'xiee`l lhen `edy cenr'

Transkrypt

1 xtiel awri axd 'xiee`l lhen èdy cenr'?lecbdkswiddpynddhwprecn ixqiwc ipiic zhiy l`ppg epiax ixac d`pfegn i`lipg iax zhiy i`lipgiaxitlrzeld`zpynxeìa iqeiiaxzrc rwxwa rweyd xhewd xeriy aeyig:gtqp?lecbdkswiddpynddhwprecn mixyr etwida yi m`,xie`l lhen èdy cenr" :epipy (f,ai) zeld` zkqna dlere zrwea d`neh - e`l mè,eptec zgz d`nehd z` ìan migth draxè."zcxeie zrwea zifke ux`d lr ekxe`l lheny lilbl,diyxtn lk mixàny itk,dpynd zpeek llgèvnlxyt`lilbdicivzgzm`èdoeicd;eizgzneeciva`vnpzndon d`nehdz`ìandlde`lyilnipindxeriydèdy,gthmexagthlrgthly yiy `vni m`.riwxd cr rwaz `ly d`nehd ipta uveg sè,eizgzy dn lkl mb,d`neh lawi lilbdly ekxe` lkl cveze` zgz `vniiy dnlk,dfk xeriy lilbdoky,d`nehlawi`llilbdlrn`vniiydnjci`ne,xzeiajex`lilbdm` 1miyxz.d`nehd oiae epia uevgi 24 etwidy lilb ly agex jzg `vnp 1 miyxza xeriyd,xeiva ze`xl xyt`y itk.reaixa meqgd ick yxcp lilbd swida migth draxè mixyr deey lilbd xhew) migth dpeny exhewa didiy,dpynd zhwep jk,dfk dxwnae,(reaixd rlv jxe`l gthlymewnlilbdicivipyzgznymillgadidi qgidzòaenkzhwepdpynd.gthmexagthlr dfqgi.xzei`le,exhewndyelyitèdlebirswideitle,l"fgmihwepyrecid aygzy ick dxew ly dtwid zeidl jixv dnk zraewd,zncewd dpyna àen d`nehdiptauevgzedizgzydnlkl`d`nehdz`ìazegthagexalde` zraexnìdyonfa.migthdyelydtiwd-dlebrìdyonfa":dilrnrwaz`ly."riax lebird lr xzi raexndy,drax`- 3

2 oebk mipexgà dlke,y"`xde y"xdk mipey`xdn lgd,dpynd iyxtn lk dpyna dlbznd dxeng dira lr micner,y"yxde l`xyi zx`tz,aeh mei 'qez `zn`,`reaixa `zn` lk" recid llkd itl dxe`kl miyer aeyigd z` ixd :ef ly eizeciny ep` mirceiy oeikn,jkitl.(`,g dkeq) "`peqklà iyneg ixze dpeny lr migth dpeny md [1 miyxza hhxeynk] ekeza meqg lilbdy raexn lymigthdzpenylxarn)mitqepgthiyneg16eplaipiepeqklìf`,migth raexngthlawlickixdj`.lilbdicivncvlkamiynegdpeny,(lilbdxhew reaixa gth ik,oeqklà gth iyneg dray `l` mikixv eppi` lilbd ly eciva etwiday lilb wxy dpynd draw recn ok m` ;oeqklà miyneg ipye gth èd 21sè22e`23didetwidm`mbixd,epteczgzd`nehdz`ìanmigth24!deey did oicd migth epl xiizyp `l" - ziy`x :ef diral mivexiz ipy ìan dpynl eyexita y"xd oiaexiraepyxit,cere.wc`l`ynegcgmeyne,cg`yneg`l`jxevdlrxzei epnn xqgy,ixnbl oeekn epi` opeqklà iyneg ixze `zn` reaixa `zn` lkc."my izgkedy enk,[lecb xzei hrn izin`d oeqkl`d=] hrn lynloiir)mipey`xdnkednkeazkxakydnlìdipydevexizay"xdzpeek,aexiw wx èd '`reaixa `zn`' ly llkdy (my dkeql ixi`nae zetqeza jxcd.miynegipyedn`xy`nxzeihrnlecbdn`reaixlyoeqkl`ddyrnle xfbp epnn, 1 recid qxebzit htyn ici lr ìd oeqkl`d jxe` zìvnl zwiiecnd jxe` z` litkdl epilr oeqkl`d jxe` z` lawl ick zeey eizerlvy reaixay hrn`l`['iynegixze`zn`']1.4`lèt`èdwiiecndjxe`d;2yxeyarlvd,l"pdlilbdcvasqepdynegajxevdxaqei-y"xdgipd-dfitl :xzei.epnn wlga zegtl e` dqy 'nr seq,dqw 'iq `"g) u"ayzd z"eya o`xec gnv oa oerny iax j` oeyllrddbdiz`vne":eilrazeke,y"xdixacz`ìan(one`dnlyoekn'cdna!èdeytpaikrci`l-l"faxdazkydf'cere':dpeyldfy 2 ilyxtqdoeilbadf!"ynegn xzei,jxevdn xzei epl xiizyi dzr ik,min siqedl jixv - gnw siqed cvaygthdlyoeqkl`djx`zdyenkixdy,ce`ndenzy"xdlyepeaygokè m` ;(114 'rd y"iir) lilbd xhew igth zpeny ly mpeqkl` jx`zd jk lilbd,migth lawp l"pd qxebzit htyn itl mqegd reaixd oeqkl` z` aygp 3 lilbdxhewigthzpenyz`mdndkpp dfy,cvlklmigth1.6569mrx`yipe xzid jxe`l deey reaixa qiqad jxe` cere reaixa avipd jxe` zieef xyi yleynay.reaixa(zipeqkl`d rlvd=).extq oeilib lr envr u"ayxd ly ddbdl dpeekdy xazqn oeqkl`l rlvd qgi iabl wxe,l"fga laewnk swiddn yily ekxe` xhewdy dgpda oiicr ekxritlmigthd24oalebirdxhewzàygpm`mbmpn`;zwiecndcinmihwepep`.l"nkè.dpira zx`yp ìyewd(8 `le migth 7.64-k didi ekxe` fè) wiecnd oeilb ß[c,ap] a"ryz fenz,oirnd 4

3 1.117 didi dfk reaix ly rlvd jxe`.[1.6 mdy] miyneg dyelye gthn xzei recn oiadl epl xefrz `l reaixd oeqkl` ly zwiecnd dcind mby jk,migth! 4 zegt`lemigth24lyswiddpynddhwp uexizmpn`?"wc`l`ynegcgmeyn"y"xdlyoey`xdevexizkxn`p`nye :miptdnknce`ndywendf in `lewl,`xnegl -wc `l opixn`c xeni`"minrt dnk zpiivn `xnbd.` swidmèlitìxdy,okmbèd`lew-o`kay'wc`l'e."?wc`lopixn` m`y `vnp,gth lr gth ly llg eiccv eliki migth 21 wx didi cenrd 24În zegt hrn cre migth 21În etwidy cenr ly eciva d`neh z`vnp meyn zexdhd z` xdhp - xzei wegx cv ezeà ze`vnp zexdhe,migth ;gthllgmyyizn`dcvnyzexnl,migth24cenrdlyetwidaoi`y aiigziedliah`llycwndzialqpkidllkeieciz`myqipkdyinoke!zxk yeniy yxec didweicdy mixwnlxaqdk cinzàen 'wc`l' ly oeirxd.a.(cere;`,fka"a;`,gdkeqoiir)lebrxtqnhewplsicrn`pzde,mixaya itl]migthdraylyxhewlawlickmigth21lyswidwitqno`kla` EwRqimigthdrayyoeikne.[π=3:mewnlkal"fgmihwepyrecidqgid xeriy,miynegdrayweicacvlkleplyiyixd-oeqklàmiyneg14epl,migth24lyxeriya`pzdhweprecnmrhmeyoiè, 5 gthlyepeqkl`!21 miwitqny cera yelyèdy(π)'i`t'jxrdlyizin`dqgidz`rci`pzd:xn`p`nye dray ly xhew lawl ick migth 21În xzei jixv eitle,aexiwa ziriaye! 6 raxè mixyr `l oiicre,xzeid lkl migth 22 jixv df itl j` ;migth lyqgidzèhwpminkgydaeyzdzeàahidgikenu"ayx:z`fzlefe. 7 izin`d qgidn ixnbl enlrzde,`xnegl oiae `lewl oia,mewn lkaπ=3.dfiyewlrcnre'iqc"eia"gh"ixdnz"eyaipxhi"xmb, :xzei hrnelitè,gthickwitqnlawpoeqkl`dlywiiecndxeriyditlmb.u"ayxd oiivy itk,epnr daihn wx oeqkl`d jxe` zlcbd oky.epxkfdy'`xnegl wc `l' ly dirad caln dyely dtwidy dxewy zxne` zeldà zncewd dpynd :ely zegkeddn mizy ìap itlznàla`.gthdxhewyitl,d`nehdiptauevgzed`nehdz`ìazxakmigth d`nehdiptauevgz`ly`vnp,zegthrn`l`gthxhewoiicro`koiìzin`dqgid opgei iax ixaca dpc (`,g) dkeq zkqna `xnbd,ok enk.`lewl df ixde,dizgzy 'c lr 'c ly reaix dkeza raxl xyt` didiy ick,zen` 24 ly swida dkeq jixvdy dribn seqal.aexiw xg` aexiw mze` zayiine,eixac lr ce`n ddnz `xnbd.zen` witqn did znàe,zen`dxyrdpenylyswidl oeekzd opgeiiaxydpwqnl`xnbd wiic miizin`d miqgid itly giken u"ayxd la`;'wc `l `xnegl'y `l`,zen` 16.8 k"trè,'wc`l'uexizlribdljixv`leìyewmeyeilroi`y`vnp,ìltdlopgeiiax

4 lhen èdy cenr" :jk df oic àen 8 b"it zeld`c `ztqeza ;cere z`f draxè mixyr etwida `diy cr eptec zgz d`neh ìan epi` xieà mixyr jl oi` xne` iqei 'x didy,dynge mixyr :xne` iqei 'x.migth riwyn cenrd caeky oeikn :xnelk."gth oda zlke` ux`d oi`y dynge x`yidlickcenrdswidlrgthcersiqedljixv,swiddon1/25 uxà lkl e`,21 `l` swidl jixv `l znà m` la`.etwida migth 24 mr `lde?uxà rwey swidd on gthy epl ztk` dn - migth 22 xzeid cibdl jiiy `l i`ce df lr?migth dyelye mixyr epl mix`yp oiicr xzeel xyt`y dcaerd xe`l mixzein iqei 'x ixac lk ixdy,'wc `l' xe`l cgeina dxeng ziyrp ìyewd.swid igth dyely e` mipy lr,xhewdonixrfnwlgzriwylmxebuxàrweydswiddongthydcaerd migthd ipy mr dpdke dpdk ffewn dfe, 9 gthd zei`n rayn zegt.mitcerd zlkeùx`d`dz`lyxytì`c,cere":myy"xdazeksqepuexiz.b rweycenrdonwlgymeynxzeijex`swidyexc:xnelk."cenrdonhrn iqei 'x zprh weica idef ixdy - ce`n midenz eixac mpn`.rwxwa ;swidl cg` gth siqedl jixvn èd okle,[hhvn envr y"xdy] `ztqeza qgiizdl jxev oi` zizkldy dhwp `xnbdy gxkda ixd.'wc `l' cibdl `xnbd zvl`p 'xign'aelit`,erlvlqgiareaixdoeqkl`lyizin`djxrle`,π ly izin`d qgil zl`yzòiivlmrhozepayi,ab`jxc.'wc`l'k±miwiiecnd±opgei'xixacxaqdly d`xpdxaca'ilinipd`pn'`kdirainljiiydn":dnzd(`,cioiaexir)y"`xdzetqez itl":uxzne?"swiddcecnpegthagxèdyxaceìai,eilrcenrllekimcèmipirl ozilminkgegwloipn`cenlzira`w,migth'bnxzeièdswiddy,oeeknxacdoi`y di`x iziine.oeekn zeidl aexw xacdy `l` oeekn epi`y t"r` cg` xacl dcne leab dn`miylyew'c`xwxn`we,xyragxdidydnlylymic,ikdciar`winp`xwc (ak'rqbqy'iqg"e`)'ogleydjexr'lrayoiiprne."xzeijex`èdyt"r`'ezeàeqi oeaygdoi`cb"rè"...:hrnkddfoteàuxznelèyy"`xdzetqezixacz`d`x`ly aizkcdnlylymindlopitlie,cecnldxezddxfbokn"n,zecndinkgitlwcwecn 'nbael`yyedfe.(bk,f`"n)'aiaqezeàeqidnàmiylyeweeztycreztynxyr',oeekn oeaygd oi``de,dywn dteb dfc `l`!cecnpe heg izip :dywe?'ilin ipd `pn' efy 'cecnpe heg iziip' dprhd lr zeprl ozipy okzi mpn`]."ok dzev dxezdy uxzne `nbecl oiieri.'`nlr `xae `ziixeà lkzq`' zpiga,weqta xewn ytgl `xnbd jxc mlern,'einexnamelydyer,enrcgtelynd'aizkci`n:opgeiiaxxn`c":a,bkd"xa,`le`riaynoiim`(a,dl)zekxazkqnaoeicdoke."dpallydznibtdngdz`x`l aalmgle...yepàalgnyioiie'weqtamiltltn`l`zeìvndz`xxalmiytgnoiè.['crqiyep`.h dkld ef my,lcp`nxwev zxecdnn wzred gqepd.xn`nd seqay gtqpa oiieri oeilb ß[c,ap] a"ryz fenz,oirnd 6

5 epazkyitkixd,oiconxae.efdprhlwwfpepi``nw`pzyokm`d`xp.witqn epl x`yi z"eyazekixàe, 10 dpyndzùxzlèds`dqpnyaehmei'qezamyoiieri exeìazìzdwqgpit'xmkqnyitk,xaclyeteqaj`,(e'iqc"eia"g)h"ixdn."oeir jixv oiicr",ef dpynl ixqiwc ipiic zhiy ycg xe` zktey ipnecnky,l`ppg epiax ixaca zpiiprn dwqit il dzlbzp dpde opgeiiaxy,lebroelgoipra`,eroiaexirlg"xdyexitaèdxaecnd.efdpynlr reaix ekezn raxl elkeiy ick migth draxè mixyr etwid didiy jixvy xne` dwiqn seqale,opgei iax ixac z` zxxane zkled `xnbde.migth 'c lr 'c ly ikp xqaiya,`peqklà iyneg ixze `zn` reaixa `zn` lk ickn" :ìyewa ly llkd itl migth 5.6 èd 'c lr 'c reaix ly oeqkl` :xnelk!"ìbq `yneg,lebrdoelgdlyswiddz`lawlickyelyadfoeqkl`litkp.'`reaixa`zn`' opgei iax jxved recn.'`yneg ikp xqaiy' epiidc,migth 16.8 miwitqny `vnpe ipiic ik xn` opgei iax" :dwiqn `xnbde?migth draxè mixyr ly swidl ebn `reaix,`raix- `reaix ebn `lebir:ixn`c,ixqiwc opaxk dl ixnè,ixqiwc."`blt-`lebir xeìaa,exazyp miax miqenlewe,jtyp ax eic zetqezd zhiy z` x`zp.ixqiwc ipiic ly mzhiy :ziqgiîgep oteà mzhiy z` miyxtnd,my,migth dpeny lr dpeny eizerlvy reaix migwel cg` lk rlvy mieey mireaix drax`l eze` miwleg el`d mireaixd ipeqkl`,migth drax` mdn ly zieefa zeavip eizerlvy xzei ohw reaix mixvei.(2miyxzd`x)lecbdreaixlqgiazelrn45 2miyxz ghyn ivg weica èd iniptd reaixd ly eghy.lecbd reaixd irax zrax` ly mi`vg drax` likn èd ixdy,lecbd reaixd reaixd jeza meqge ohwd reaixd z` mqegd lebir hhxyp mireaixd ipy oia reaixdnmiraxdyelyweicaèd[π=3lyaexiwditl]dflebirlyeghy.lecbd ghy] `raix - `reaix ebn `lebir :ixqiwc ipiic ly llkd èt` edf. 11 lecbd zeierh lr miriavnsè,melklired `l ik mixirnd myiypìyecigaey"yxa oiire.eizepeayga.'i`t'ad`vezdzltkdeenvraqeicxdzltkdepiidc,r 2 πìdlebirghyaeyigzgqep.48:64=3:4-e,8x8=64 èd mqegd reaixd ghy,4x4x3=48 ok m` èd meqgd lebird ghy

6 meqgy ohwd reaixd] `blt- `lebir ebn `reaix,[lecbd reaixdn rax xqg lebird. 12 [lecbd reaixdn ivg eghy,lebird jeza eyxitopgei'xe`xnbdy`l`. 13 π=3 lyqgiditloaenk,wiiecnlkdo`kcr zexevd swidl rbepa mb mipekp el`d miqgidy ìd ixqiwc ipiic zpeeky,migth 32 èd,migth dpeny erlvy,lecbd reaixd swid m`:xnelk.zexaecnd xekfk eghyy] mdipiay lebirde,migth 16 etwid didi ekeza meqgd reaixdy ixd.migth 24 etwid didi[lecbd reaixd ghyn 3/4 64 likn migth dpeny erlvy reaix:xzeia mitixg micxeqa`l liaen df xac reaixd ixde.migth 16 wx likn drax` erlvy reaix eliè,miraexn migth!miraexn migth 32 likdl xen` ède,lecbd reaixdn ivg weica eghy ohwd ipiicygxkdadfitlymixirn(opgeiiaxed"ca,eroiaexir)zetqez:cerez`f ly epeqkl` ixdy,`peqklà oin` ixz - `reaixa `zn` ik exaq ixqiwc reaixd ly eizerlve,migth dpeny - lecbd reaixd agexk èd ohwd reaixd zrax`lymdipeqklòdohwdreaixdlyeizerlvj`. 14 drax``lòpiòhwd mbe migth drax` jxeà mdizerlvy okziid;lecbd reaixdn epwligy mireaixd?dfd jxeà mdipeqkl`,"i`d ilek ied `lc opifgw `dc,ìd `le" dxirn ok` dkeq zkqna `xnbd.dfky drhen oteà xryl ixqiwc ipiic elki cvik àeh midnz mipey`xde opgei iax dcina erh jìd,dnize" miazek (`reaix d"c a,g) dkeqa zetqezd xnelyie?epi`yxaclrllkeyrjìd-xacdeccn`lyxg`nc,ixqiwcipiice mewnd oiprl zn` ède,'`blt `lebir ebn reaix' ly df oeyl mcia dlawc dpey oteà 'qezd miyxtn oiaexira."siwnd hegd jxe` oiprl `le [ghyd=] opgei iaxy `l`,llk swidd oiprl `le ghyl epeekzd ok` ixqiwc ipiicy,zvw.swidd oiprl mixacn mdy eayge mdixaca erh `xnbde erci md.ixqiwc ipiic ly mzerhl mrh zvw ozep (a,er) oiaexira `"ayxd lebird swid ivg l` xyi ew qgi df it lrye,etwidn yily èd lebird xhewy lcad`ll,aividfdqgidyexaqmdj`;2:3lyqgièdqiqaeldeednewdy :(3miyxzd`x)lebirdz`dvegyewdmwennokid o"aixd yexita lynl oiir]'`blt `lebir ebn `reaix' milind xaqda zexg` zehiy opyi...opgei 'xc `zlin ivexzl ez` ixqiwc ipiic" (ek 'nr ` zefepba qtced) dkeq zkqnl lr lebird xzi lebird jez zeraexn zen`'c oiyeryk xnelk,`blt `lebir ebn `reaixe dnè"ilyivge,xyrdyyldlerzen`rax`lyswidc,`reaixlyswiddivgreaxd oiierie,"opgei'xhiwpczen`raxèmixyrodode,zen`dpenyepiidc,eilrlebirdlcb.odipia lcad oi` ghyd aeyig mvrl j`[oiaexirl `"ahixd yexita mb.lebirdghyz`hrnlicbnizin`dqgid."iedikd`peqkl`lkcedl`xiaqc"exnà,jklfnexile`reaixd"ceqmyi"yxmb oeilb ß[c,ap] a"ryz fenz,oirnd 8

7 ,ervnà lebird z` dvegd ewl dliawnd zywdy myk itèdirvn`dewldlyqgid:xnelk,12ìd,8ekxe`y 4 ekxe`y xzei ohwd ewd dqiqay zywd mzrcl jk,3:2 dyiydidièdjkitle,3:2:qgiezeàdididkxe`dkxe`.migth xeniwa ielz xacd ixdy,oekp epi` dfd qgidy oaenk dxenw lebird z` dvegd ewl dliawnd zywd :zywd ozepa dfa yi la` ;xzei daxd dkex` ok lre,xzei daxd 3miyxz lr zi`xpy dpwqnl ribdl ixqiwc ipiic elki cvik mrh. 15 jk lk zkxten dipt oekp,'riax-lebirdlrxziraexndnk'lyllkd:mrhcerile`siqedlxytè mqegdraexnlyetwide,exhewndyelyitèdlebirlyetwid:swiddiablmb,ai) zeldàdpynd.reaixdrlvèdy,xhewdndraxìtdididflebirekeza gzet da `die [dxewly] dtiwda `di dnk":swidd iabl df qgizpiivn xak (e,drax` - zraexn ìdy onfa,migth dyely dtiwd - dlebr ìdy onfa?gth raexn oia qgid ik e`x ixqiwc ipiicy oeikn."riax lebrd lr xzi raexndy s`y exriy md,ghyd oiprl oiae swidd oiprl oia 4:3 èd ekeza meqgd lebirl oiprl ode ghyd oiprl od oekp ekeza meqgd raexnd oiae lebird oia qgid.swidd dcaera rbxk wtzqp ep`,didiy ji` ixqiwc ipiic ly mzrca xeìad didi,2:3 ly miqgi md ekeza èlkd reaixl lebir oia miqgidy mixaeq ixqiwc ipiicy ipy èd reaixd swid sè - lebird ghyn yily ipy èd reaixd ghyy xnelk ly enk mixaqd zlef] ixqiwc ipiic ly mdixaca oeibd èvnl zepeiqp eid ik oiievi miliren mpi`y mixaqd,ixqiwc ipiic ixaca erh `xnbde opgei'x ik mixne`d'qezd dn rcei ipiè" oiaexira `"ahixd orehy itk,edpynl cg`n dirad z` wizrdl `l` mipianep`ydnopgei'xoiad`lyjnvrlrdnz:cere,opgei'xazerhdzelzlepgeexd migthc"ketwidyoelglrxaicyopgei'xmbyyxtnoiaexiraedkeqaixi`nd.["mda eqpkiy epiid,ghyl opgei'x oeekzd'etwida' dlnay wgec ède,eghyl `l` oeekzd `l llk ozp `l opgei 'xy `vnp :miywen eixac la`.migth draxè mixyr etwid jeza eètwidz`zrclilanoelgdghyz`cecnlozip`lixdy,eze`cecnllwyxeriy mixacd z`fcaln!xhewd e`swidd zòzi?d`vezd z`zzlel dn ok mè,exhew èd mye,dkeq zkqna eixacl miliawne mini`zn oiaexira opgei 'x ixacy mi`xn sè,swidldpeekdi`cemye,mcìpadraxèmixyrdtwidamiayeiydkeqlrxacn zexnl,ixqiwc ipiicl xyw oi` ef `xninly oreh èdy `l`,jk my yxtn ixi`nd oiierie]gscseqmy'qezaemyoiieri,ixqiwcipiicixacz`mys`dìan`xnbdy,(151'nr,`wlgseq,`pliezxecdn)boniqwecxdaepnceciaxl'zkqnìlb'z"eya `leghylqgiaoiaexiraedkeqa zeibeqaopgeiiax zexninz`yxtlozipikxaeqd.[swidl qgia 15 9

8 edfe,16 etwidy reaix ekeza mqeg 24 etwidy lebir jkitl.lebird swidn yily.'clr'ceizerlvyreaixweica l`ppg epiax ixac zeld`c `ztqezd z` ìan,oelg oipra my oiaexirl eyexita l`ppg epiax dpde dfe.likdl mileki eicivy reaixd aeyigae xieà lhend cenra zwqerd,epxkfdy z`ìanepi`xieàlhendcenr:b"itzeldà[`ztqeza]`pz":myg"xdoeyl d"kjloi`,d"kxneìqei'x,migthc"ketwida`diycrepteczgzd`nehd."gth zlke` ux`d oi`y migth ozipy reaixa wqer oiaexira opgei iax :àeh midenz g"xd ixac dxe`kl j` xevil ozipy reaixa zwqer zeldà `ztqezd eliè,lebird ly ellg jeza xevil i`ce zeldà `ztqezd :cere z`f? 16 mixacd ipy oia xywd edn,lebird iciva `zn`' mzhiyl ixdy,ixqiwc ipiice opgei iax zrcl dxe`kl dni`zn dpi` reaixlyepeqklòkmè,zetqezdeazkyitk,'`peqklàoinìxz-`reaixa oeqklèplyiy`vnp.migth16èd,ekezameqg[8exhewy]cenrdy,'glr'g reaixelitèaraxlickxzedeicdfe,lilbdicivlycvlknmigthdrax`ly 12didietwidemigth4lyxhewalilbwitqdlxen`mzhiyl.migthipyly ex`yiy,migth8didiekxe`-ekezameqgdflilbyreaixlyoeqkl`;migth lrgthlyreaixmdnxefbllkepe,lilbdicivlycvlknmigthipymdnepl!gth zeldà `ztqezde dpynd ixeriy ixqiwc ipiic zhiy itl `weecy d`xp mpn` ly llkd.oeqkl`d aeyiga zxg` dhiy mdl dzid ik xnel d`xpe.miwiiecn,jkitl, 17 mcia laewn did `l 'oeqklà iyneg ixze `zn` - `reaixa `zn`' heytdcrvdzèhwp`lmd,lilbdicivayllgdghyzàygleybipmdyk eynzyd `l`,ekeza meqg lilbdy reaixd ly epeqkl` z` aygl - dxe`kl `reaixe,`raix- `reaix ebn witpc `lebir:mdicia miwfgen eidy millkd ipya.oeqkl`dxeriyzèxfbmdmyne,`blt`lebirebnwitpc aeyiga zxg` dpad ok` dler `fegn yi` i`lipg iax ixacn ik d`xp oldl.reaix ly epeqkl` mpn`,cenrd ly ellga wqerd yexit rivnd g"d zn z`nehn a"it c"a`xa oiieri zhiy oiae `ztqezd oia xywn g"xd eliè,ixqiwc ipiic zhiy itl epi` i`ce eyexit iptnyyegdiqei'xzhiyldpadoi`c"a`xdlyeyexititl:z`fzlefe.ixqiwcipiic.cenrdlyellgèd`yepd`linnixdy,rwxwacenrdzriwy lyetwidqgilyllkdznerl,llkdpynaxkfenepi`'`reaixa`zn`'lyllkdokè,ai) zeld` zpyna mdipy mixkfpd'riax lebird lr xzi raexn' ly llkde,exhewl lebir.mewn meya yxetna inlyexia xkfp epi`'`reaixa `zn`' llkdy mb oiivl yie.(e oeilb ß[c,ap] a"ryz fenz,oirnd 10

9 d`pfegn i`lipg iax zhiy èd dxhewy dlebr xir inegz zriawa zwqer (a,ep sc) oiaexira ìbeqd 4miyxz zxne` my zàend `ziixa.dn` miitl` xird z` miaiygn zay megz oiprly jkitle,miitl` lr miitl` ly reaixk,'zepxwd' mewn z` xird iayez mixkyp z` ekeza mqegd reaixd ly zeieefd epiid lrzetcerel`zeieefoky,xirdlylebird xird z`vnp" :zxne` `ziixad.lebird raxè o`kl zen` ze`n rax` zxkzyn.(4miyxzd`x)"o`klzen`ze`n llkd lr iepa `ziixad ly dpeayg iyneg ixze `zn` - `reaixa `zn`",dn` iyneg 4,000 mdilr siqen zen` miitl` ly oeqkl` jkitl,"`peqklà,lebirdn hlead oeqkl`d ly cg` cvl ze`n rax`.zen` ze`n dpeny mdy.ipyd cvl ze`n raxè iy` ax z` l`yy `fegnn i`lipg ax ly eziiyew zàen ìbeqd jynda raye oiziyed`nziy?d`nipnzipd,riax-lebrdlrxziraexn dnk,ickn"."!ied`zlizikp dnk" ixde,reaixd lr jk lk scer didi oeqkl`y okzi cvik l`y i`lipg ax qgidz`raewdfdllkdi`lipgaxlyezpadle,"riax-lebirdlrxziraexn didi,miitl` èd lebird xhew m`.reaixd ly epeqkl`l lebird ly exhew oia riax èdy lebird xhewn yily eilr xzi lebird z` mqegd reaix ly epeqkl` xqg raye miyy ze`n yy èd miitl` ly yilyy oeikne.raexnd oeqkl`n.dfdxeriyamìkreaixdlrxzioeqkl`ddidi`l,yily mghyawqer'lebirdlrxziraexn'lyllkdyi`lipgaxldpermyiyàx yxtdd,reaixdlyoxwloxwngznpdoeqkl`dlrmipcep`ykla`,mitebdly la`.'`peqklà iyneg ixze `zn`,`reaixa `zn`' oky,xzei lecb èd `zn` - `reaixa `zn`" ik dzid ezrcy micnl ep` i`lipg ax ly eziiyewn,0.4 od zeiying izye, èd yily) zegt hrn dfy,"`peqklà yilye.(zfi`n rayn zegt zvw èd yxtdd ipiic ly oey`xd htynd ivgn ely llkd z` cnl èdy xiaqn i`lipg iax raexndnk"dpeyzvwgeqipae`,"`raix-`reaixebnwitpc`lebir":ixqiwc ztqezl qgiizn dfd llkdy xaq i`lipg axy `l` ;"riax - lebird lr xzi xnel à llkde,ekeza èlkd lebird on reaixd zeieef zehleay dhilad siqezyk ixdy] oeqkl`d on rax epiidc,lebird xhewn yily ìd ztqezdy 11

10 on rax didi yily lke,miyily drax` lawz,ekxe` lr lebird xhewn yily.[ycgd jxe`d ebn witpc `reaix" ixqiw ipiic htyn ly ipyd ivgd mby okzi ef dpad itl lecb exhew- reaix ekeza mqegd lebir:oipr eze`l weica qgiizn"`blt `lebir.(5 miyxz d`x) miizy it reaixd zerlvn dkeqa opgei iax zxnin weica ixd idefe :lebr oelge dlebr dkeq iabl oiaexirae lyerlvnmiipyitlecblebirdlyexhew lebiray `vnp,ekeza meqgd reaixd [24 èd etwid `linne] dpeny exhewy xhewde,rax` erlvy reaix qpkidl lkei lknzenè`migthipyhelailebirdly ipiic ly millkd ipy.reaixd ly cv oiay wgxna èt` miwqer ixqiwc meqgd lebird oiae reaix ly eizeieef 5 miyxz lebird zezyw oia wgxna :jtidle,ekeza.ekeza meqgd reaixd zerlv oiae witpc `reaix' oeyla xzeia zayiiznd ìd ixqiw ipiic zxnin ly ef dpad lebirdn ivg iniptd reaixd oi` laewnd yexitd itl oky,'`blt `lebir ebn xnel ìd '`blt' dlina dpeekde,[swida e`,ghya e`] yily ipy `l` df yexit.ekeza lebird z` `lekd oevigd reaixdn ivg èd iniptd reaixdy "`raix `reaix ebn witpc `lebir" ixqiwc ipiic exn`y enk oky,zvw wegc xnele jiyndl mdl did jk,ekezay lebirl mqegd reaixd oiay qgil epeekzde reaixl lebird oia qgid edfy "(yily) `zliz - `lebir ebn witpc `reaix"!ekeza èlkd oiay qgil weica mipeekzn ixqiwc ipiic ok` i`lipg ax zpad itl la` rlv jxe`n mipy it weica èd lebird ly xhewd oky,iniptd reaixl lebird reaix ekeza liki 8 exhewy lebiry mdly dgpdd itl] ekeza èlkd reaixd.[4 erlvy i`lipgiaxitlrzeld`zpynxeìa dheytk dpynd xàzz,i`lipg iaxk xeaq zeld`c `pzdy gipp m`,dzrn!weicae reaix ly epeqkl`.migth dpeny èd exhew,migth 24 etwidy cenr,xen`k ipye migth ipy epiidc,migth dpeny ly yily cer lelki lebird z` mqegd weica edfixde,(6 miyxzd`x) oxwlkayilyegthlwlgzndfdjxe`d.yily 202 oeilb ß[c,ap] a"ryz fenz,oirnd 12

11 ax itl gth lr gth reaix ly epeqkl` `zn` - `reaixa `zn`' xaeqy i`lipg zeldà `pzd ixac!'`peqklà yilye axlyezpaditlìltdlèt`miwiiecn ixze `zn`' oia lcadd :xen`ke.i`lipg lcad èd 'yilye `zn`' oiae 'iyneg m` `vnp.zei`n rayn zegt,icnl ohw `zn`'y exaq `l ixqiwc opaxy ok 6miyxz itk '`peqklà oin` ixz - `reaixa ynn ìd efk zerh oky,zetqez exaqy,xzei cer oeqkl`d xeriy z` epihwd md:jtidl `l`,'miipirl d`xpd xac' xcba.reaixd rlvn yily wx èdy exaqe ly llkd on ely oeqkl`d llk z` ìved i`lipg iax :zpiiprn dcewp oiivpe lebirdlyexhewlrbepaezeòiadèdoky,"riax-lebirdlrxziraexndnk" s` ìan zeld`c `pzd,dpde.mqegd reaixd ly epeqkl`n raxa ohwy,meqgd dpynd ìdy,e dpyna "riax lebird lr xzi raexn" ly dfd llkd z` èd llkz`xfb,i`lipgiaxenk,`pzdyxazqn.daepwqry'cenr'zpynlzncewd el `vi eitle,'riax lebird lr xzi raexn' ly llkd on reaix ly oeqkl`d. 18 'iyneg ixz' `le,reaixd rlv lr yily xzi oeqkl`dy iqeiiaxzrc ezrcl;migth25lyswidjixvndiqei'xzrcahidzxàznyoaenkdfitl lr zprypd zieefd qepiqew lr qqeand aeyige,rwxwa rwey swiddn cg` gth gthd iwlg mirwey swidd on cg` gth cbpky d`xn lbrnd swidn 1/50 erlvn 1.3 it èd reaixd oeqkl`y dgpdd it lr zeldà dpynd xeìa ly df oeirx 'qn,oli`xazhiqxaipe`lyireaysc)oàvfreaexaxbceclymxn`naxakàed dàedy dhiy it lr dpynd ly aeyigd jxc zxaqen myy `l`.(f"pyz zweg,192 eici lry] 2 yxey z` miaygn ditle,oedzq miig axdl 'miig ux`' xtqd zncwda zixìpil divletxhpi` z`xwpd dhiy,miaexiw ly dxeva[reaixd oeqkl` z` miaygn jkitle,oldlc dgqepa,aeyigd ly xzei ipey`xde heytd alya dynzyd dpynd) df xaqd itl mpn`.(1 + (2-1) / (4 1) = 1 + 1/3 :yilye cg` èd xeriydy dlaiw epiax ixaca o`k epwqr epè,ixqiwc ipiic zhiyl zeldà dpynd oia xyw mey oi` llkdonxfbpok`dfdaexiwdy`vnp,zrkepazkydnitl.mixacdoiaxywnyl`ppg cbpldcnrìdddgqepd`lymigikeni`lipgaxixacmbyild`xpe.ixqiwcipiicly eliè.'riax lebird lr xzi raexn dnk' lyllkd lr eixac z` qqan èd oky.eipir xziraexn'lyllkloeqkl`daeyigjxcoiaxywmeyoi`l"pdixìpildaexiwditl.'riax lebird lr 18 13

12 xeriydidi,π=3lyaexiwdz`qetzpmè,πlywiiecndxeriyditlxhewdon,xhewdzriwyxeriyzìqeiiaxayigcvikzrcldyw. 19 migth0.066driwyd xaq èdy xexa mewnlkn.miqepiqewde miqepiqdiqgi eiptl eid`l ghal ik lebirdicivagthlrgthlyreaixxevilxyt`didi`lxakyznxebdriwydy iyneg ixze `zn` - `reaixa `zn`' ly llkd itl ixyt` izla dfe.meqgd.lirl epgkedy itk,'oeqklà okxe` mb didi dfe,yilye migth dpeny didi exhew migth 25 etwidy lebir `zn`' ly llkd itl dfk reaix ly oeqkl`d.eze` mqegd reaixd zerlv ly zeieefn zg` lkay `vnp.gthd ly 14/18-e migth ipy siqei 'oeqklà yilye 7/18 ceregthèdepeqkl`yohwreaixraxlxyt`lebirdz`mqegdreaixd, 20 oeqkl`d on 3/4 zeednd,dfk reaix ly eizerlv.yilye gthn xzei hrn,migth xeriyz`xzedeicdqkngthdiwlg1/24lyefztqez.migth1/24ceregthod xeriya la`,'wc `l' mpn` o`k yi.gthd zei`n rayn zegt èdy,driwyd xeriyy xaq iqei iaxy mb okzie.epnn mlrzdl znà xyt`y ce`n xirf.elyaeyigdjxcdziddnweicaxexa`loky,xzeilecbdriwyd z``le,zeld`ly`ztqezdz``weechhivl`ppgepiaxydaiqdefyokzie,llko`klxeywepiìqei'xlyepicixdy,`ltdfe.oiceze`dayxetnydpynd ik giken iqei 'xy `l`?`ztqezd z` zgwle dpynd z` weayl g"x d`x dne.ixqiwcipiiclymdillkitlriepadpyndoic ixqiwc ipiic ik zetqezde i"yxzrcl ztqep dgked efy ixd,epixac mipk m` eqipy itk `le,3:2 èd ekeza meqgd raexnl lebird swid qgiy exaq mnvr yxtl (ary 'iq g"e` r"eye a,er oiaexirl exeìaa oiir) `"xbd e`,ixi`nd itl `weec `l` wiiecn oteà zyxtzn dpi` zeldà dpynd oky,mdixaca. 21 ekeza meqgd reaixl lebird swid qgi ly ef dqitz.gtqpa d`x aeyigd zxev z`.oeqkl`don3/4ìdreaixdrlvy`vnp,erlvnyilyalecbreaixdoeqkl`mìxdy ly oey`xd gqepl zeaeyg zexrd xirdy xaxb cec x"c axl al axwn dcen ip`.minyd on letk exky.mipiipr dnka iipir z` xi`de,xn`nd oeilb ß[c,ap] a"ryz fenz,oirnd 14

13 rwxwa rweyd xhewd xeriy aeyig:gtqp rwxwdiptlzgznrewyetwidngthe,migth25swidalilbdlyjzgepiptl aygl ick.b èd rwxwd iptl zgzn rweyd xhewd rhw ;(wqexnd ewd),gthivglyzywlrzprypd,α zieefd qepiqewa xhewd z` militkn ep` eze`.zelrn 7.2 = 360/50 epiidc.lbrnd swidn 1/50 ìdy :okl a = r * cos (α) = r * cos(7.2) = 0.992r :miiwn,driwyd jxe` èdy,b-y o`kne b = r - a = r 0.992r = 0.008r :jkn raep 7.957= 25/π= r eply dxwna m` b = * = migth epiidc,25/3 didi r ik,hrn aeyigd dpzyiπ = 3 ly aexiwd z` qetzp m` :b ly exeriy didi fè,yilye dpeny b = * = gthdzei`nraylribi`lxhewdzriwyxeriydxwnlka 15