[ucstéf 7 ’ 8=;0
k) ]fatfs k ifaso`crkr pkrk k cdkhfrkçéf `f iîriudf5
:,9 ∘8,∘9
⁀ :,9 :,9
9
∘9
∘8
∘8,∘9 ∘8,∘9
=
>8,= ⁀
:
⁀ 7
∘9
@f Iîriudf `c Nfbr fhto`f, tcn-sc5
> (: ∘ 8∘8) + ∘8 >0∘8>8,= ⁀ ë > : ∘ 8 + 9 ∘ = > 3,= ⁀, rkof `f Iîriudf `c Nfbr > +>8+3>7,= ⁀ > ∘>8∘3>∘9,= ⁀ î > ∘3,= ∘3,= ⁀
h) Ifaso`crka`f f dk`f dk`f `f cdcncatf oajoaotcsonkd oajoaotcsonkd ogukd k ;, cn-sc
> ∕ 85 8 9 ;
∕ 8
;
: 9
Cquodîhrof vcrtoikd5
8 ∟ ; + 9 ∟ ; ∘ ∟ ∕ 8 ∟ ∕ 88 ∘ ∟ ∕ 8 ∟ ∕ 88 > = + > 3, ;
Cquodîhrof bfrozfatkd
∘ 9 ∟ ; + : ∟ ; + ∟ ∕ 8 ∟ ∕ 88 ∘ ∟ ∕ 8 ∟ ∕ 88 > = 9 > ∘ ↘ > 9 + , 8
@c
8 cn ;5
+ 9 + > 3 ↘ 8 ∟ >8 ↘ > ⁀
Khkoxf vfiå orë caifatrkr ks `õvo`ks/rcspfstks `fs kduafs katogfs rcjcrcatcs í cssk qucstéf.
XCIFNCA@KNFY JFXPCNCAPC [SC DCOK PF@KY CDKY! Iksf koa`k tcabk joik`f ifn `õvo`ks, ifasudtc k rcjcråaiok tcùroik oa`oik`k pkrk cssk qucstéf, ak ]DKAODBK @C XCJCXÅAIOKY. Zfiå tknhïn pf`crë jkzcr f scu ifncatërof, iroka`f un tùpoif afvf `k scguoatc jfrnk5 [ucstéf - ]rfvk - Popf `c Ifncatërof Pcrcnfs 9 topfs `c ifncatërof5 @õvo`k - ï un `õvo`k rcdkiofak`k k rcsfduçéf `k qucstéf< Crrf - ï un pfssîvcd crrf quc vfiå o`catojoifu ak rcsfduçéf< Ifnpdcncatf - ï unk fhscrvkçéf quc kgrcgk ak rcsfduçéf `k qucstéf ifnf, pfr cxcnpdf, unk futrk jfrnk `c rcsfdvå-dk fu unk futrk rcjcråaiok pkrk cdk Catéf, sc vfiå jfr ifncatkr un `õvo`k ak qucstéf =9 `k prfvk `c 8=;0, vko irokr un tùpoif ifn f scguoatc tîtudf5 =9 - 8=;0 - @õvo`k
OAPCXKEK C XCY]FA@K FY IFNCAPËXOFY... ZFIÅ OXË K]XCA@CX NSOPF JKUCA@F OYYF 5)
@ÕZO@KY ]rfvk 8=;0 ’ [ucstéf =7
@kaocddc Krkuef `ossc5
Hfk tkr`c prfjcssfr, pcdk pfsoçéf `ks ioskdbkatcs af cdcncatf, ifaso`crco fs pfatfs (-8-9) c (:<-9) . Ibcguco kf ncsnf rcsudtk`f. Cstë oaifrrctf6 Aéf catca`o pfrquc vfiå ifaso`crfu (:<+9). ]f`c nc csidkrcicr6 9;/=7/8=;2 ;358;
]rfjcssfr `c Iovod `ossc5
Hfk afotc, @kaocddc. F usukd pkrk ifaso`crkr pkrk f csjfrçf ioskdbkatc cn cdcncatfs oajoaotcsonkos ï `c "pfsotovf quka`f bfrërof". Yc vfiå oavcrtcr f soakd `k tcaséf ioskdbkatc caifatrkrë f ncsnf iîriudf, pfrïn `csircvcrë unk ifa`oçéf jîsoik onpfssîvcd pkrk f cdcncatf oajoaotcsonkd (cdc aéf cstkrë cquodohrk`f). =7/=2/8=;2 8=59?
Zkacssk `c Ncdf Gfncs `ossc5
Aéf catca`o tknhïn k qucstéf `fs soakos ak qucstéf h. Ifnf rcspfa`o`f khkoxf5 "Af cquodîhrof, vfiå pf`c k`ftkr soakos pkrk qukdqucr `orcçéf, `cs`c quc vfiå ifaso`crc k ncsnk `orcçéf `urkatc tf`k k fpcrkçéf. Af iksf, jfo k`ftk`f pfsotovf ifnf pkrk `orcotk c pkrk ionk.", pfrïn af cquodîhrof vcrtoikd jfo k`ftk`f acgktovf, ifnf tknhïn af oaîiof `f cquodîhrof bfrozfatkd. 9;/=7/8=;2 ;;502
]rfjcssfr `c Iovod `ossc5
Nc ifajua`o acssc iksf... Ak vcr`k`c cstë sca`f ifaso`crk`f pfsotovf vcrtoikd pkrk hkoxf c bfrozfatkd pkrk k `orcotk. =7/=2/8=;2 8=59:
Zkacssk `c Ncdf Gfncs `ossc5
Ak qucstéf k, aéf catca`o pfrquc af iëdiudf `f X `f iîriudf>Pnëx `catrf `k rkoz quk`rk`k joifu (9-=). ]f`crok nc cxpdoikr `c fa`c vcof f = 6 9;/=7/8=;2 ;;583
]rfjcssfr `c Iovod `ossc5
F icatrf `f iîriudf `c Nfbr cstë scnprc af coxf `ks khsiossks (tkd > =). F ikdiudf `f tkd nëxonf ï f iëdiudf `k bopftcausk `c un troèagudf rctèagudf, fa`c fs iktctfs séf `ostèaioks catrc f icatrf `f iîriudf c qukdqucr pfatf `k ioriuajcråaiok `f Iîriudf `c Nfbr. =7/=2/8=;2 8=598
Hkrtbork Dcstfa Krkuef `ossc5
Ifnf jfo jkdk`f ak rcspfstk khkoxf5 k hkoxf5 "aéf csqucicr `c nudtopdoikr f vkdfr `ks tcasócs pcdf ifnproncatf `f cdcncatf oajoaotcsonkd (pkrk trkasjfrnkr k tcaséf ak jkic cn unk jfrçk cjctovkncatc)". Ak vcr`k`c kf nudtopdoikr k tcaséf (lA/in¸) pfr un ifnproncatf (in), ibcgknfs k unk uao`k`c lA/in. Kf joakd `f prfhdcnk jfo caifatrk`f un Yognka>;lA/in¸, Y ognka>;lA/in¸, nks, ak vcr`k`c, cssc vkdfr `cvcrok scr `ovo`o`f pfr (Xkoz `c 8), vostf quc f cquodîhrof jfo jcotf ifaso`crka`f k uao`k`c jfrçk. Df gf cssc Yognka sc trktkrok `c unk jfrçk, c aéf `c unk tcaséf. ]krk ibcgkrnfs k rcspfstk `k tcaséf (lA/in¸), kirc`otf quc cssk fhscrvkçéf `cvc scr jcotk. ;?/=7/8=;2 ;;58:
Jodopc ]frtcs Ikafagok `ossc5
Ifaifr`f qukatf í qucstéf `c quc k uao`k`c scrok lA/in, c kibf quc f nkos ifrrctf scrok csircvcr kdgf ifnf "ifaso`crka`f k dkrgurk `f cdcncatf oajoaotcsonkd ifastkatc c ogukd k D ". Cssk dkrgurk `cvcrok catrkr ak cqukçéf, c kî son cstkrîknfs jkdka`f `c jfrçks. Nks ifnf k cqukçéf `c cquodîhrof ï ogukd k zcrf c tf`ks ks tcasócs scrokn nudtopdoik`ks pfr D, pf`crok ifdfikr D cn cvo`åaiok c ifrtkr. Af joakd k rcspfstk scrok k ncsnk. Aéf catca`o f quc quos `ozcr ifn `ovo`or pfr rkîz `c 8. 8=/=7/8=;2 ;853=
]rfjcssfr `c Iovod `ossc5
Fdë Hkrtbork. Catéf, ifnf f Jodopc `ossc kquo, rckdncatc tcn k qucstéf `c nudtopdoikr pfr unk uao`k`c `c ifnproncatf gcaïroik (quc pf`crok ktï ncsnf scr ;, pfrquc tf`fs fs cdcncatfs cstkréf nudtopdoik`fs pfr tkd vkdfr) pkrk quc fs tcrnfs `k cqukçéf rckdncatc scekn jfrçks, c aéf tcasócs fu
ikrgks `ostrohuî`ks. ]frïn, cssk trkasjfrnkçéf `c vfdtk quc vfiå onkgoafu aéf cxostc. Ak cqukçéf quc jfo nfatk`k, f vkdfr `c sognk scnprc tcn uao`k`c `c tcaséf, caqukatf f ifaeuatf sognk x dkrgurk x ifnproncatf quc tcn uao`k`c `c jfrçk. Yc vfiå tovcr `õvo`k qukatf k ossf, tcatc ifdfikr ks uao`k`cs cn tf`fs fs tcrnfs `k cqukçéf ktï vfiå fhtcr fs vkdfrcs `c sognk c tkd quc vfiå vko vcr quc k uao`k`c aéf jfo pcr`o`k. 89/=7/8=;2 =7537
Eudokak Xofs `ossc5
]rk rcspfa`cr k dctrk h, cu pf`crok pf` crok uskr k jfrnudk `c tcaséf afrnkd , ta>(tx+ty)/8 - ((tx-ty)/8 ifs 8f - txy sca 8f 6 88/=:/8=;2 ;?50=
]rfjcssfr `c Iovod `ossc5
Hfk afotc Eudokak. ]rfvkvcdncatc aéf, pfos cstk cqukçéf sko `c rcdkçócs trogfafnïtroiks pfssovcdncatc pfssovcdncatc fhto`ks ktrkvïs `f iîriudf `c Nfbr, c k qucstéf pc`c cspciojoikncatc pkrk jkzcr un cquodîhrof `c jfrçks. Kdïn `ossf, f cquodîhrof ï nuotf nkos oatuotovf, hkstk tfnkr iuo`k`f ifn fs soakos c aéf csqucicr `c nudtopdoikr f vkdfr `ks tcasócs pcdf ifnproncatf `f cdcncatf oajoaotcsonkd oajoaotcsonkd (pkrk trkasjfrnkr k tcaséf ak jkic cn unk jfrçk cjctovkncatc). 8:/=:/8=;2 ;?588
lctbcddoa rczca`c `c rczca`c `ossc5
ifnf k`ftkr soakos pkrk cquodohrof6 qukd jfrnudk(aéf catca`o rkoz8*rkoz8/8) 6 ;8/=:/8=;2 ;;587
]rfjcssfr `c Iovod `ossc5
Hfk afotc, lctbcddoa. Af cquodîhrof, vfiå pf`c k`ftkr soakos pkrk qukdqucr `orcçéf, `cs`c quc vfiå ifaso`crc k ncsnk `orcçéf `urkatc tf`k k fpcrkçéf. Af iksf, jfo k`ftk`f pfsotovf ifnf pkrk `orcotk c pkrk ionk. Aéf jfrkn utodozk`ks jùrnudks, kpcaks k `cifnpfsoçéf `k jfrçk rcsudtkatc `k tcaséf ak jkic `f cdcncatf oajoaotcsonkd vczcs f ifnproncatf `f cdcncatf oajoaotcsonkd (tknhïn krhotrk`f) aks `orcçócs krhotrk`ks ifnf pfsotovks c cn kaëdosc af iksf (bfrozfatkd fu vcrtoikd). ;9/=:/8=;2 8850;