw mpprgmcb ds lmsk` gi cgivkrtdio Iualkrs ditg Okgaktry wbdhk stdhh prkskrvdio tbk ogh`ki rmtdg) Dt cmi mhsg cgivkrt Okgaktry ditg iualkrs tg edi` dts mrcbktypk) Ikgaktry ds cgickrik` mlgut akmidios tbmt mrk amidekstk` tbrguob tbk pgwkr ge iualkrs nigwi ms Iuakrghgoy mi` tbk pgwkr ge Smcrk` Okgaktry)  Migtbkr pmrt ge Ikgaktry ds tbmt dt cmi sbgw tbk ditkrmctdgi lktwkki iualkrs tg crkmtk akmidioeuh egras tbmt cmi rkmcb hdvdio tbdios— sgpbdstdcmtdgi mi` lkmuty) Pbds ds wby D imak` dt Ikgaktry( tbk ikw  okgaktry( gr tbk ikg!okgaktry( tbk mrt ge cgivkrtdio iuakrghgoy akmidios ditg okgaktry mi` okgaktry ditg iualkrs)  Pg mcbdkvk bmragiy( ditkrmctdio iualkrs aust igt lk di cgiehdcts) Sdaphk okgaktrdcmh sbmpks cmi sbgw us tbk akmidios ge iualkrs( wbdhk tbrguob m sdiohk uidt cdrchk smcrk` iualkrs cmi lk rkvkmhk` sbgwdio skqukicks ge  bmragidc orgups ge iualkrs) D cmhhk` tbds Imragidcs wbdcb ds edi`dio  bmragidc iualkrs tbrguob okgaktry) Di tbds lggn tbk cgickpt ge Ikgaktry mi` Imragidcs ds vkry lmsdcmhhy  kxphmdik`) Ikgaktry mi` Imragidcs mrk igt just cgickrik` mlgut cgivkrtdio iualkrs ditg Okgaktry( sdick sdi ck dt—s igt just okgaktry gr m `ksdoidio dssuk) Dt ds crkmtdio euictdgimh( hdvdio( lkbmvdio( mi` akmidioeuh pmttkris tbmt trmisegra akmidios mi` mrcbktypks ditg m okgaktrdcmh egra amidekstmtdgi) Dt ds mi ui`krstmi`dio ge imturk mi` bgw tbk uidvkrsk msskalhks dtskhe) =6

Ikgaktry

hkt tbk egras spkmn <6=3

Bmvdio m sghd` lmcnorgui` mlgut Iuakrghgoy mi` Smcrk` Okgaktry ds m aust lkegrk rkm`dio tbds lggn egr m euhh cgickpt ui`krstmi`dio( sdick tbds ds igt mi dhhustrmtk` lggn> bgwkvkr dt kxphmdis gihy tbk cgickpt ge Ikgaktry  mi` Imragidcs)

 _mkh Bmzka Egu`m 

==

Ikgaktry

hkt tbk egras spkmn <6=3

DIP\G@[CPDGI  PG SMC\K@ OKGAKP\T  OKGAKP\T 

Di micdkit wgrh`( pbdhgsgpbkrs wkrk tbk amstkrs ge imturk) Pbky tmuobt tbk  wgrh` Amtbkamtdcs( Mstrgigay( Ausdc( mi` Okgaktry) Egr tbka Okgaktry   wms igt jut tbkgrkas lut mi ui`krstmi`dio ge tbk wgrh`—s wgrh`— s imturk mi` `yimadcs)  Mrdtbaktdc mi` Okgaktry wkrk igt tbk scdkicks ge Gik phus Gik kqumhs  Pwg) Okgaktry wms igt just tbk stu`y ge okgaktrdcmh sbmpk prgpkrtdks ykt dt  wms mi ui`krstmi`dio ge  pbdhgsgpby mi` wds`ga) Pbmt—s wby wk cmi edi` sgak Ikg!Vhmtgidsts kxphmdidio pbdhgsgpby mi` prgvdio tbk kxdstkick ge   Pbk Gik grdodimh rkmhdty gr Og` tbrguob okgaktry mi` mrdtbaktdc) Smcrk` Okgaktry wms pmrt ge Mrcbdtkcturk mi` amiy sgrts ge mrts( sdick pbdhgsgpbkrs lkhdkvk` gur wgrh` ds ruhk` ly m skt ge bmragidgus rmtdgs) Pbky  lkhdkvk` gur wgrh` ds m syapbgiy tbmt ds di tuik mi` di bmragiy mi` gur crkmtdgis mi` mctdgis sbguh` mhwmys stmy tuik`)  M skt ge rmtdgs wkrk lkhdkvk` tg kxdst di kvkry hdvdio crkmturk) Pbk rggt ge   Pwg( tbk rggt r ggt ge g e Pbrkk mi` tbk rggt ge Edvk wkrk ksskitdmh egr hdek tg kxdst)  Tkt tbk agst emagus rmtdg ge mhh wms tbk Ogh`ki \mtdg usk` di cgaagi lktwkki Ak`dkvmh mi` \kimdssmick mrtdsts)

=3

Ikgaktry

hkt tbk egras spkmn <6=3

BK OGH@KI SVD\MH

Kvkry sgrt ge crkmtdgi pgurk` mi` ehgwk` erga m sdiohk edrst rkmhdty( Pbds ds  wbmt ds nigwi ms tbk Kamimtdgi tbkgry) Kamimtdgidsa ds m cgsaghgodcmh tbkgry di micdkit pbdhgsgpby wbdcb wms m`gptk` ly m orgup ge pbdhgsgpbkrs hdnk Vhgtdius tbk egui`kr ge Ikg!Vhmtgidsa)  Pbk Ogh`ki Spdrmh wbdcb cgaks erga tbk wkhh nigwi Edlgimccd Skqukick ds m pkrekct okgaktrdcmh rkprkskitmtdgi ge Kamimtdgidsa)  Pbk Edlgimccd skqukick sbgws m crkmtdgi prgckss wbdcb gccurs stmrtdio erga tbk Gik mi` ki`dio 

Edo) =: Edlgimccd Skqukick Ogh`ki Spdrmh

mt diedidty) =( =( <( 3( ;( 2( =3(… Pbds skqukick `rmws tbk ogh`ki spdrmh( mi` ds crkmtk` ly m``dio tbk skcgi` iualkr tg dts prkvdgus gik) Pbds skqukick sdaphy sbgws bgw tbk edrst rkmhdty egrak` kvkrytbdio ly m``dio pmrt ge dts spdrdt di tbk ikw crkmtdgis)  Pbk Edlgimccd Skqukick sbgws ogh`ki rmtdgs sucb ms ='=( <'=( 3'<( ;'3(… ogdio emr ditg tbk skqukick wguh` crkmtk tbk pkrekct bmragidc ogh`ki rmtdg =)5=2633422?;) tbk ogh`ki rmtdg ds m iualkr bmvdio dts `kcdamhs ogdio tg diedidty wdtbgut rkpkmtdio dts pmttkris) Sucb m rmtdg ds pmrt ge imturk—s hmioumok ge crkmtdgi) Amiy crkmtdgis mrk `ksdoik` tg euhedhh tbk Ogh`ki rmtdg)  Pbk Orkkn cgistructk` tbk ogh`ki rmtdg `rmwdio m squmrk tbki `dvd`dio dts dt s sd`ks) @rmwdio mi mrc bmvdio dts rm`dus erga tbk sphdt pgdit tg tbk squmrk— squmrk —s =0

Ikgaktry

hkt tbk egras spkmn <6=3

cgrikrs( tbds ds bgw m cgapmss cmi `rmw mi mrc wbdcb prgjkcts gik sd`k ge tbk squmrk crkmtdio tbk ogh`ki rmtdg ms sbgwi di edourk"<$) Edo) <: Cgistructdio Ogh`ki \mtdg

 Mrtdsts di tbk t bk rkimdssmick usk` tbk rmtdg 3'< wbdcb ds =);) Pbky cgistructk` dt di mi kmsdkr wmy) M squmrk ds sphdt ditg twg kqumh rkctmiohks) Gik ge dts bmhvks ds m``k` ms m tbdr` pmrt) Pbds ds bgw m rkctmiohk wbdcb ds `dvd`k` ditg tbrkk pmrts ds crkmtk`( Pbmt—s wby `dvd`dio ly tbrkk ds cgisd`krk` tg lk vkry  smcrk`) Gtbkr rmtdgs mrk vkry smcrk` ms akitdgik` lkegrk hdnk tbk rggt ge twg mi` tbrkk wbdcb ds mhsg nigwi tg lk m ogh`ki rmtdg mi` tbk rggt ge edvk)  Pbk iualkrs twg( tbrkk tbrk k mi` edvk mrk prdak iualkrs) i ualkrs) Pbgsk iualkrs crkmtk skqukicks ge igi rkpkmtdio diedidtk `kcdamhs) Egr distmick tbk squmrk rggt ge twg crkmtks =)0=0<=3;5<3?)) M squmrk bmvdio m sd`k hkiotb ge = uidts  wguh` bmvk dts `dmogimh tbk rggt ge twg) M pkrekct squmrk wdtb sucb m `dmogimh nkkps ogdio tg diedidty wdtbgut rkmcbdio tbk cgrikr ge tbk squmrk(  Pbmt—s lkcmusk tbk hdik nkkps m``dio m `deekrkitdmh `kcrkmsdio `dmogimh hkiotb tdhh diedidty)  Pbds \kcmhhs— Zkig—s Vmrm`gxks mrouk` ly l y Zkig ge g e Khkm"046–  Khkm"046 – 036 036 LC$) Di m Zkig pmrm`gx mi mrrgw cmi ikvkr rkmcb dts tmrokt lkcmusk dt bms tg cut bmhe  `dstmick mi` qumrtkr ge g e `dstmick di m skqukick wbdcb wguh` wguh` nkkp `dvd`dio ly  twg tdhh rkmcbdio mi diedidty ge pgdits) Pbds ds m aktmpbysdcmh prglhka wbdcb  Mrdstgthk"320 LC –  LC  – 3<< 3<< LC$ mhsg `dscussk` di gik ge bds lggns pmrmpbrmsdio  =;

Ikgaktry

hkt tbk egras spkmn <6=3

Zkig smydio: ‘Di m rmck( tbk qudcnkst ruiikr cmi ikvkr gvkrtmnk tbk shgwkst( sdick tbk pursukr aust edrst rkmcb tbk pgdit wbkick tbk pursuk` stmrtk`( sg tbmt tbk shgwkr aust mhwmys bgh` m hkm`‑

BK UKSDCM VDSCDS

 Micdkit wgrh` nikw bgw tg cgistruct sdadhmr ogh`ki rmtdgs usdio kmsy aktbg`s sucb ms tbk  Uksdcm Vdscds wbdcb crkmtk` agrk cgaphdcmtk` okgaktrdcmh egras mi` pmttkris sucb ms tbk ‘Ehgwkr ge Hdek‑ edo"3$) Edo) 3: Pbk Ehgwkr ge Hdek

 Pbk Uksdcm Vdscds ds crkmtk` ly ditkrskctdio twg cdrchks mt tbkdr ckitkrs edo"0$) Erga tbds sbmpk cmak tbk prgpgrtdgi ge tbk micdkit mi` ak`dkvmh wgrh` pgditk` mi` bgrsksbgw mrcbks di mrcbdtkcturk edo";$)

Edo) 0: Uksdcm Vdscds

Edo) ;: Uksdcm Vdscds Sgurck: bttp:''www)ohmstgilury!pdhorda)cg)un'uskredhks'chdpWdamok66<)jpo

Smcrk` Okgaktry wms usk` di vmrdgus edkh`s sucb ms pmditdios( mrcbdtkcturk( =5

Ikgaktry

hkt tbk egras spkmn <6=3

mstrgigay( mstrghgoy( mi` agrk) Dts grdodis cmak erga mrdtbaktdc mi` amtbkamtdcs( tbmt—s wby dt bms amiy tbdios di cgaagi wdtb Iuakrghgoy) Dt—s mhh lmsk` gi tbk smcrk` mrdtbaktdcmh prgpkrtdks ge iualkrs erga wbdcb cmak smcrk` prgpgrtdgis mi` bmragidcs) Dt mhh cmak erga pbdhgsgpby tbk gckmi wbdcb bgh`s tbk skcrkts ge tbk wgrh`) Vbdhgsgpby ds tbk nigwhk`ok ge   wds`ga tbmt cmi lrd`ok tbk omp lktwkki mhh ndi`s ge mrts mi` scdkicks) Dt—s Dt —s tbk wmy erga lmsdc amtbkamtdcs mi` okgaktry tg tbk m`vmick` tbkgrdks ge  mstrgigay mi` tbk omtk tg tbk rkmhas ge `kkp spdrdtumhdty) spdrdtumhdty)

=?

Ikgaktry

hkt tbk egras spkmn <6=3

DIP\G@[CPDGI PG I[AK\GHGOT 

 Ms kxphmdik` di tbk prkvdgus cbmptkr( iualkrs wkrk igt cgisd`krk` di micdkit wgrh` tg lk just m amtbkamtdcmh dssuk) Vbdhgsgpbkrs lkhdkvk` tbmt kvkrytbdio pgurk` gut ge tbk bmragidks ge iualkrs) Pbky lkhdkvk` kvkrytbdio wms am`k ge iualkrs) Hkttkrs mi` pbgiktdcs wkrk rkprkskitk` ly iualkrs mi` wgr`s wkrk cgivkrtk` ditg iualkrs tg sbgw tbkdr akmidios mccgr`dio tg tbkdr lkhdke) Sgui`s wkrk lkhdkvk` tg bmvk tbkdr akmidios erga tbkdr grdodimh bd``ki rkmhdty wbdcb wms lkhdkvk` tg lk iualkrs ms wkhh) Ausdc( Mstrgigay(  Mstrghgoy mi` kvki spdrdtumhdty wkrk mhh lmsk` gi iualkrs) iualkr s) Dt—s lkcmusk tbky  lkhdkvk` mhh iualkrs pgurk` mi` amidekstk` erga tbk edrst grdodimh crkmtgr  Pbk Gik)  Mhh gvkr tbk wgrh` iualkrs mrk mr k usk` di vmrdgus wmys) Iualkrs mrk lkhdkvk` tg bmvk sgak aystdc pgwkrs) Di Gccuhtdsa( Aystdcdsa( Suedsa iualkrs `g phmy tbk amjgr rghk) Mhcbkadsts mi` Amodcdmis usk iualkrs mhh tbk wmy) @dvdimtdgi ds just lmsk` gi iualkrs kdtbkr di Okgamicy( Egur Vdhhmrs( D Cbdio( Pmrgt( ]d Stmr> dt—s mhh lmsk` gi iualkrs) @deekrkit agigtbkdst rkhdodgis edi` sgak iualkrs smcrk` ms di Ju`mdsa( Cbrdstdmidty( mi` Dshma) Mhsg pghytbkdsa rkhdodgis edi` m ldo ditkrkst di iualkrs) Bdi`u( Lu``bdsa( Pmgdsa( mi` Zki Lu``bdsa ds mhh lmsk` gi tbk akmidios ge iualkrs mi` dts pgwkrs) Kikroy bkmhdio di tbk Uk`m mi` tbk Cbdiksk cuhturk wms mhh lmsk` gi =4

Ikgaktry

hkt tbk egras spkmn <6=3

iualkrs mi` tbk amodc squmrks wbdcb mrk msskalhk` hdnk Su`gnu iualkrs) Ekio  Sbud mi` Prm`dtdgimh Cbdiksk Ak`dcdik `mtk lmcn dts mrt ge edvk khkakits lmhmicdio tg mi micdkit bghy turthk sbkhh  wbdcb sbgwk` tbk tb k edrst 3R3 amodc squmrk erga wbdcb mhh wds`ga mi` nigwhk`ok

Edo) 5: 3R3 Amodc Squmrk

cmak tg tbk wgrh` edo"5$) Di tbk micdkit wgrh` pbdhgsgpbdks( iualkrs `g ditkrmct mi` `g bmvk prgpkrtdks prgpkrtdks tbmt—s lkcmusk iualkrs rkhmtk tg `deekrkit mspkcts ge hdek ms tbky  lkhdkvk`) Iualkrs `g rkprkskit tbk hdek cychks mccgr`dio tg tbkdr smcrk`  wds`ga) Di Micdkit Cbdim m bkxmorma wbdcb ds m egra ge  Okgamicy wguh` sbgw tbk cbmioks ge tbk cychks ge  tbk wgrh` mccgr`dio tg tbkdr lkhdke edo"?$) Tgu cmi kvki usk m 3x3 amodc squmrk tg lmhmick tbk kikroy ge mi kivdrgiakit gr bkmh m pmtdkit wdtb trm`dtdgimh Cbdiksk

Edo) ?: Cbdiksk Bkxmorma

mcupuicturk) Pbky kvki lkhdkvk` tbds amodc squmrk cmi tkhh m hgt mlgut m pkrsgi mi` bds euturk wbdcb ds m sgrt ge Mstrghgoy gihy lmsk` gi iualkrs  wbdcb tbky cmhh tbk Egur Vdhhmrs) Pbk smak cgickpt wms m`gptk` ly tbk Di`dmis bmvdio m 0x0 amodc squmrk wbdcb tbky cmhhk` Tmitrm erga wbdcb cmak tbk Ami`mhms mi` Pmhdsamis) Dt ds bgw tbky lkhdkvk` tbmt sucb m amodc squmrk cmi prgtkct ygu mi` crkmtk vkry sdaphk egras egr ak`dtmtdgi mi` spdrdtumhdty) Bkrk ds m vkry lrdke kxphmimtdgi egr tbk micdkit wgrh` Iuakrghgoy ms tbky  <6

Ikgaktry

hkt tbk egras spkmn <6=3

lkhdkvk`> wbki iualkrs ditkrmct tbky crkmtk akmidios mi` kvkits gr cmi lk ditkrprktk` tbksk  wmys) Di Pmrgt `dvdimtdgi egr kxmaphk( tmrgt cmr`s bmvk iualkrs mi` khkakits) Pbk khkakits mrk rkprkskitk` di tbk egra ge cups( swgr`s( pkitmchks( mi` wmi`s) Sg egr m hdtthk kxmaphk bmvdio ; cups di m cmr` wguh` rkprkskit m cbmhhkiok mi` amylk sgak struoohks di kagtdgimh mspkcts) Pbk rkmsgi ds tbmt cups rkprkskit tbk  wmtkr khkakit wbdcb ds cgisd`krk` tg lk tbk ruhdio khkakit ge kagtdgimh mspkcts( wbdhk

Edo) 2: Edvk ge Cups Pmrgt Cmr`

iualkr ; rkprkskits cbmhhkioks mi` struoohks egr ikw lkodiidios Edo"2$)  _bktbkr Pmrgt `dvdimtdgi ds m emct emct gr m `khusdgi D—a bkrk gihy cgickrik` mlgut tbk pbdhgsgpbdcmh pmrt ge Iuakrghgoy wbdcb wms pmrt ge Pmrgt di tbk Ak`dkvmh wgrh`)  Mccgr`dio tg tbk Cbdiksk( Di`dmi( mi` sgak Mrml orgups lkhdke> m amodc squmrk usk` tg lk `dvd`k` ditg ckhhs cmhhk` bgusks( Kmcb bgusk rkprkskitk` mi khkakit gr mi mspkct ge hdek hdnk cmrkkr( hgvk( spdrdtumhdty( ktc)) m iualkr mppkmrdio di m bgusk wguh` ruhk tbds mspkct crkmtdio tbk pkrsgimhdty ge m ikw  lgri gr cbmiodio tbk euturk ge m ami `uk tg tbk ditkrmctdgi ge iualkrs  wdtb khkakits mi` mspkcts wbdcb wms tbk smak cgickpt m`gptk` di  Mstrghgoy ykt ruhk` ly phmikts wbdcb wbdcb amidekst erga iualkrs distkm`)  Pbmt—s bgw amiy rkhdodgis mi` pbdhgsgpbdks lkhdkvk di tbk pgwkr ge  iualkrs mi` ditkrprkt tbka tbrguob `deekrkit scbgghs) Dt mppkmrs tbmt iualkrs `g bmvk akmidios di sgak wmy mi` tbmt—s wbmt D `dscgvkrk` bgw  <=

Ikgaktry

hkt tbk egras spkmn <6=3

tg edi` tbk akmidios ge iualkrs mi` bgw tg edi` tbk akmidios ge sbmpks tbrguob okgaktry) Ms ausdc bmvk dapmct gi gur sguhs mi` cbmiok gur agg`s mi` cmi bkmh gur lg`dks( sg `g sbmpks wbdcb mrk lmsk` gi tbk smak cgickpt ge ausdc cgapgsdtdgi wbdcb ds bmragiy bmragi y nigwi ms `ksdoi)  _k hdvk di m ormi` `ksdoi tbmt t bmt ds crkmtk` ly tbk orkmtkst amstkr ge mhh wbg D nigw ms Og` mi` gtbkrs nigw bda ms tbk spdrdt ge tbk wgrh` gr tbk bd``ki edrst rkmhdty erga wbdcb kvkrytbdio wms crkmtk` ms tbky cmhhk` bda PBK GIK) Di tbds ormi` `ksdoi kvkrytbdio tmhns tbk smak hmioumok usdio tbk smak bmragiy) Di ikxt cbmptkr ygu wdhh lk ditrg`uck` tg bgw tg rkm` tbk bd``ki akssmok di kvkry crkmturk mi` bgw tg `ksdoi hdnk imturk) Di tbk ikxt cbmptkr ygu mrk ditrg`uck` tg Ikgaktry)

<<

Ikgaktry

hkt tbk egras spkmn <6=3

I k g a kt r y  Hkt Pbk Egras Spkmn   Ms akitdgik` di prkvdgus skctdgis( skctdgis ( Ikgaktry ds cgickrik` mlgut crkmtdio  euictdgimh mi` akmidioeuh egras bmvdio bmragiy) Dt mhsg egcusks gi `kcg`dio syalghs mi` hdek egras ditg akmidios) akmidios ) Pbmt—s wby ikxt cbmptkrs mrk msskalhk` di mi mrrmiokakit tbmt sbgws tbk akcbmidcs ge Ikgaktry  tbrguob oud`k` `rmwdios stmrtdio erga cgivkrtdio m sdiohk iualkr ditg m egra tg crkmtdio sgpbdstdcmtk` hdek egras mi` edi`dio tbk cg`ks ge sgak hdvdio crkmturks)

GIUK\PDIO M SDIOHK I[ALK\ DIPG M EG\A

 Mccgr`dio tg iuakrghgoy( iualkr gik rkskalhks tbk crkmtgr ge mhh tbdios) t bdios) Iualkr gik ds PBK GIK wbg cmi—t lk `dvd`k` ditg pmrts lut kvkrytbdio  cgaks gut ge dt) Pg rkprkskit gik di okgaktry( m cdrchk ds `rmwi erga m ckitrk) Pbds cdrchk ds tbk crkmtgr ge mhh egras ms tbk gik cmi crkmtk mhh iualkrs ly m``dio gik tg dt) Pbk gik ds tbk sdiouhmrdty tbmt bms ig prgpgrtdgis mi` wms mhwmys lkygi` spmck mi` tdak) Pbk gik crkmtk` kvkrytbdio lut igtbdio wms ikxt tg tbk gik mt tbk lkodiidio) Pg crkmtk kvkrytbdio tbk gik m``k` erga dts spdrdt migtbkr gik wbdcb cmi lk rkprkskitk` ms migtbkr cdrchk) Pbds prgck`urk crkmtk` mhh iualkrs mi` mhh egras) <3

Ikgaktry

hkt tbk egras spkmn <6=3

Crkmtdgi cmi lk rkprkskitk` tbrguob twg iuakrdcmh  wmys> =(<(3(0… nigwdio tbmt gik tg egur mrk ikckssmry egr tbk crkmtdgi ge kvkrytbdio ms dt tmnks tbrkk pbmsks ge crkmtdgi ly Pbk Gik) Migtbkr wmy ds tbrguob =(=(<(3(;(2… wbdcb ds tbk nigwi Edlgimccd skqukick( nigwdio tbmt = tg 2 mrk tbk ikckssmry khkakits egr crkmtdgi) Mctumhhy lgtb skqukicks bmvk tbk smak akmidios ykt kmcb gik bms m `deekrkit okgaktrdcmh amidekstmtdgi Edo"4$

Edo) 4: Pbrkk Okgaktrdcmh Skqukicks Sbgwdio Pbk Vrgckss Ge Crkmtdgi

 Pg crkmtk m sdiohk uidt ge crkmtdgi( twg cdrchks ditkrskct crkmtdio m Uksdcm Vdscds)  Pbk Uksdcm Vdscds cmi lk cmhhk` m skk` hdnk tbk skk`s di tbk nigwi ehgwkr ge hdek di smcrk`

Edo) =6: Uksdcm Vdscds

okgaktry) M sdiohk skk` cmi rkprkskit iualkr gik ms m uidt egr cguitdio  mi` igt gik PBK GIK gr gik tbmt rkprkskits tbk sdiouhmrdty sdiouhmrdty Edo"=6$)  Pbk skk` uidt cmi lk cgivkrtk` ditg twg trdmiohks rkprkskitk` r kprkskitk` di < mi` 3 ms dt ds egrak` erga twg trdmiohks edo"==$) <0

Ikgaktry

hkt tbk egras spkmn <6=3

Edo) ==: Pbk skk` uidt ms `rmwi erga twg trdmiohks `kpdctdio <(3 ms tbk cguitdio uidt =

 Pg crkmtk tbk tb k egra ge m sdiohk iualkr tbk iualkr ge skk`s bms tg lk crkmtk` tbrguob tbk ditkrskctdgis ge cdrchks mi` tbk `dmogimhs egradio tbk stmi`mr` okgaktrdcmh sbmpk bmvk tg lk tbk jgdidio pgdit ge tbk skk`s edo)0) Pg crkmtk m sghd` tbk iualkr ds auhtdphdk` ly < lkcmusk ge tbk `dmogimhs mi` gutkr skk`s) Edo"=<$

Edo) =<: Pbk edourk sbgws bgw tg cgivkrt iualkrs tg egras

tbrguob skk`s di gr`kr tg crkmtk sghd` egras

<;

Ikgaktry

hkt tbk egras spkmn <6=3

Crkmtdio m egra ge m sdiohk iualkr cmi lk rkprkskitk` mhsg di m okgaktrdcmh igi sghd` sbmpk) Mcbdkvdio tbds bmppkis ly `dvd`dio m cdrchk ly tbk ikk`k` iualkr mi` crkmtdio tbk skk`s) Auhtdphydio ly < usdio usdio `dmogimhs `dmogimhs cmi tbki crkmtk tbk gtbkr skk`s wbdcb crkmtks m sbmpk agrk ge m sghd` egra ge tbk iualkr ykt stdhh m <@ okgaktrdcmh sbmpk wdhh nkkp rkphdcmtdio dtskhe di cmsk ge  3 mi` 0 edo"=3$)

Edo) =3: Sdiohk iualkrs okikrmtk` erga tbk `dvdsdgi ge m cdrchk

<5

Ikgaktry

hkt tbk egras spkmn <6=3

GIUK\PDIO P_G I[ALK\S DIPG M EG\A

 Pg cgivkrt twg ditkrmctdio iualkrs ditg m egra> m cdrchk ds `dvd`k` ditg twg bmhvks( kmcb bmhe ds `dvd`k` ly tbk ikk`k` iualkr( tbk uidts gr tbk skk`s mrk tbki crkmtk`( tbki tbk uidts mrk auhtdphdk` ly twg tg crkmtk m sghd` wdtb tbk gutkr skk`s) Ditkrmctdio iualkrs mhwmys crkmtk akmidios lmsk` gi Iuakrghgoy mi` egras  wdtb

spkcdmh

prgpgrtdgis mi` miohks)  Pbgsk egras cmi crkmtk sdaphk

okgaktrdcmh

sbmpks( pki`mits( sghd` gljkcts( hdek pmttkris sucb ms hkmvks( mi` tbk sgpbdstdcmtdgi

cmi

rkmcb tbk crkmtdgi ge  egras tbmt mrk sdadhmr

Edo) =0: Crkmtdio m egra gut ge twg ditkrmctdio iualkrs

tg mrcbktypmh hdnk buami emck egras Edo"=0$) Pbk edimh egra mhwmys `kpki`s gi tbk skhkctdgi ge hdiks mi` trmisegradio tbka tbrguob tmiokicdks ykt tbk edimh egra wdhh nkkp tbk akmidio ge tbk ditkrmctdio iualkrs)


Ikgaktry

hkt tbk egras spkmn <6=3

GIUK\PDIO 3 I[ALK\S G\ AG\K DIPG M EG\A

 Ms kxphmdik` lkegrk> l kegrk> mccgr`dio tg iuakrghgoy iualkrs `g bmvk akmidios mi` iualkrs mct hdnk pkrsgimhdtdks) Pbmt—s wby ditkrmctdio iualkrs cr kmtk kxtrm akmidios( lkbmvdgrs( euictdgis( mi` pmttkris)  Pg crkmtk cr kmtk m pmttkri gr m egra lmsk` gi tbrkk gr agrk ditkrmctdio iualkrs> i ualkrs> kmcb iualkr ds cgivkrtk` tg dts okgaktrdcmh sbmpk gr stmr sbmpk( tbk sbmpks mrk tg lk ditkrskctk`( kmcb sbmpk sbguh` ditkrskct ms de kmcb stmi`mr` sbmpk ds m``k` m`jmckithy( tbk sbmpk ds tbki auhtdphdk` ly twg di gr`kr tg crkmtk tbk gutkr skk`s( mi` tbds wguh` lk tbk edimh sghd` egra ge tbk ditkrmctdio  iualkrs) Mrcs mi` cdrchks cmi lk crkmtk` ms kxphmdik` lkegrk sdick mhh tbds okgaktrdcmh pmttkri cgaks erga tbk skk`s mi` cdrchks Edo"=;$) Edo"=;$) Pbds egra cmi lk usk` mhsg ms m `ksdoi ord` wbdcb wdhh bgh` tbk prgpgrtdgis mi` miohks ge  dts iuakrdcmh ditkrmctdgi prkskrvdio akmidios)  Pbds wmy cgivkrtdio ditkrmctdio iualkrs ditg egras cmi lk mcbdkvk` tbrguob m vkry sdaphk prgck`urk mi` stdhh prkskrvk akmidios) M Egra cmi mhsg lk cgivkrtk` ditg iualkrs ly cguitdio dts skk`s tbkrkegrk ui`krstmi`dio dts akmidio( lkbmvdgr( mi` euictdgi)  Pbds egra ds crkmtk` erga tbk ditkrmctdgi ge ;( 5( mi` 3 wbdcb crkmtks m sghd` egra tbmt ds sdadhmr tg tbk buami snuhh erga dts ergit mi` lmcn wdtb auschk) <2

Ikgaktry

hkt tbk egras spkmn <6=3

Edo) =;: Cgivkrtdio 3 ditkrmctdio iualkrs ditg m sghd` egra gr m pmttkri

<4

Ikgaktry

hkt tbk egras spkmn <6=3

Imragidcs Pbk Ditkrmctdio Bmragidc Iualkrs  Imragidcs ds cgickrik` mlgut edi`dio akmidios ge iualkrs tbrguob okgaktry) Ms sbgwi di tbk prkvdgus pmoks( iualkrs cmi ditkrmct crkmtdio  egras) Di gr`kr egr tbksk egras tg crkmtk bmragidc akmidios( sgak prgpkrtdks ge iualkrs bmvk tg lk ui`krstgg` lmsk` gi okgaktry) Smcrk` iualkrs ms nigwi di amiy cuhturks cmi mhsg lk ui`krstgg` tbrguob Okgaktry) Dt mhh cgaks erga tbk `dvdik Gik erga wbdcb mhh smcrk` iualkrs mi` okgaktry mppkmrk` tbrguob dts amidekstmtdgis) Mhh egras cmi lk ui`krstgg` mi` lkcgak di pkrekct bmragiy gick rkhmtk` tg tbk divdsdlhk cdrchk tbk hdobt ge Pbk Gik) Dt ds tbk mrt ge nigwdio tbk Mrcbktypks( ui`krstmi`dio tbka( tbkdr ditkrmctdgis( di gr`kr tg bmragidzk tbka)

DI@DIO BM\AGIDC I[ALK\S

Di gr`kr tg edi` bmragidc iualkrs( iualkrs aust lk rkprkskitk` di tbkdr okgaktrdcmh egras) Ms kxphmdik` prkvdgushy m cdrchk bms tg lk `dvd`k` ditg tbk ikk`k` iualkr di gr`kr tg crkmtk dts stmr sbmpk) Pbkrkegrk mi miohk cmi rkprkskit iualkrs) Pbmt—s wby tbk miohk 356 cmi rkprkskit tbk gik( wbdhk < cmi lk rkprkskitk` ly =26( 3 ly =<6( 0 ly 46( ktc)))  Pg edi` < bmragidc iualkrs( iualkrs bmvk tg lk cgivkrtk` cgi vkrtk` ditg miohks 36

Ikgaktry mi`

gik

ge

tbk

iualkrs

sbguh`

hkt tbk egras spkmn <6=3

lk

cgaphkakitmry tg tbk gtbkr gik) Sg de wk wmit tg edi` tbk bmragidc iualkr ge 3 dt wguh` lk 5 sdick tbk cgaphkakitmry ge =<6 ds 56 wbdcb mrk tbk miohks ge 3 mi` 5( smak egr iualkrs 0 mi` 0 rkprkskitk` ly 46 mi` 46 `korkks)  Micdkit cdvdhdzmtdgis cdvdhdzmtdgis `dvd`k` tbk cdrchk ditg 5

Edo) =5: Pbk sdx ms tbk pkrekct

ditkrskctdgis ge 5 cdrchks

skctgrs kmcb rkprkskitk` m wbghk gik) _bdhk dt ds lkhdkvk` tbmt 56 wms cbgski tg lk tbk miohk ge tbk gik wbghk skctgr sdick dt cmi lk `dvd`k` ly  amiy iualkrs) Bgwkvkr D lkhdkvk tbmt tbk rkmsgi egr cbggsdio cb ggsdio 5 ms m wbghk gik egr kmcb skctgr wms lkcmusk 5 ds tbk gihy iualkr tbmt pkrekcthy edts tbk skk`s ge 5 ditkrskctdio cdrchks wdtb tbk ckitrmh gik tbk skvki Edo"=5$) Cbggsdio tbk 356 cmi lk `uk tg tbk Huid!Sghmr smcrk` micdkit cmhki`mrs(  wbdhk 56 ds `dvdsdlhk ly amiy iualkrs mi` ds tbk pkrekct 5 `dvdsdgis ge tbk 356) Di gr`kr tg edi` 3 bmragidc iualkrs tbk miohk =26 cmi stdhh lk usk` egr tbk cgaphkakitmry miohks ge tbk trdmiohk) Ms egr 0 iualkrs tbk miohk 356 cmi lk usk`) Iualkrs agrk tbmi egur cmi usk tbk suaamtdgi ge tbk ditkrimh miohks ge stmi`mr` sbmpks gr tbk `dvdsdgis ge tbk cdrchk wbdcb wdhh lk pmrt ge  tbk 356 mhsg) Pbk sua ge ditkrimh miohks ge miy pghyogi ds "i!<$*=26 wbkrk i ds tbk iualkr ge sd`ks gr miohks)  M orgup ge bmragidc bmr agidc tbrkk tbr kk iualkrs cmi lk: 5(5(5 ' 0(5(=< '3(=<(=< ' 3(2(<0 ' 3(4(=2 ' 0(;(<6 ' 0(2(2 ' ;(0(<6 ' ;(;(=6 ' 2(3(<0 ' 2(;(=6 ' 4(0(?< )

3=

Ikgaktry

hkt tbk egras spkmn <6=3

 MC\K@ I[ALK\S I[ALK\S Ly `dvd`dio m cdrchk ditg kqumh `dvdsdgis iualkrs cmi crkmtk wbghk iualkrs ge `dvdsdgis ms =(<(3(0(;(5( 2(4(=6(=<(=;(=2(<6(<0(36(35(06(0;(56(?<(46(=<6( =26(356) Pbds ds m skt ge smcrk` iualkrs wbdhk tbkdr miohks mrk tbk `dvdsdgi ge tbk 356 `korkks ly tbgsk iualkrs wbdcb crkmtk m rkvkrsk skqukick ge  smak

iualkrs:

356(=26(=<6(46(?<(56(0;(06(35(36(<0(<6(=2(=;(=<(=6(4(2(5(

;(0(3( < (=) Samhh miohks sucb ms 0; `korkks cmi lk usk` di dts cgaphkakitmry  egra wbdcb ds =26!0;1 =3; `korkks) Pbk cguit ge iualkrs di tbds skt ds <0  wbdcb ds 5 mccgr`dio tg iuakrghgoy wbdcb ds tbk pkrekct p krekct `dvdsdgi ge m cdrchk)  Pbk suaamtdgi ge tbds skt prgvd`ks tbk iualkr ==?6 wbdcb ds 4 mccgr`dio  tg iuakrghgoy tbk pkrekct bmragidc iualkr ms wdhh mhsg lk kxphmdik` di ikxt ekw pmoks lmsk` gi tbk okgaktrdcmh egra ge 4) Lkcmusk mhh iualkrs mrk crkmtk` ly tbk Gik mi` mhh bmvk m ckitrmh cdrchk mt wbdcb tbk ckitrk ge tbk skk`s ds hgcmtk`( m gik cmi lk m``k` tg mhh tbds skqukick crkmtdio migtbkr smcrk` orgup ge iualkrs tbmt ds: ?(==(=3(=5(=4(<=(<;(3=(3?(0=(05(5=( ?3(4=(=<=(=2= mi`( 35=) Pbk cguit ge iualkrs di tbds skt ds =5 wbdcb ds ? mccgr`dio tg iuakrghgoy wbdcb mrk smcrk` iualkrs ms wdhh lk kxphmdik` di tbk ikxt pmoks) Sdaphdeydio tbk edrst skt ge iualkrs ly iuakrghgoy crkmtks m ikw skt tbmt ds =(<(3(0(;(5(2(4(=(3(5( 4(<(5(3(4(0(4(5(4(4(3(4(4 wbdhk tbk gtbkr skt cmi lk sdaphdedk` tg ?(<(0(?(=(3(?(0(=(;(=(?(=(=(0(=( ?(<(0(?(=(3(?(0(=(;(=(?(=(=(0(=(=) =)

3<

Ikgaktry

hkt tbk egras spkmn <6=3

 MC\K@ SDALGHGOT 

[i`krstmi`dio akmidios ge smcrk` egras gr smcrk` okgaktry ds tgtmhhy tbk smak tbdio ms ui`krstmi`dio tbk akmidios ge iualkrs mi` miohks di tbk divdsdlhk pmttkris lkbdi` egras) Dt ds tbk smak tbdio tg crkmtk akmidios lmsk` gi tbds bd``ki smcrk` hmioumok wbdcb ds mhh Smcrk` Sdalghgoy) Sgak iualkrs di Iuakrghgoy bgh` sgak akmidios sucb ms Gik tbk sdiouhmrdty gr tbk uidty(

Pwg tbk pghmrdty( Pbrkk tbk crkmtdgi( Egur tbk

Kmrtb mi` stmldhdty( ktc… Akmidios ge iualkrs cbmiok mccgr`dio rkhdodgis

tg mi`

cuhturks( pbdhgsgpbdks)

 Pbkrkegrk sgak cuhturks edi` iualkr =3 tg lk ge lm` hucn  ykt gtbkr cdvdhdzmtdgis edi` =3 tg lk m bghy iualkr) Bkrk D—a igt sbgwdio lm` gr ogg` hucn

iualkrs

gr

kvki

akmidios di rkhdodgis ykt D—a sbgwdio akmidios tbmt mrk

Edo) =?: Stmi`mr` Sbmpks \kskalhdio Iualkrs

`krdvk` erga okgaktry mi` stdhh cmi edt wdtb pbdhgsgpby mi` iuakrghgoy) Sgak iualkrs iualkr s mrk lkhdkvk` tg bmvk m okgaktrdcmh egra sucb ms gik wbdcb ds `kpdctk` ms m cdrchk gr m ckitrmh pgdit mi` rkskalhks sdiouhmrdty mi` diedidty( iualkr twg ds lkhdkvk` tg lk tbk hdik gr tbk twg pgdits lkdio pghmrdty( 33

Ikgaktry

hkt tbk egras spkmn <6=3

iualkr tbrkk tbr kk ds `rmwi ms m trdmiohk tbmt rkskalhks trdidty di tbrkk pgdits mi` crkmtdgi sdick dt—s tbk edrst okgaktrdcmh sbmpk( iualkr egur ds lkhdkvk` tg lk tbk squmrk tbmt rkskalhks stmldhdty hdnk m structurk wdtb egur pdhhmrs gr tbk kmrtb bmvdio tbk egur `drkctdgis "Igrtb( Kmst( Sgutb( mi` _kst$( wbdhk gtbkr stmi`mr` sbmpks rkskalhk sgak gtbkr iualkrs Edo"=?$) Imragidcs kxphmdis tbk akmidios tbrguob sbmpks mi` ms kxphmdik` lkegrk sbmpks mrk crkmtk` erga tbk ditkrskctdgis ge cdrchks mt m ckitrmh cdrchk) Dt wms mhsg kxphmdik` tbmt iualkrs mrk tbk `dvdsdgis ge tbk gik gr tbk cdrchk tbmt—s  wby tbk structurk ge stmi`mr` okgaktrdcmh sbmpks cgak erga er ga tbk `dvdsdgi ge  m cdrchk Edo)4)

Edo) =2: Iualkrs Ms Pbk @dvdsdgis ge M Cdrchk

Iualkr Gik: Pbk pgdit gr tbk ckitrk gr tbk cdrchk mi` ms kxphmdik` dt rkprkskits diedidty( Pbk Gik( Pbk crkmtgr ge mhh tbdios( [idty mi` sdiouhmrdty) 30

Ikgaktry

hkt tbk egras spkmn <6=3

Iualkr gik ds tbk Mrcbktypk ge tbk crkmtgr( tbk Bkrg gr tbk Hkm`kr mi` tbk smcrk` strkma) Iualkr Pwg: Pbk pghmrdty lktwkki twg pgdits tbmt crkmtks ditkrmctdgi) Iualkr twg ds tbk edrst pbmsk ge crkmtdgi wbdcb crkmtk` tbk edrst skk` ykt dt bms ig prgpgrtdgis) Dt cmi rkprkskit strgio ditkrmctdgi tbmt cmi cmusk cgiehdcts `uk tg tbk miohk =26 sdick tbk twg pgdits gppgsk kmcb gtbkr) dt rkprkskits gppgsdtdgi) Iualkr twg ds tbk Mrcbktypk ge pghmrdty( tbk ekadidik pmrt ge tbk ami tbmt ikk`s ditkrmctdgi( mi` trduapbmh vdctgry di lmtthks) Iualkr twg rkprkskits tbk khkakit Edrk) Iualkr Pbrkk: Pbk edrst crkmtdgi lkegrk tbk Kmrtb di tbk bkmvkihy wgrh`) Dt ds tbk skcgi` pbmsk ge crkmtdgi wbdcb crkmtk` tbk edrst twg `dakisdgimh sbmpks gr phmimr sbmpks) Pbds pbmsk ds tbk stmrt ge prgpgrtdgis mi` miohks) Dt ds tbk edrst stkp tgwmr`s akmidios) Mi` sdick dt—s cgapgsk` ge tbrkk pgdits bmvdio mi miohk =<6 lktwkki tbka dt rkprkskits trdik wbdcb ds mi miohk bmvdio ig cgiehdcts) Pbmt—s lkcmusk wbki gik ge tbk tbrkk pgdit hgm`s gi tbk gtbkr twg( tbky cmi lkmr tbk hgm` hdnk tbk mrcb structurks gr mrcm`ks) Iualkr tbrkk ds tbk Mrcbktypk ge pkmck mi` ds tbk mrcbktypk ge bkmvkis( tbk bkmvkihy `dvdik crkmtdgi mi` ktkridty) Iualkr tbrkk rkprkskits tbk khkakit mdr) Iualkr egur: Pbk crkmtdgi di tbk Kmrtbhy wgrh` wbdcb ds m cgrruptk` wgrh`) Dt ds tbk tbdr` mi` edimh pbmsk ge crkmtdgi wbdcb cmi crkmtk tbrkk tbr kk `dakisdgimh sghd`s mi` egras) Sdick dt—s cgapgsk` ge egur pgdits bmvdio 46 `korkks lktwkki kmcb( dt rkprkskits stmldhdty mi` lmhmick de bgrdzgitmh( ykt tbk rkhmtdgi 46 `korkks wbdcb ds cmhhk` tbk squmrk ds igt m ogg` rkhmtdgi ms dt cmi cghhmpsk lkcmusk ge crmcns de vkrtdcmh) De iualkr egur wbdcb rkprkskits tbk 3;

Ikgaktry

hkt tbk egras spkmn <6=3

kmrtb m``k` tg dts spdrdt tbk bkmvkis dt cmi rkmcb tbk trdik tg edi` tbk Gik)  Pbds cmi lk kxphmdik` tbrguob m pdhhmr bgh`dio m buok stgik wdtb m =<6 `korkks suppgrtdio trdmiohk gr usdio `gaks mi` mrcbks di ludh`dios) Ms tbk  Mrcbks mi` `gaks edx tbk kmrtbhy ludh`dios tg og vkrtdcmhhy tgwmr`s tbk sny( tbk wgrh` wms edxk` ly tbk Bghy Spdrdt) Pbk egur ds tbk mrcbktypk ge tbk skhe  gr tbk psycbk tbmt struoohks momdist cgrruptdgi trydio tg lk `dvdik) Iualkr egur rkprkskits tbk khkakit Kmrtb) Iualkr Edvk: Pbk edrst crkmturk gi tbk kmrtb mi` cmi rkprkskit buamis) Sdick mhh iualkrs cmi lk crkmtk` erga = tg 0 mi` crkmtdgi ds tbrguob 3 stmoks metkr tbk gik) Dt mppkmrs hdnk iualkr edvk cmi lk 0.= wbdcb ds m``dio  m spdrdt gr hdobt erga tbk Gik tg tbk kmrtb odvdio dt hdek mi` prgtkctdgi momdist cgrruptdgi( gr crkmtdio buamis erga tbk kmrtb) Edvk skk`s cmi crkmtk m buami emck bmvdio < kyks( m igsk( mi` hdps bmvdio m sphdt di dts bmhe) Iualkr ; ds tbk bkm` mi` egur hdals bmvdio m ckitkr wbdcb rkprkskits tbk psycbk mi` dts ckitrmh skhe di di tbk bkmrt) Dt ds tbk Mrcbktypk ge hdek( prgtkctdgi mi` struoohk momdist `kmtb) Iualkr Sdx: Dt rkprkskits ditkrcgursk mi` hgvk sdick dt—s tbk ditkrcgursk ge  twg tbrkks gr twg trdmiohks) dt ds 3x<( 3.3) Pbk miohk 56 ds mi miohk tbmt crkmtks mhh ikckssmry miohks ge hdek wdtbgut wdtbgut tbk squmrk gr tbk 46 46 `korkks) Dt dichu`ks gppgsdtdgi( trdik( mi` skxtdhk) _bki rkmcbdio tbk sdx tbk edvk m``s tg dts spdrdt gik gr buamis m`` tg tbkdr spdrdts ly m``dio gik tbrguob tbk bghy rdtumhs ge amrrdmok( ditkrcgursk( hgvk mi` lgi`) Iualkr 5 ds tbk ditkrmctdgi ge pghmrdtdks tbmt crkmtks pkmck( igt wmrs mi` cgiehdcts) Dt ds tbrguob `deekrkicks( vmrdktdks( pghmrdtdks( mi` cbmioks> hgvk( pkmck mi`  wds`ga cmi lk mcbdkvk`) Di tbk emck dt m``s tbk kyk cbmnrm ms m sdxtb skk` 35

Ikgaktry

hkt tbk egras spkmn <6=3

egr tbk buami emck) Iualkr sdx ds tbk mrcbktypk ge bghy amrrdmok( bghy  rdtumhs( disdobt( cgiscdgusikss( Ditkordty( wds`ga mi` amodc) Iualkr sdx rkprkskits tbk khkakit _mtkr) Iualkr Skvki: Dt rkprkskits wbghkikss wbghkik ss mi` tbk pkrekct sguh) M cdrchk cmi—t lk `dvd`k` ditg skvki) Skvki ds lkygi` tbk sdx mi` dt ds tbk pkrekctdgi ge tbk pkrekctdgi) Dt ds tbk ? tb ad``hk cdrchk gr tbk ckitrk ge tbk 5 wbdcb ds tbk gik mi` m``dio gik tg tbk 5 tg edi` Pbk Gik) Iualkr skvki ds tbk mrcbktypk ge  tbk iglhks( tbk `dvdik sguhs( tbk mscki`dio amstkrs( smdits( tbk trkk ge hdek( ehydio tg tbk bkmvkis( tbk skvki wmrs tgwmr`s cgitrghhdio tbk diikr skhe) Iualkr skvki rkprkskits Ktbkr) Iualkr Kdobt: Dt rkprkskits uidvkrsmh ditkrmctdgis mi` pkrekct stmldhdty mi` lmhmick ly twg ditkrmctdio egurs) Iualkr kdobt rkprkskits tbk cgaphktk tbrkk `dakisdgimh sghd` egras crkmtk` mt tbk tbdr` pbmsk ge crkmtdgi ly tbk egur) M hdik !wbdcb ds iualkr twg! cmi crkmtk m <@ sbmpk wbki bmvdio  migtbkr hdik) Pbkrkegrk twg ly twg crkmtks m < `dakisdgimh sbmpk) Di gr`kr tg crkmtk m 3@ sghd` tbkrk aust lk m tbdr` hdik m
Ikgaktry

hkt tbk egras spkmn <6=3

squmrks) Pbds amodc squmrk wms usk` ly mhh cdvdhdzmtdgis) Iualkr 2 ds tbk mrcbktypk ge tbk Mhcbkadst mi` tbk skmrcb egr tbk ogh`ki sguh mi` tbk ogh` qumhdtdks) Dt—s mhsg mi mrcbktypk egr Aystdc rdtumhs mi` gccuhtdsa) Iualkr Idik: Dt rkprkskits bmragiy mi` di`dvd`umtdgi) Dt ds tbk ditkormtdgi ge tbk uicgaagi mi` tbk gppgsdtks) Dt—s tbk `kkp spdrdtumhdty mi` dibkrdtk` pmrmigramh) Iualkr idik ds tbk `dvdsdgi ge tbk cdrchk ly 06 `korkks) Pbds crkmtks amiy pgssdldhdtdks ge ditkrmctdgis wdtbgut cgiehdcts ykt ikk`s spdrdtumhdty gtbkrwdsk ig ditkrmctdgis wguh` tmnk phmck) Pbk stmr ge idik cmi egra m 3@ sghd` wbki m``dio migtbkr 4 skk`s wbdcb crkmtks tbk =2) Mi` sdick =2 ds m pkrekct `dvdsdgi ge tbk cdrchk m``dio tbk ckitrmh cdrchk wguh` crkmtk =4 wbdcb ds m pkrekct bghy iualkr) Ms tbk 4 ds `kkphy spdrdtumh mi`  wdsk m``dio gik tg dts =2 crkmtks tbk =4( mhsg wbki m `kkphy spdrdtumh mi`  wdsk pkrsgi nkkps skkndio egr Pbk Gik( Pbk Gik m``s hdobt tg bds sguh mi` edi`s bds wmy tg kihdobtkiakit) Pbk idik ds tbk mrcbktypk ge Cggpkrmtdgi( Cghhmlgrmtdgi( Pbk pkmck amnkr( Pbk Vsycbdc( tbk kihdobtkik` sguh( Oigstdcdsa)

32

Ikgaktry

hkt tbk egras spkmn <6=3

IOHKS GE DIPK\MCPDGI

Amiy miohks ge ditkrmctdgi cmi lk egui` erga tbk miohks ge kmcb iualkr)  Miohks cmi lk kmsdhy `krdvk` ly tbk suaamtdgi ge tbk smak miohk) Mhh iualkrs mrk erga Pbk Gik mi` Vmrt ge tbk Gik( tbmt—s wby tbky mhh hkm` tg  Pbk Gik wbdcb ds tbk miohk 356 `korkks)

Iualkr Gik: 356 Iualkr Pwg: =26 =26((356 Iualkr Pbrkk: =<6 =<6((<06 <06((356 Iualkr Egur: 46 46((=26 =26(
34

Ikgaktry

hkt tbk egras spkmn <6=3

Dt mppkmrs erga tbk prkvdgus miohks tbmt tbk miohks =26( =<6( mi` 46 mrk vkry  ksskitdmh miohks egr crkmtdgi) Pbky mrk tbk miohks tbmt cmi egra okgaktrdcmh pmttkri ord`s mi` edt pkrekcthy) Ly `dvdsdgis mhh miouhmr iualkrs cmi lk prg`uck`) =26'<146( =<6'<156( 46'<10; =<6'0( =<6'3106) Dt mppkmrs momdi tbmt mhh iualkrs mi` mhh egras cmi ly crkmtk` erga gik tg egur) Egr kxmaphk tbk egur bms m twg mppkmrdio di tbk=26 lut di m ikw amidekstmtdgi bmvdio tbk 46 mi`
06

Ikgaktry

hkt tbk egras spkmn <6=3

\MDPS ge OKGAKP\DCMH I[ALK\S

Iualkr Gik: ds tbk bd``ki trmdt tbmt mhh iualkrs mi` sbmpks bmvk mi` cmi gihy lk skki wbki cgaphktk mi` pkrekctk`) Iualkr Egur: dt bms tbk trmdt ge twg mi` ikk`s tbk twg) Iualkr Edvk: dts trmdts mrk bd``ki mi` ds hgst de dt `d` igt skmrcb egr Pbk Gik sdick dt wms crkmtk` erga tbk egur wdtb m``dio gik tg dts sguh) Iualkr Sdx: dt bms tbk trmdts ge twg mi` tbrkk mi` ikk`s tbka) Iualkr Skvki: Dt ds tbk edvk metkr edi`dio dts wmy tg Pbk Gik) Iualkr Kdobt: Dt bms tbk trmdts ge twg mi` egur mi` ikk`s tbka) Iualkr Idik: Dt bms tbk trmdts ge tbrkk mi` tbrkk)  M orgup ge bmragidc iualkrs lmsk` gi trmdts ds <(0 ' <(3(5' ;(?' <(0(2' 3(5(4

0=

Ikgaktry

hkt tbk egras spkmn <6=3

 M\AGIDZDIO  M\AGIDZDIO SMC\K@ MIOHKS MIOHKS

Vrkvdgushy dt wms kxphmdik` tbmt tbkrk ds m rkhmtdgi lktwkki iualkrs mi` miohks) Miohks akitdgik` prkvdgushy cmi okikrmtk agrk miohks ly  sultrmctdio tbka erga =26 gr 356) Eghhgwdio tbk smak prkvdgus ruhks ge  bgw tg bmragidzk iualkrs ly tbk =26 mi` 356 suaamtdgis( bmragidzk` miohks cmi lk egui` ly cgivkrtdio bmragidc iualkrs ditg miohks) Bkrk ds m orgup ge bmragidc miohks: 56(56(56 ' 46(56(36 ' =<6(36(36 ' =<6(0;(=; ' =<6(06(<6 ' 46(?<(=2 ' 46(0;(0; ' ?<(46(=2 ' ?<(?<(35 ' 0;(=<6(=; ' 0;(?<(35 ' 06(46(; ) Agrk miohks cmi lk egui` ly tbk trmdts ge iualkrs sucb ms 46(=26' 56(=26(=<6' 0;(=26(46'06(=<6)

0<

Ikgaktry

hkt tbk egras spkmn <6=3

 M\AGIDC  M\AGIDC I[ALK\S— I[ALK\S— _BKKH

Lkcmusk iualkrs mrk cgapgsk` ge amdi idik iualkrs erga = tg 4 mi` 4 ds m bmragidc iualkr tbmt bmragidzks iualkrs( iualkr idik cmi rkprkskit m wbkkh) Pbkrkegrk m cdrchk ge idik iualkrs kmcb mt m skctgr ge tbk 4 `dvdsdgis cdrchk cmi rkprkskit iualkrs lkdio di bmragiy Edo"=4$)

Edo) =4: Bmragidc Iualkr—s _bkkh

 Pbk idik iualkrs di tbk wbkkh cmi sbgw m cychk tbmt ds sdadhmr tg buami hdek) M ami ds lgri mt tbk gik erga tbk spdrdt ge Pbk Gik( bk stmrts edobtdio  mi` crydio wbki mt tbk twg( bk tbki stmrts tg hkmri mi` lk agrk crkmtdvk mi` hgvk tg crkmtk tbdios wbki mt tbrkk( bk tbki stmrts tg lk rmtdgimh mi` cgrruptk` sdick bk stmrts bmvdio kxpkrdkick mt tbk egur( Metkr tbds bk lkdios tg lk m buami wbg ds rkspgisdlhk egr bdaskhe mi` stmrts tg edi` bdaskhe  lkdio m ami mt tbk edvk) Pbk ami tbki stmrts tg edi` agrk purpgsk di tbk  wgrh` sg bk okts amrrdk` amrr dk` mt tbk sdx( tbki t bki bk stmrts tg edi` miswkrs tdhh bk edi` edi` bds sguh mi` ds cgiikctk` wdtb bds spdrdt mt tbk skvki) M ami wbg edi`s bds  wmy tg bds sguh stmrts tg lk ditg aystdcdsa gr gccuhtdsa gr rkhdodgus lkhdke( l khdke( rdtumhs( mi` lk wdsk mt tbk Kdobt( mi` metkr lkdio sg `kkp cgiikctk` wdtb tbk 03

Ikgaktry

hkt tbk egras spkmn <6=3

hdobt di bdaskhe gr lkdio rkehkctk` erga Og` bk stmrs lkdio kihdobtkik` mt tbk idik) De m pkrsgi rkmcbks mhh tbksk hkvkhs bk tbki kmts erga tbk trkk tr kk ge hdek mi` stmrts m ikw cychk di m ikw ktkrimh wgrh`) Iualkr bmragidks cmi lk mcbdkvk` erga tbds wbkkh) Amiy skqukicks cmi lk `khdvkrk` sucb ms =(3(;(?(4' <(0(5(2' =(0(?' <(;(2' 3(5(4') Ditkrmctdgis ge iualkrs prgvd`k akmidios( egr kxmaphk=(3(;(?(4 ds agrk ge  m pkmckeuh mi` spdrdtumh skqukick skqukick stmrtdio erga tbk gik tbki t bki edi`dio tbk Gik tdhh edi`dio bmragiy mi` pkmck)

00

Ikgaktry

hkt tbk egras spkmn <6=3

GHG\S MI@ I[ALK\S

Iualkrs cmi lk cgivkrtk` ditg cghgrs stmrtdio  erga Lhmcn mi` ki`dio wdtb _bdtk) Iualkr gik ds Lhmcn( twg ds \k`( tbrkk ds Grmiok( egur ds Tkhhgw( edvk ds Orkki( sdx ds Lhuk( skvki ds Di`dog( kdobt ds Udghkt( mi` idik ds _bdtk Edo"<6$)

Edo) <6: Cghgrs mi` Iualkrs

Dt mppkmrs erga tbk wbkkh tbmt Lhmcn wms tbk stmrt ge tbdios nigwdio tbmt gik bkrk ds m pbmsk gr m stmok mi` igt Pbk Gik wbg ds tbk crkmtgr) Crkmtdgi stmrtk` mt \k` ms `mys stmrt erga tbk sui skt di amiy cuhts mi` rkhdodgis  wbdhk edrk ds \k`) Vkmck mt tbrkk mppkmrs mpp kmrs tg bmvk tbk Grmiok cghgr wbdcb ds m bkmhdio cghgr( wbdhk egur ds Tkhhgw wbdcb ds tbk kmrtb cghgr) Edvk ds tbk Orkki kikroy ge tbk buami bkmrt) Sdx ds tbk lhuk wmtkr cghgr( skvki ds Di`dog wbdcb ds m bkmhdio spdrdtumh cghgr) Kdobt ds Udghkt wbdcb ds mhsg m spdrdtumh cghgr) Ms egr idik dt ds tbk bmragiy tbmt rkmcbks kihdobtkiakit mi` tbk stmrt ge m ikw cychk wbdcb ds _bdtk gr _bdtk hdobt( gr ktkridty)  Pbds wbkkh ds igt m wbkkh egr skhkctdio cghgrs ms tbk =< cghgr wbkkh( ykt dt ds usk` gihy tg amtcb cghgrs wdtb iualkrs tg bmvk tbkdr akmidios)

0;

Ikgaktry

hkt tbk egras spkmn <6=3

BK KI@ GE CTCHKS PBK =3

 Ms kxphmdik` prkvdgushy `dvd`dio tbk cdrchk prgvd`ks m skt ge iualkrs mi` miohks wbdcb ds =(<(3(0 (;(5( 2(4(=6(=<(=;(=2(<6(<0(36(35(06(0;(56(?<(46(=<6( =26(356) Dt wms mhsg kxphmdik` tbmt tbds skt cmi lk sdaphdedk` ms tbk skqukick =(<(3(0(;(5(2(4(=(3(5( =(<(3(0(;(5(2(4(=(3(5( 4(<(5(3(4(0(4(5(4(4(3(4(4) 4(<(5(3(4(0(4(5(4(4(3(4(4)  Pbds skqukick bms sgak prgpkrtdks sdick dts suaamtdgi prgvd`ks tbk iualkr =3; wbdcb ds tbk cgaphkakitmry miohk ge 0; tbk kdobt mi` tbk iualkr 4 wdtb m``dio dts uidts) Pbds skqukick mhsg bms gtbkr prgpkrtdks ly  m``dio dts iualkrs wbdcb prgvd`ks smcrk` iualkrs egr kxmaphk> =.<13( 3.01?( ;.51==(ktc…Pbk smak skqukick cmi lk m``k` ly migtbkr wmy   wbdcb ds sdadhmr tg m``dio tbk tb k Edlgimccd skqukick tbmt m``s smcrk` iualkrs hdnk m``dio =.<13(<.31;(3.01?( 0.;14) Kmcb wmy ge m``dio tbk skqukick prgvd`ks migtbkr orgup ge smcrk` iualkrs) Bkrk ds tbk edrst skt ge  iualkrs

:3(?(==(=?(0(=;(2(=<(=3(=;(=<(=2)

Pbk

skcgi`

skt

ds

3(;(?(4(==(=0(=?(=6(0(4(=;(==(2(4(=<(=3(=;(=;(=2(=<(=<(=2)  Ms kxphmdik` lkegrk( idik rkprkskits tbk pbysdcmh cdrchk ms dt cgitmdis tbk idik iualkrs wbdhk di bmragiy) Iualkr idik wms mhsg kxphmdik` tg lk mi ki` ge m cychk mi` m stmrt ge m ikw cychk) Pbmt—s wby iualkrs di t bk skqukick =(<(3(0(;(5(2(4(=(3(5( 4(<(5(3(4(0(4(5(4(4(3(4(4 crkmtk m skqukick tbmt nkkps ogdio di cychks tdhh ki`dio mt tbk hmst 4) Lkcmusk tbk 4 ds tbk ki` ge  kmcb cychk tbds skqukick ds pmrt ge =3 cychks) Pbk cychks nkkp rgtmtdio  05

Ikgaktry

hkt tbk egras spkmn <6=3

mrgui` tbk ckitkr ge tbk idik iualkrs wbkkh tdhh tbk hmst mi` edimh cychk tbk tbdrtkkitb

cychk)

Bkrk

mrk

tbk

iualkrs

di

kmcb

cychk:

=(<(3(0(;(5(2(4'=(3(5(4'<(5 =(<(3(0(;(5(2(4'=(3(5(4'<(5'3'4'0'4'5'4'4' '3'4'0'4'5'4'4' 3'4'4 Edo"<<$) Kmcb

cychk

ge

tbk

skqukick

cmi

lk

suaak`

tg

lk

=='=4'2'3'4'0'4'5'4'4'3'4'4) Pbk Amymis lkhdkvk` =3 tg lk tbk ki` ge  cychks tbmt tbk hgio cguit cmhki`mr cguitk` egr) Pbky P bky mhsg usk` tg `dvd`k `dvd`k tbk ykmr ditg m cychk ge =2 agitb kmcb <6 `mys) Dt ds igw chkmr tbmt erga tbk suaamtdgi ge kmcb twg iualkrs di tbk skqukick crkmtks=< iualkrs wbdhk tbk hmst ds =2 mi` tbk =2x<61356 wbdcb ds tbk iualkr ge `mys di mi micdkit Huid!sghmr ykmr) =< ds m systka ge cychks tbmt wk usk kmcb `my wbdhk tbk=3 ds tbk ki` ge cychks) Pbmt—s wby =2 cmi rkprkskit tbk =< cychks gr agitbs  wbdhk =3 ds tbk ki` ge cychks mi` tbk cgadio ge tbk ikw sui mccgr`dio tg tbk Amymis)

Edo) <<: Pbk =3 Cychks ms \kprkskitk` gi Pbk Iualkrs _bkkh

0?

Ikgaktry

hkt tbk egras spkmn <6=3

Iualkr =< ds usk` tg rkprkskit tbk pkrekct uidvkrsmh cychks mi` ditkrmctdgis ms dt ds m vkry smcrk` iualkr tbmt cgaks gut ge <( 3( 5( mi`=<) Dt mhsg bms tbk ditkrmctdgis ge 3 mi` 0) Pbmt—s wby iualkr twkhvk bms mhh smcrk` miohks ge  ditkrmctdgi> =26( =<6( 46( 56) Pbksk miohks cgak erga cgivkrtdio =< tg dts miohk wbdcb ds 36 tbmt prgvd`ks 36(56(46(=<6(=;6(=26(<=6(<06(
okgaktry

ly

tbk

ditkrcgursk ge twg trdmiohks  wbdcb

crkmtks

tbk

sdx)

Bmvdio tbk pkrekct 5 di dts sghd` egra crkmtks tbk =< ly  m``dio tbk gutkr skk`s ge  tbk 5) Pbds ds `gik ly  auhtdphydio tbk 5 ly < wbdcb crkmtks tbk =< cychks di m ykmr( di m `my( di m idobt( tbk zg`dmc( bmragidc

m

amodc

wbkkh(

cghgrs

wbkkh(

huimr cychks pkr ykmr( tbk mspkcts di mstrghgoy cbmrts mi` tbk agst bmragidc

Edo) <3: Iualkr twkhvk crkmtk` erga tbk ditkrcgursk ge < trdmiohks

miohks =<6( mi` 56) Dt mhsg crkmtks tbk pkrekct iualkr 56 tbmt ds tbk iualkr ge adiutks di mi bgur wbdcb wms kxphmdik` kmrhdkr di tbk prkvdgus pmoks Edo"<3$) 02

Ikgaktry

hkt tbk egras spkmn <6=3

\GSSDIO I[ALK\S % DIPK\CG[\SK

 _bki auhtdphydio twg iualkrs ly kmcb gtbkr( m prg`uct ds prg`uck`) Iualkrs mrk prg`uctdgis ge gtbkr iualkrs) Pbky mrk tbk rksuht ge  rkprg`uctdgi gr ditkrcgursk tbmt tmnks phmck lktwkki twg iualkrs gr agrk pgssdldhdtdks ge iualkrs) Egr distmick iualkr =< ds tbk ditkrcgursk ge twg pgssdldhdtdks 3x0 mi`
[AAMPDGI( DIPKO\MPDGI % C\GSSDIO

 M``dio twg tg egur crkmtks 5( tbmt—s wbki ditkormtdio m squmrk wdtb m hdik  wbdcb prg`ucks m bkxmogi ykt m `kegrak` bkxmogi) Dt ds smd` tbmt mhh iualkrs cmi lk crkmtk` erga gik tg egur mi` tbmt—s pgssdlhk sdick tbky bmvk tbk agst ksskitdmh trmdts) Ditkormtdio twg iualkrs gr m``dio twg ge tbka ikk`s m rkmrrmiokakit prgckss egr tbk ditkrimh miohks ge tbk sbmpk di gr`kr tg kxdst) 04

Ikgaktry

hkt tbk egras spkmn <6=3

 _bki crkmtdio tbk sdx ms m rksuht ge  ditkormtdio <.0 di tbk pbysdcmh wgrh`( tbk sguh ge sdx stmrts tg kxdst ms m akmidio gr m cgickpt gr hdnk mrcbktypks) Di gr`kr tg kxdst dt aust tmnk m ikw egra mi` lkcgak m ikw  crkmturk) Pbmt—s wbki tbk 5 ds odvki spdrdt erga Pbk Gik di gr`kr tg kxdst) _bki tbk 5 stmrts tg nigw dt ds m 5 mi` igt m <.0 dt tbki stmrts tg edi` dts grdodimh trmdts wbdcb cgaks erga tbk ditkrcgursk ge tbk 3x<) Bkrk tbk 5 stmrts tg lk egrak` hdnk m ektus di tbk wgal ge bds agtbkr) Pbk miohk 56 tbmt prgvd`ks lgtb =<6 mi` =26 cmi tbki crkmtk tbk sbmpk)  Miohks mrk tbk amidekstmtdgis mi` tbk mctdgis ge tbk spdrdt tbmt ds dibkrdtk` erga  Pbk Gik) Miohks mrk tbk t bk stmrt ge tbk crkmtdgi

Edo) <0: Miohk msskalhy mi` rkmrrmiokakit

prgckss) Miohks mi` prgpgrtdgis prg`uck` ly miohks mrk amidekstmtdgis tbmt mct tbrguob tbk hmw ge dts purpgsk) Pbmt—s  wby tbk miohk crkmtks tbk sbmpk tbrguob tbk mrkm ge kmcb trdmiohk di kmcb skctgr ge tbk sbmpk) Pbk miohk ge 5 di tbds cmsk ds 56 wbdcb msskalhks tbk bkxmogi di dts pkrekct egra bmvdio tbk trmdts ge 3 mi` < mi` tbk ditkormtdgi gr suaamtdgi ge < mi` 0 Edo"<0$

;6

Ikgaktry

hkt tbk egras spkmn <6=3

Ikgaktry Egras Ly Pbk Mutbgr

 _bdhk `kvkhgpdio Ikgaktry D trdk` tg cgistruct sgak egras tg prgvk tbmt iualkrs cmi lk cgivkrtk` tg egras mi` vdck vkrsm ms kxphmdik` di prkvdgus cbmptkrs) Dt mhh stmrtk` wbki D egui` tbmt tbgsk iualkrs cmi amidekst di sucb mrcbktypmh egras bmvdio smcrk` s mcrk` prgpgrtdgis) Mi` Pbmt—s wbki D ui`krstgg` tbmt tbds cmi lk mpphdk` tg mhh edkh`s ge hdek stmrtdio erga cmrtggi `rmwdio mi` cbmrmctkr `ksdoi tg mimtgay mi` midamh egras) D egui` dt cmi lk mpphdk` tg micdkit wgrh` sdalghgoy mi` kvki ag`kri pbysdcs) Dt cmi bkhp us ui`krstmi` mhhgtrgpks ge aghkcuhks mi` vdrus okgaktrdcmh egras) Ikgaktry cmi og vkry emr tg Imigtkcbighgoy mi` agrk) Kvki phmtgidc sghd`s( okg`ksy( mi` mi` Ermctmh Okgaktry cmi lk mpphdk` usdio smak smak aktbg`s ge bmragidks mi` miohks ge ditkrmctdgis `dscussk` `dscussk` di prkvdgus cbmptkrs) Di tbds cbmptkr D sbgw ygu sgak ge ay vkry lmsdc rguob snktcbks tbmt D `rkw wbki D wms `kvkhgpdio Ikgaktry ) D—a sbgwdio tbds sg ygu adobt skk sgak vkry lmsdc kxmaphks ge cgivkrsdgis erga iualkrs tg sdaphk egras) KGAKP\T \G[OB SNKPCBKS

D crkmtk` tbk emck di edo"<;$ erga iualkrs ?(0(0) Erga tbk prgpkrtdks ge tbgsk iualkrs tbds mrcbktypk pkrsgimhdty ds ge m strgio mi` vkry wdhhdio  cbmrmctkr tbmt bmr`hy cbmioks dts adi` ykt bms amodcmh mldhdtdks mi` supkr pgwkrs) Pbds cbmrmctkr bms m vkry stmlhk mi` lmhmick` imturk)

Edo) <;: M emck crkmtk` erga ?(0(0

;=

Ikgaktry

hkt tbk egras spkmn <6=3

 Pbk lkmst ds m egra tbmt crkmtks tbk mrcbktypk ge Hdgis( Cmts( mi` gtbkr hdvdio  crkmturks) Dt ds crkmtk` erga 5(5(5 wbdcb akmis tbmt sucb mrcbktypks bmvk vkry strgio  spdrdtumh mldhdtdks ykt cmi lk vkry kvdh edo"<5$) Amylk tbmt—s wby dt ds lkhdkvk` tbk mitdcbrdst bms tbk iualkr 555) Amylk tbmt—s wby cmts

Edo) <5: Pbk Hdgi Crkmtk` Erga 5(5(5

mrk mhsg lkhdkvk` tg bmvk sgak aystdcmh pgwkrs- Tkt 5(5(5 ds m pmttkri bmvdio  prgpgrtdgis tbmt cmi crkmtk amiy gtbkr egras mi` ds vkry uskeuh) Ig gik cmi smy cmts mrk kvdh lkcmusk tbky bmvk m lkmst mrcbktypk)

@gos( Pbds gik wms vkry euiiy lkcmusk D wms trydio tg crkmtk m pgwkreuh amidekstmtdgi ge tbk iualkr =4 wbki tbds `go mrcbktypk mppkmrk` erga 3(;(;(5 edo"
Edo)
Erga 3(;(;(5

ms `dscussk` kmrhdkr) =4 ds pgwkreuh ykt hgvdio mi` di bmragiy) =4 ds kvki cgisd`krk` tg lk tbk oumr` ge spdrdtumh omtks) Dsi—t tbds tbk s pdrdt ge `gos7  Pbk hgvdio( tbk pgwkreuh( tbk oumr`dio( mi` tbk agst di bmragiy wbki di hgvk)

;<

Ikgaktry

hkt tbk egras spkmn <6=3

 Pbk Koyptdmi Spbdix di tbk Odzm Vhmtkmu edo"<2$( Pbds wms gik ge ay `dscgvkrdks  wbki D wms skmrcbdio egr tbk agst stmlhk egras ge okgaktry mi` iualkrs) =5 wbdcb cgaks erga 0x0 gr
Edo) <2: Pbk Spbdix Crkmtk` Erga 0(0

pgwkr `uk tg tbk lmhmick di =5( lgh`ikss mi` pgwkr di 2( stmldhdty mi` wdhh di 0( mi` tbk moorkssdvkikss di iualkr <) Pbds ds wby tbk prgpgrtdgis ge  tbds emck mrk vkry pgwkreuh mi` bmvk m bd``ki akssmok tbmt wk mhh ekkh wbki  wk skk dt)

 Pbk cbdcnki wms tbk euiidkst wbki D wms trydio  sgak iualkrs di bmragiy sucb ms 0(2(2 mi` m cbdcnki mppkmrk` edo"<4$) Ge cgursk ms D akitdgik` lkegrk sucb cgaldimtdgis cmi lk l k usk` tg crkmtk gtbkr sbmpks mi` egras) Pbds just sbgws

Edo) <4: Pbk Cbdcnki crkmtk`

bgw gur imturk ds ruhk` ly m skt ge rmtdgs( miohks

erga 0(2(2

mi` prgpgrtdgis tbmt cmi sdaphy lk ui`krstgg` tbrguob iualkrs mi` cgivkrtk` tg smcrk` sbmpks mi` hdek egras)

;3

Ikgaktry

hkt tbk egras spkmn <6=3

Gik ge ay kvdh cbmrmctkrs tbmt D crkmtk` erga m orgup ge iualkrs 0(5(0(4 edo"36$) D rkakalkr ekkhdio mermd` wbki D skki dt lkcmusk D usk` tg `rkma ge dt) D ekht lkttkr sgakbgw metkr `rmwdio dt amylk tbds wms m Cmrh Juio—s di`dvd`umtdgi prgckss gr sgak sgrt ge mrt tbkrmpy wbki D rkvkmhk` m bd``ki

Edo) 36: M cbmrmctkr crkmtk`

mrcbktypk erga ay psycbk mi` tggn cgitrgh gvkr dt)

erga 0(5(0(4

 Ms akitdgik` di tbk lggn ditrg`uctdgi( Pbds ds igt m euhh dhhustrmtk` lggn lgg n ge  Ikgaktry) Ikgaktry ds emr lkygi` mhh tbksk kxmaphks mi` bms aucb agrk cmpmldhdtdks( daphdcmtdgis( mi` mpphdcmtdgis) Nkkp ygur crkmtdvdty mi` hdstki tg ygur bkmrts tg ui`krstmi` imturk—s hmioumok) Stmy tuik` mi` `ksdoi hdnk imturk lkcmusk imturk tmhns) [sk ygur adi`( lg`y( mi` spdrdt) [sk ygur cgapmss( ruhkrs mi` prgtrmctgrs( tg hkt tbk egras spkmn)

;0

Ikgaktry

hkt tbk egras spkmn <6=3

\ KEK\KICKS KEK\KICKS =! \dcbmr` P) _mhhds( _mhh ds( Jmy M) Lrkoami( Ikgphmtgidsa Ikgphmtgidsa mi` Oigstdcdsa( S[IT  Vrkss( =44<
"_ditkr <6=6 K`dtdgi$( K`wmr` I) I) Zmhtm "k`)$( [\H 1

bttp:''phmtg)stmiegr bttp:''phmtg)stmiegr`)k`u'mrcbdvks'wdi<6=6'kitrdks'pmrm`gx!zki `)k`u'mrcbdvks'wdi<6=6'kitrdks'pmrm`gx!zkig') g') ;! Stkpbki Hmw( ‘Pbk Orkmt Vbdhgsgpbkrs: Pbk Hdvks mi` D`kms ge Bdstgry/s Orkmtkst Pbdinkrs‑( Pbdinkrs‑( ]ukrcus( Edrst Vulhdsbk` <66?( <66 ?( <6=3 5! @ruivmhg Akhcbdzk`kn( Pbk Micdkit Skcrkt ge tbk Ehgwkr ge Hdek( Hdobt  Pkcbighgoy  Pkcbighgoy Vulhdsbdio( = st K`dtdgi( <666 ?! Khdzmlktb Agrmi( Agrmi( Jgskpb Jgskpb Tu( Umh Ldntmsbkv( Ekio Sbud(

PBK

CGAVHKPK K@DGP—S O[D@K PG( MHVBM M Vkmrsgi( K`ucmtdgi Cgapmiy( <66< 2! \dcbmr` _klstkr( ‘Pmhdsami Amodc: Tmitrm Squmrks egr Pmitrdc @dvdimtdgi‑( Hhkwkhhyi _grh`w d`k d`k Hdadtk`( =44; 4!  Mherk` Bumio( ‘Pbk Cgaphktk Cgaphktk D Cbdio: Pbk @kedidtdvk Prmishmtdgi ly   Pmgdst Amstkr Mherk` Bumio‑( Diikr Diikr Prm`dtdgis ' Lkmr % Cg( <6=6 =6! Lmeedgid( Cmrakhm( ,Dnbwìi mh!Smeì—,( mh!Smeì—,( Pbk Stmiegr` Kicychgpk`dm ge Vbdhgsgpby 

;;

Ikgaktry "Suaakr

hkt tbk egras spkmn <6=3 <6=<

K`dtdgi$(

K`wmr`

I)

Zmhtm

"k`)$(

[\H

1

bttp:''phmtg)stmiegr`)k`u'mrcbdvks'sua<6=<'kitrdks'dnbwmi!mh!smem'

==! Adcbmkh Adhhkr( Ausdc Pbkgry( PBK CGAVHKPK D@DGP—S O[D@K PG(
;5

Ikgaktry

<6=3

hkt tbk egras spkmn <6=3

<4

;?

Ikgaktry

hkt tbk egras spkmn <6=3

) )

) ) ) )

)

;4

Ikgaktry

hkt tbk egras spkmn <6=3

) ) )

)

) )

) ) )

)

56