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8/4/2019 Simulation Hypothesis and Intelligent Design, are we living in a Computer Simulation?
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Obeompts tdnt dnvm prbvme usmcua ke brfmrkeh tdkehs mnskay nttnke suod ne nutdbrktybvmr us tdnt wm cbrhmt tdmkr Mnrtday brkhkes nef noompt tdml ns uenatmrn`am cnots.
Vdm pntd bc sokmetkcko nfvneom ks bctme lnfm klpnssn`am cbr n abeh tklm tdrbuhd
suod mrrbrs bur obeomptkbes bc Wdyskona Pmnakty one emvmr `m fmckektkvm: wm lustnawnys `m rmnfy tb natmr tdml, tb natmr, tdnt ks, tdm nxkblntko `nsks bc pdyskos
Na`mrt Mkestmke
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Wrbhrnllkeh lnss, spnom neftklm ke n Skrtuna ]ekvmrsm
Nrm wm akvkeh ke n Oblputmr
_kluantkbe2
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Vdm Skrtuna ]ekvmrsm9
Vdm Lntrkx ks n >;;; sokmeom ckotkbe ckal tdnt fmpkots n fystbpkne cuturm ke
wdkod rmnakty ns pmromkvmf `y lbst dulnes ks notunaay n skluantmf rmnakty onaamf
"tdm Lntrkx", rmcmrmeokeh `btd Wantb's Naamhbry bc tdm Onvm nef Wytdnhbrns qubtm
naa ks eul`mr. Vdm _kluantkbe Dypbtdmsks prbpbsms tdnt naa rmnakty, bur mnrtd nefbur uekvmrsm, ks ne nrtkckokna skluantkbe, lbst akjmay n oblputmr skluantkbe.
Vdks tmxt ketrbfuoms tdm lntdmlntkos bc n vkrtuna uekvmrsm. Kt ks `nsmf be ncbrluan cbr n vkrtuna mamotrbecm< 6
0r?(r < 03?0=). @y rmvmrsm mehkemmrkeh tdksmamotrbe K one rm-obestruot tdm pdyskona fklmeskbes bc bur uekvmrsm ns hmblmtrkona
cbrls: lnss < >, tklm < 0, amehtd < 000. ]skeh tdmsm cbrls, K one tdme fmrkvmtdm obestnets bc pdyskos (H, d, o, m, lm, j@). Vdm _K uekts (jh, l, s, N, J br O)
rmfuom tb n skeham uekt u. Kc tdm anws bc pdyskos one `m obestruotmf crbl n fmmpmrsmt bc anws tdme obuaf tdmrm `m n fmmpmr rmnakty wktd us ns tdm klnhm bc tdks rmnakty.
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Vdm Wrbhrnllmr9
Hbf vs. sokmeom fm`ntms tmef tb `m rmstrkotmf tb tdm prmlksm tdnt n Hbf fbms
ebt emmf sokmeom nef tdnt sokmeom fbms ebt emmf n Hbf. Ns sokmeom nef Hbf nrm
tdus smme ns lutunaay mxoauskvm tdmrm nrm cmw, kc ney, smrkbus nttmlpts tb obestruotlntdmlntkona lbfmas bc n uekvmrsm wdbsm prkeokpam nxkbl fbms rmqukrm n Hbf (tdm
Ketmaakhmet Fmskhe prmlksm). Dbwmvmr, kc tdmrm ks n Hbf `mdkef tdm >6 `kaakbe ymnr
baf uekvmrsm bc lbfmre pdyskos, `mkeh tdm uekvmrsm bc Mkestmke nef Fkrno rntdmr
tdne tdm naamhbrkona 8 fnys bc ormntkbe, nef tdus `mhkeekeh wktd tdm `kh `neh, tdme
wm lust nsj dbw wbuaf DM fb kt2 Xdnt obestruotkbe tmodekqum lkhdt n Hbf usm2
Wantbs Onvm fmsork`ms n Skrtuna ]ekvmrsm lbfma tdnt rmsml`ams n Oblputmr_kluantkbe. Vdm nenabhy ks tdnt bc us ns odnrnotmrs wktdke n oblputmr hnlm wdb
nrm hkvme ne ketmaamot, n crmmfbl bc odbkom nef n amnrekeh onpn`kakty sb tdnt tdm
hnlm lny tdme pany but, prmsuln`ay wktd ne uefmtmrlkemf butoblm, curtdmrlbrm
tdm uatklntm purpbsm bc tdm hnlm ks ebt rmvmnamf tb tdm panymrs (us). Vdks dbwmvmr
rmqukrms tdnt tdm panymrs (us) lust tdme pmromkvm tdmlsmavms nef tdmkr skluantmf
rmnakty ns `mkeh tdnt bc n rmna pdyskona nef lntmrkna wbraf (bur lnss spnom tklm
uekvmrsm). Kt ks n pbssk`am sbautkbe tb suod n vkrtuna skluantmf uekvmrsm tdnt ks tdm
tdmlm bc tdks tmxt nef kt ks tdm nenaysks bc tdm lntdmlntkos `mdkef tdks sbautkbe tdnt
suhhmsts n oblputmr obfm nef tdks ks okroulstnetkna mvkfmeom cbr n Wrbhrnllmr.
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Wantbs Naamhbry bc tdm Onvm9
Vdm Hrmmj pdkabsbpdmr Wantb wrbtm n fknabhum, tdm Naamhbry bc tdm Onvm(obllbeay jebwe ns Wantbs Onvm), `mtwmme dks `rbtdmr nef _borntms ke wdkod dm
oblpnrmf us tb prksbemrs odnkemf ke crbet bc n onvm wnaa. @mdkef tdm prksbemrstdmrm ks n ckrm nef luod notkvkty, dbwmvmr `mkeh odnkemf, tdmy one smm beay tdm
sdnfbws bc tdks notkvkty prbimotmf `y tdm ckrm betb tdm wnaa ke crbet bc tdml.
Mxpmrkmeokeh beay tdm onvm wnaa, tdmy wbuaf tdkej tdnt tdm sdnfbws fkspanymf be
tdnt wnaa nrm rmna nef sb tdmsm sdnfbw klnhms wbuaf cbrl tdmkr rmnakty.
Bem fny n prksbemr msonpms crbl tdm onvm: smms tdm sue, sjy, anef butskfm,nef rmtures tb tmaa dks cmaabws bc tdm wbefmrs bc tdm rmna wbraf. Vdks dbwmvmr
`moblms dmrmsy ns kt odnaamehms tdmkr noouluantmf wksfbl, tdmkr jebwamfhm nef
tdmkr odmrksdmf `makmcs: tdm wnaas bc tdmkr onvm. _borntms, wdb ks tmaakeh tdks stbry,
wrbtm bc tdm rmturemm: wbuaf dm ebt sny wktdDblmr... `mttmr tb `m tdm pbbr smrvnet
bc n pbbr lnstmr, nef tb mefurm neytdkeh, rntdmr tdne tdkej ns tdmy fb nef akvm nctmrtdmkr lneemr.
_borntms dklsmac wns smetmeomf tb fmntd cbr ebt `makmvkeh ke tdm hbfs bc tdmstntm nef cbr obrruptkeh ybueh lkefs.
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Ke Wantb's tdmbry bc Cbrls, dm nrhumf tdnt ebe-pdyskona cbrls rmprmsmet tdm
lbst noourntm rmnakty, nef tdus _borntms prksbemrs wbuaf lkstnjm nppmnrneom cbr
rmnakty. Vdmy wbuaf tdkej tdm tdkehs tdmy smm be tdm wnaa (tdbsm sdnfbws) wmrm rmna:
`ut tdmy wbuaf jebw ebtdkeh bc tdm rmna onusms `mdkef tdm sdnfbws. Vdus wdme n
prksbemr smms tdm sdnfbw bc ne nppam prbimotmf betb tdm onvm wnaa dm wkaa fmoanrm
tdnt ks ne nppam, `ut ke rmnakty dm ks beay fmsork`keh tdm sdnfbw bc tdm rmna nppam.
Wantb tdus nrhums tdnt tdm prksbemrs nrm uskeh tdmkr anehunhm tb rmcmr tb
sdnfbws bc tdm rmna tdkehstdnt onst tdm sdnfbws. Xdme wm stntmtdks ks ne nppam, wm nssbokntm tdm wbrf nppam tb tdm pdyskonanppam wdkod wm dbaf ke bur dnefs, `ut dm nrhums tdnt wm nrm uskeh
tdks wbrf tb oansskcy ne klnhm bc tdm rmna nppam. Ke _borntms vkmw
bur anehunhm rmcmrs ebt tb tdm enlms bc tdm pdyskona b`imots tdntwm one smm `ut nrm notunaay enlms bc tdkehs tdnt wm oneebt smm,
tdkehs tdnt wm one beay hrnsp wktd tdm lkef, eb 0 nppams nrm tdm snlm nef sb tdm
wbrf nppam rmcmrs tb ne nppam tmlpantm, tdnt crbl wdkod nppam-emss fmrkvms. Xm
lny mnt tdnt wdkod wm oansskcy ns ne nppam `ut tdm notuna wbrf nppam rmcmrs tbsblmtdkeh tdnt wm dnvm emvmr mxpmrkmeomf. Akjmwksm, wm lny noqukrm obeompts `y
bur pmromptuna mxpmrkmeom bc pdyskona b`imots, `ut wm wbuaf `m lkstnjme kc wm
tdbuhdt tdnt tdm obeompts tdnt wm hrnsp wmrm be tdm snlm amvma ns tdm tdkehs wm
pmromkvm. Burs lny `m n pmromkvmf rmnakty.
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Beom, Yduneh Ydbu frmnlmf dm wns n `uttmrcay, n `uttmrcay cakttkeh nef cauttmrkehn`but, dnppy wktd dklsmac nef fbkeh ns dm pamnsmf. Dm fkfe't jebw tdnt dm wns
Yduneh Ydbu. _uffmeay dm wbjm up nef tdmrm dm wns, sbakf nef uelkstnjn`am
Yduneh Ydbu. @ut dm fkfe't jebw kc dm wns Yduneh Ydbu wdb dnf frmnlt dm wnsn `uttmrcay, br n `uttmrcay frmnlkeh tdnt dm wns Yduneh Ydbu. @mtwmme Yduneh
Ydbu nef tdm `uttmrcay tdmrm lust `m sblm fkstkeotkbe!
-wkjk/Ydunehzk
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Vdm Wrbhrnllmf ]ekvmrsm9
Ke tdm oansskona Emwtbekne vkmw, spnom wns smme ns n ? fklmeskbena struoturm
wktdke wdkod wm ckef ntbls nef panemts. Vklm wns an`mamf tdm 6tdfklmeskbe nef
tdus wm obuaf fmckem mvmets `y hkvkeh tdm (?-F) abontkbe ob-brfkentms nef `y ckxkehtdm tklm: wdmtdmr nrrnehkeh tb lmmt ke tdm 8tdcabbr bc n ak`rnry be ?6tdnef L strmmt
nt >pl br fmsork`keh tdm br`kts bc tdm panemts.
Nctmr Mkestmke ketrbfuomf tdm rmantkvm ns bppbsmf tb tdm Emwtbekne n`sbautm
uekvmrsm, pdyskos obl`kemf spnom nef tklm ketb n skeham 6-F spnom-tklm ns tdm
lmnes tb mxpanke b`smrvmf neblnakms tb tdm oansskona wbraf-vkmw.
Antmr strkeh tdmbrkms wmrm ketrbfuomf, bccmrmf ns n pbtmetkna sbautkbe tb tdm
Vdmbry Bc Mvmrytdkeh, `ut tdmy rmqukrm mxtrn fklmeskbes bc spnom-tklm, ke `bsbeko
strkeh tdmbry, spnom-tklm ks 03-fklmeskbena, supmr-strkeh tdmbry ks >7-fklmeskbena
nef supmr-hrnvkty tdmbry >>-fklmeskbena.
Obevmrsmay tdm Neokmet ]ekvmrsm, `mkeh tdm ]ekvmrsm bc tdm neokmet Hrmmj
pdkabsbpdmrs nef tdm mnstmre lystkos: rnehkeh crbl Wytdnhbrns tb tdm Vnb, wns
fmsork`mf lntmrknaay ke hmblmtrkona tmrls (tdm Hrmmjs) nef nasb syl`bakonaay
wdmrm suod syl`baksl wns nasb mxprmssmf ke tmrls bc hmblmtrkona sdnpms, nef
lney bc tdmsm hmblmtrkms nrm stkaa naaufmf tb tbfny ns meobfkeh `btd bpme nef
dkffme lmnekehs.
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Ns tdm lbfma fmsork`mf ke tdks tmxt prbhrmssmf, natdbuhd mxprmssmf ke tmrls bc
tdm lbfmre uekvmrsm, nxkbls `mhne tb nppmnr nef tdmsm nxkbls lbst oabsmay
rmsml`amf tdm Neokmet ]ekvmrsm, natdbuhd tdks wns ebt brkhkenaay ketmefmf.
Vdks lbfma obuaf `m oansskckmf uefmr Lntdmlntkona ]ekvmrsm Dypbtdmsks ketdm Wytdnhbrmne smesm (ns pbpuanrkzmf `y tdm sok-ck oanssko Vdm Lntrkx)nef ns n_kluantkbe Dypbtdmsks (n prbhrnlln`am vkrtuna uekvmrsm). Kt suhhmsts tdnt bur
pdyskona uekvmrsm ks ne klnhm prbimotmf wktdke n vkrtuna uekvmrsm wdkod `btd
rmsml`ams tdm `anoj dbam bc lbfmre pdyskos nef tdm Sbkf bc Hmemsks.
Vdm lbfma ks obestruotmf nrbuef n dypbtdmskzmf cbrluan cbr n vkrtuna (`anoj-dbam) mamotrbe. Crbl tdks cbrluan wm one rmvmrsm mehkemmr tdm uefmraykeh struoturms
bc bur cnlkaknr pdyskona fklmeskbes bc lnss L, spnom A, tklm V, vmabokty S, odnrhm
NHmblmtrkona cbrls tdme mlmrhm tdnt rmsml`am sdnpms tdnt wm nrm cnlkaknr wktd,(pbket, okroam, spdmrm, fbuhdeut tbrus) na`mkt tdmy nrm beay lntdmlntkona cbrluans.
Vdmy nrm ebt bc bur pdyskona wbraf.]skeh tdmsm hmblmtrkona cbrls: lnss L, tklm V
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obestnets (H, d, o, m, lm, j@) wdkod nrm tdm crnlmwbrj bc burpdyskona uekvmrsm, nef kt ks tdm prmokskbe bc tdmsm rmsuats wdkod
hkvms vmrnokty tb tdks lbfma cbr tdm rmsuats nrm obeskstmet wktd tdm
antmst mxpmrklmetna vnaums (jebwe ns OBFNVN 07>6).
Curtdmrlbrm K nl uskeh beay 0 ckxmf lntdmlntkona obestnets
(napdn nef Blmhn: , ) nef 0 sonanrs. K nasb rmpanom bur lnssspnom tklm odnrhm tmlpmrnturm uekts wktd n skeham fklmeskbe u, cbr
(jh, l,s,N, j) nrm dulne obestruots nef ebt tdm uekts bc tdm Hbfs.
K tdus nrhum tdnt tdm lntdmlntkos bc tdks tmxt suhhmsts tdnt wmnrm kedn`ktkeh n vkrtuna uekvmrsm tdnt ks fmvmabpkeh noobrfkeh tb n prm-fmtmrlkemf
smt bc lntdmlntkona ruams odbsme suod tdnt tdm prmsmet uekvmrsm, crbl tdm `kh `neh
uetka tbfny, keoaufkeh dulne akcm, wns ml`mffkeh ketb tdm brkhkena sburom obfm.
Vdmsm lntdmlntkona ruams wmrm smamotmf suod tdnt tdmsm hmblmtrkona cbrls obuaf
obl`kem tb cbrl oblpamx `mdnvkbrs, wm onaa tdks swnrl ketmaakhmeom nef K curtdmrsu`lkt tdnt wm nrm ne mxnlpam. Bur pdyskona rmnakty ks tdus n prbimotkbe, suod ns
Wantb fmsork`mf, `ut wktdke tdks vkrtuna rmnakty.
@ut kc bur uekvmrsm rmsml`ams n oblputmr skluantkbe, ns tdm lntdmlntkos bc
tdks lbfma wbuaf smml tb suhhmst, tdme wm lkhdt tdme nsj: wdb prbhrnllmf tdks
skluantkbe nef wdy2
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Wantbs Onvm9
Vdks tmxt ketrbfuoms n lbfma bc n Skrtuna ]ekvmrsm. Ke tdm ckrst smotkbe, Wnrts K
& KK, K ketrbfuom tdks lbfma ke tmrls bc nxkbls tdnt rmsml`am tdbsm bc tdm Neokmet
]ekvmrsm ymt K nl fmsork`keh obllbe pdyskona pdmeblmen, wnvm-pnrtkoam funakty
cbr mxnlpam. K tdme abbj nt sblm bc tdm pdkabsbpdkona klpakontkbes bc suod n lbfma.
Ke tdm smobef smotkbe, Wnrts KKK& KSK mxpnef upbe tdm pdyskos bc tdks lbfma
nef ketrbfuom tdm `nsko lntdmlntkos, cbr wktdbut tdks `nojhrbuef tdm lbfma oneebt
`m npprmokntmf. K nasb try tb obevmy n smesm br cmmakeh cbr dbw tdm uekvmrsm usms
tdks lntdmlntkos, cbr natdbuhd tdm hmblmtrkms fmsork`mf dmrm nrm quktm sklpam (naatdm cbrluans one `m sbavmf wktd n `nsko onaouantbr), kt wkaa qukojay `m b`smrvmf tdnt
tdmy nrm usmf ke wnys tdnt nrm uecnlkaknr tb us nef wkaa rmqukrm emw lntdmlntkona
lmtdbfs tb fmobfm.
Vdmrm ks skhekckonet lntdmlntkos ke tdks tmxt, tdks oneebt `m nvbkfmf cbr kt ks
tdm lntdmlntkos upbe wdkod tdks tdmbry ks obestruotmf, nef ney tmxt wktdbut n sbakfcbuefntkbe ks sklpay n oblpkantkbe bc pdkabsbpdkona luskehs, dbwmvmr K dnvm trkmf
tb struoturm tdm tmxt sb tdnt tdm tdmbry mvbavms ke oblpamxkty, amst K absm rmnfmrs tbb
qukojay. Wnrts Knef KKone `m smme tdmrmcbrm ns tdm `nojfrbp tb Wnrts KKK nef KS.
Akjmwksm kt ks tdm lntdmlntkos nef ebt ly ketmrprmtntkbe tdnt ks klpbrtnet, tdm
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rmnfmr ks kevktmf tb frnw tdmkr bwe obeoauskbes crbl tdm cbrluans prmsmetmf dmrm
cbr tdm klpakontkbes bc suod n lbfma nrm cnr-rmnodkeh.
Curtdmrlbrm, tdks lbfma klpakms tdnt bur pdyskona rmnakty ks n prbimotkbe wktdke
n vkrtuna rmnakty, nenabhbus tb n oblputmr skluantkbe. Vdm tmxt prmsmets hmblmtrkona
sbautkbes tb obllbe pdyskona pdmeblmen suod ns rmantkvkty nef hrnvkty: tdmsm
sbautkbes sdbuaf `m smme, ebt ns pdyskona mxpanentkbes cbr b`smrvntkbes bc tdm
lbfmre uekvmrsm `ut ns nahbrktdlko (sbctwnrm) rbutkems tdnt one skluantm tdbsm
pdyskona pdmeblmen. Ke btdmr wbrfs, K nl fmsork`keh sbautkbes tb tdmsm pdmeblmen
(hrnvkty, rmantkvkty, mamotrbes mto.) ebt crbl tdm pmrspmotkvm bc n pdyskokst trykeh tb
mxpanke tdml crbl wktdke n pdyskona uekvmrsm, `ut rntdmr ns n prbhrnllmr wdb ks
nsskhemf tdm tnsj bc nppaykeh n lntdmlntkona tdmbry tb hmblmtrkona cbrls ke suod n
wny tdnt wktdke dks uekvmrsm skluantkbe smac-nwnrm brhneksls one ebt beay mlmrhm,
`ut tdnt tdmy wkaa tdme pmromkvm tdmlsmavms ns `mkeh wktdke n pdyskona mevkrbelmet
nef ns dnvkeh n crmm-wkaa.
Mnod cbrluan tdus prmsmetmf ke tdks tmxt tdus fmsork`ms n pnrtkouanr cueotkbe:
obesmqumetay mnod cbrluan dns kts bwe stbry tb tmaa nef tdks stbry ks tdm stbry bctdm uekvmrsm ktsmac
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Vdm Fkamlln bc Fklmeskbes
@mdkef kt naa ks surmay ne kfmn sb sklpam, sb `mnutkcua, tdnt
wdme wm hrnsp ktke n fmonfm, n ometury, br n lkaameekulwm
wkaa naa sny tb mnod btdmr, dbw obuaf kt dnvm `mme btdmrwksm2 Dbw
obuaf wm dnvm `mme sb stupkf cbr sb abeh2
Ibde Nrodk`naf Xdmmamr
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Vdm `akef lme nef ne mampdnet9
Vdm oanssko pnrn`am bc tdm `akef lme
nef ne mampdnet, pnrt bc @uffdkst, Inke,
_uck nef Dkefu cbajabrm, tmaas bc n hrbup
bc `akef lme wdb mnod tbuod ne mampdnet
tb amnre wdnt kt ks akjm. Mnod cmmas n
fkccmrmet pnrt, `ut beay bem pnrt, suod ns
tdm skfm br tdm tusj. Vdmy tdme oblpnrm
ebtms nef amnre tdnt tdmy nrm naa ke
fksnhrmmlmet, natdbuhd mnod nrm bc obursm
obrrmot. Nctmr rmnakzkeh tdmkr lkstnjm tdmy
nrm n`am tb rmobestruot tdm mampdnet.
Vdmrm nrm lney pnrnlmtmrs tdnt wm usm tb fmsork`m bur mevkrbelmet: skzm,
sdnpm, obabr, tmxturm, wmkhdt, tmlpmrnturm nef sb be Kc mvmrytdkeh wns `anojtdme wm wbuaf dnvm eb lmnes `y wdkod tb lmnsurm obabr cbr tdmrm wbuaf `m ebobabrs tb lmnsurm nef sb lmnsurmlmet rmqukrms n hrnfkmet, kc tdmrm nrm eb `kh
nppams tdme tdmrm one `m eb slnaa nppams, tb lmnsurm tmlpmrnturm wm one fmckem 7O
nef tdme lmnsurm naa tmlpmrnturm rmantkvm tb tdks 7O (`ut tdks wbuaf ebt `m pbssk`am
kc mvmrytdkeh wns tdm snlm tmlpmrnturm cbr tdme tdmrm wbuaf `m eb tmlpmrnturm tb
lmnsurm), akjmwksm wm one odbbsm n lmfkne nppam nef oblpnrm naa nppams tb kt. Nef
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sb wdnt wm nrm fbkeh ks b`smrvkeh > nspmot bc bur uekvmrsm, odbbskeh n rmcmrmeom
cbr tdnt nspmot, nef tdme fmckekeh n uekt (obabr, wmkhdt) nef n lmnsurmlmet sonamcbr tdnt uekt. Vdks lny `m wdy Wantb `makmvmf tdmrm mxksts ne kllntmrkna ]ekvmrsm
bc cbrls, pmrcmot nspmots bc mvmryfny tdkehs suod ns tn`ams nef `krfs, nef tdnt bur
b`imots (nef kfmns) nrm sdnfbws bc tdmsm uekvmrsna rmcmrmeom cbrls br tmlpantms.
_okmeom usms n prmoksm systml bc lmnsurmlmets wdme fmsork`keh bur uekvmrsm,
wbrfs suod ns lnss, hrnvkty, vmabokty, tklm, mamotrkokty nrm pnrt bc bur amxkobe. Vdks
tdme rnksms tdm qumstkbe, wdkod nspmots bc bur uekvmrsm tdnt wm lmnsurm nrm n pnrt
bc tdm pdyskona uekvmrsm (k.m.9 tdm spmmf bc akhdt) nef wdkod nrm prmsuln`ay purmay
dulne obestruots (k.m.9 nrt npprmokntkbe).
Kc n onr trnvmas >77lkams br >77jl ke > dbur tdme wm one onaouantm tdm vmabokty
S ns >77lpd br >77jlpd. Kc wm jebw tdm fkstneom (A77jl) nef tklm (Vdr),
tdme wm jebw tdm vmabokty (S < AV < >77jlpd), obevmrsmay kc wm jebw vmabokty
(>77jlpd) nef tklm (>dr), wm one onaouantm tdm fkstneom (A < SV < >77jl) nefsb cbrtd. Vdks tdme rnksms n prb`aml, kc K jebw 0 bc tdmsm prbpmrtkms tdme K one
onaouantm tdm tdkrf, nef sb wdkod 0 bc tdmsm ? prbpmrtkms ASV (amehtd, vmabokty, tklm)
nrm cuefnlmetna2 Kc K one usm tklm nef vmabokty tb lnjm spnom (A
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lnss, memrhy, mamotrko odnrhm nef sb be. Kc M7, tdm lnss bc tdm mamotrbe lm< .;>7;?40;>m-
?7, Waneojs obestnet d < .330373;=8m-??, wm one wbrj `nojwnrfs tb fmobfmtdm mampdnet.
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Vdm Lntdmlntkona ]ekvmrsm9
Hmblmtry tdus oblpamtmf ks mvkfmetay n enturna sokmeom: wm lny ke cnot rmhnrf ktns tdm lbst neokmet `rneod bc pdyskos
N. MkestmkeBur `rnkes nrm onpn`am bc amnrekeh n`but tdkehs butskfm bur pdyskona wbraf nef
butskfm bur bwe mxpmrkmeom suod ns n`strnot lntdmlntkos. Vdmbrkms bc hmblmtry,
suod ns Wytdnhbrns rkhdt neham trkneham tdmbrml rmantm tb obeompts tdnt nrm emvmr
mxpmrkmeomf ke bur fnkay akcm: pmrcmotay strnkhdt akems wktd eb tdkojemss tdnt
ketmrsmot nef cbrl eul`mrs suod ns tdm squnrm rbbt bc 0 tdnt dnvm eb sbautkbe. Ke n?-F wbraf tdmrm one `m eb squnrms br okroams, cbr mvme tdm tdkeemst okroam stkaa dns n
tdkojemss, br pmrcmotay spdmrkona sdnpms cbr pk () tbb dns eb mxnot sbautkbe.
Vdmsm nrm ebt obeompts wdkod lny `m enturnaay b`smrvmf ymt pmbpam jebw bc
tdml nef ebt lmrmay tb n supmrckokna amvma. Vdks puzzamf Wantb wdb obeoaufmf tdnt
suod jebwamfhm wdkod any butskfm tdnt wdkod wm lny jebw dnf oblm tb us crbl
tdm Hbfs.
Akjmwksm snormf hmblmtry prmsulms tdnt tdm uekvmrsm wns ormntmf `y Hbf
noobrfkeh tb n spmokcko hmblmtrkona pane: ke mssmeom kt ks n smnrod cbr tdm ckehmrprket
bc Hbf ke tdm lnjm-up bc tdm dmnvmes. Vdm `makmc tdnt Hbf ormntmf tdm uekvmrsm
tdus dns neokmet brkhkes, Wautnrod nttrk`utmf kt tb Wantb. _uod snormf hmblmtry obuaf
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dbwmvmr dnvm pmrcmot okroams nef squnrms cbr kt emmf ebt `m obestrnkemf `y tdm
pdyskona aklktntkbes bc bur ?-F wbraf.
Vdus n pmrcmot okroam br n pmrcmot squnrm lny mxkst wktdke tdm klnhkentkbe bc
lntdmlntkoknes nef ke tdm rmnal bc tdm Hbfs `ut ebt mxkst ns n pdyskona metkty
wktdke n pdyskona wbraf, tdm cbrluan cbr tdm nrmn bc n okroam cbr mxnlpam one `m
wrkttme prmoksmay ns r0`ut sbavmf beay tb ne npprbxklntkbe (mvme kc wm usm pk tb >lkaakbe fkhkts prmokskbe kt ks stkaa ebt mxnotay pk, smm `mabw).
Lntdmlntkona rmnaksl dbafs tdnt lntdmlntkona metktkms mxkst kefmpmefmetay bc
tdm dulne lkef. Xm fb ebt kevmet lntdmlntkos, `ut rntdmr fksobvmr kt. Vrknehams,cbr mxnlpam, nrm rmna metktkms tdnt dnvm ne mxkstmeom.
Vdm lnibr prb`aml bc lntdmlntkona Wantbeksl ks tdks9 prmoksmay wdmrm nef
dbw fb tdm lntdmlntkona metktkms mxkst, nef dbw fb wm jebw n`but tdml2 Ks tdmrm
n wbraf, oblpamtmay smpnrntm crbl bur pdyskona bem tdnt ks booupkmf `y tdm
lntdmlntkona metktkms2 Xdnt ks tdm rmantkbesdkp `mtwmme tdmsm twb wbrafs, burpdyskona wbraf bc lnss nef spnom nef tklm nef mamotrb-lnhemtksl nef tdm
lntdmlntkona wbraf tdnt Wantb nef Wytdnhbrns spbjm bc wdmrm rnfkus nef nrmn nef
vbaulm nrm purmay lntdmlntkona obeompts wktdbut pdyskona aklktntkbes2
80=?=;674>0464>>>86=704
6>7087>;?4=0>>7===;366300;64;=6;?7?4>;366044>7;8=33=;??663>0468=3640?? 4384?>3=0
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Vdm Pmnal bc tdm Hbfs9
Vdmrm nrm lney pnrnlmtmrs `y wdkod K one fmsork`m ly anptbp: skzm, obabr,
wmkhdt, lmlbry, spmmf akjmwksm tdm odnkr K skt be, tdm pme tdnt K nl dbafkeh, neftdm wbraf n`bvm nef `mabw lm. Kefmmf tdks ks tdm odnrnotmrkstko bc n pdyskona
uekvmrsm, tdnt wm lny fmsork`m mvmrytdkeh crbl mamotrbes (lnss, wnvmamehtd,
odnrhm, spke) tb nppams (obabr, tnstm) tb hnanxkms. Abbsmay wm lny fmckem tdmsmpnrnlmtmrs ns fklmeskbes (k.m.9 tdm fklmeskbes bc ly anptbp nrm), nef sb fmckem npdyskona uekvmrsm `y kts fklmeskbenakty ke obetrnst tb Wantbs lntdmlntkona wbrafbc tdmbrmtkona cbrls. Vdm qumstkbe tdme `moblms, obuaf tdmrm `m ne notuna metkty cbr
wdkod eb fmsorkptkbe one `m lnfm: cbr tdmrm ks eb lnss br amehtd br tklm br neybtdmr fklmeskbena pnrnlmtmr `y wdkod suod n fmsorkptkbe lny `m cbrluantmf.
Hbf ks `y fmckektkbe tdm oanssko mxnlpam, cbr ns sbbe ns wm fmsork`m Hbf wm
nrm nutblntkonaay nasb fmsork`keh tdnt wdkod DM ks ebt, kc Hbf ks rmf tdme DM ks ebt
hrmme, kc `kh tdme DM ks ebt slnaa, nef sb ney fmsorkptkbe wm lnjm bc Hbf aklkts
Hbf nef tdks obetrnfkots tdm vmry fmckektkbe bc n Hbf ns `mkeh `mybef fmckektkbe.
Nef sb ns abeh ns bur pdyskona uekvmrsm dns fmcken`am pnrnlmtmrs, Hbf oneebt
`m wktdke, cbr ns sbbe ns Dm ks wktdke bur uekvmrsm Dm one `m fmckemf nef Dm ks
tdme aklktmf `y tdks fmckektkbe, ns n rmsuat Dm ks eb abehmr Hbf. Vdm lnibr rmakhkbes
rmsbavmf tdks prb`aml `y uskeh n lkffamlne: Lbsms spbjm tb n `urekeh `usd,Imsus dnf tdm Dbay _pkrkt, Lbdnllmf tdm nehma Hn`rkma
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Vbdu wn `bdu ks n Dm`rmw pdrnsm cbuef ke tdm @bbj bc Hmemsks >90 tdnt
fmsork`ms tdm mnray uekvmrsm. Kt ks usunaay trnesantmf ns vbkf,cbrlamss,sdnpmamss, suhhmstkeh tdnt tdm prm-uekvmrsm nasb dnf eb pnrnlmtmrs `y wdkod n fmsorkptkbe
obuaf `m lnfm btdmr tdne sklpay Kt Ks, wdkod lny mxpanke wdy Hbf spbjm bc
dklsmac sklpay ns K Nl mdymd nmr mdymd: K nl tdnt K nl, Mxbfus ?9>6, br `ymeoblpnsskeh mvmrytdkeh: K nl tdm ckrst nef K nl tdm anst. Ksnknd 6693.
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Vdm Ckehmrprket bc Hbf9
Vdm fm`ntm bvmr tdm brkhke bc bur uekvmrsm ks fkvkfmf `mtwmme twb lnke
hrbups: tdm rnefbl uekvmrsm bc sokmeom, tdnt bur uekvmrsm ks `ut ebt cbr ney
pnrtkouanr rmnsbe, nef tdm uekvmrsm bc tdmbabhy, tdnt tdm uekvmrsm ks ke sblm smesm
paneemf, tdmrm ks ne ketmaakhmeom (n Hbf) `mdkef kt, nef sb tdm uekvmrsm ks `monusmkt obuaf ebt `m btdmrwksm.
_okmeom tmefs tb suppbrt tdm rnefbl uekvmrsm, oanklkeh tdnt ne butskfm
ketmaakhmeom, ketmaakhmet fmskhe njn n ormntbr, ks kedmrmetay cnktd `nsmf nef sb
`mybef tdm sokmetkcko lmtdbf: cbr mxnlpam, n tdmbry lny prmfkot tdnt wntmr wkaa`bka nt >77O, sokmeom one tdme obefuot mxpmrklmets tb tmst tdks dypbtdmsks, tdm fntn
tdme suppbrtkeh, br ebt, tdnt dypbtdmsks, obevmrsmay n cnktd `nsmf dypbtdmsks oneebt
`y fmckektkbe `m tmstmf br vmrkckmf. N Hbf dypbtdmsks dns tb tdmrmcbrm rmay beokroulstnetkna mvkfmeom, tdnt tdmrm ks n pnttmre tb bur uekvmrsm wdkod oneebt `m
mxpankemf `y ney tdmbry ke pdyskos, tdks pnttmre `mkeh tdm ckehmrprket bc Hbf, tdntlnrj tdnt Dm amct be Dks ormntkbe.
Vdm Neokmet ]ekvmrsm wns fmkty-`nsmf: wm lbrtnas akvkeh be n pdyskona wbraf
wktd tdm Hbf(s) nef tdm spkrkts kedn`ktkeh tdm lystmrkbus dmnvmes. Obesmqumetay
bvmr tdm lkaameekul nef obetkeukeh mvme tbfny, lney bc tdbsm abbjkeh cbr suod n
ckehmrprket dnvm rmcmrrmf tb tdm syl`baksl bc tdm Neokmets.
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Ke tdm lbfma prbpbsmf ke tdks tmxt n onefkfntm cbr suod n ckehmrprket bc Hbf
mlmrhms, kt one `m obestruotmf crbl tdm lntdmlntkos bc n rbtntkeh okroam, ke pdyskos
kt obuaf `m fmckemf ns n `anoj-dbam mamotrbe, nef wm tdme ckef tdnt tdks mamotrbe
nppnrmetay bsokaantms `mtwmme bur lntmrkna wbraf bc lnss, spnom nef tklm nef tdm
fklmeskbeamss lntdmlntkona rmnal bc tdm Hbf(s), quktm pbssk`ay trnescmrrkeh
kecbrlntkbe ke tdm prbomss.
Vdks bsokaantkbe bc tdm mamotrbe `mtwmme bur pdyskona uekvmrsm nef tdnt
fklmeskbeamss vbkf K tdme prbpbsm ks n rmsuat bc rbtntkbe, tdnt nctmr > oblpamtm
rbtntkbe tdm mamotrbe fksnppmnrs crbl bur pdyskona wbraf lblmetnrkay ketb tdntfklmeskbeamss rmnal beay tb tdme rmnppmnr wktdke burs.
Xdkast ke bur pdyskona wbraf tdm mamotrbe dns cnlkaknr pnrnlmtmrs bc spke nef
odnrhm nef wnvmamehtd, tdmsm pnrnlmtmrs one `m lmnsurmf nef tdnt wdkod one `m
lmnsurmf lny akjmwksm `m an`mamf, nef sb tdmsm nrm fklmeskbemf pnrnlmtmrs, `ut
nctmr mnod oblpamtm rbtntkbe tdmsm fklmeskbena pnrnlmtmrs (bc odnrhm N, amehtd brspnom A nef tklm V), tdm pnrnlmtmrs tdnt obevmy mamotrbe-emss tb tdm mamotrbe,
lblmetnrkay bvmranp nef oneoma: mamotrbe uekts (NA)?/V < >.
Vdnt fklmeskbemf mamotrbe dns amct bur pdyskona wbraf: kt dns `moblm n
lntdmlntkona cbrluan, n sdnpmamss hmblmtrkona cbrl. Kt ks n vkrtuna mamotrbe.
Kt ks tdm mampdnet.
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Ke tdm `mhkeekeh wns tdm wbrf (Ibde >9>)9
K one oabsm ly myms nef pkoturm n okroam ke ly lkef, tdks ks ebt n okroam ktsmac
`ut ne klnhm bc n okroam, nef wm obuaf fmckem tdks klnhm ns n lntdmlntkona cbrl.
Ns sbbe ns K frnw br btdmrwksm obestruot n okroam tdme K dnvm n pdyskona okroam, nef
tdks pdyskona okroam dns n pdyskona rnfkus wdkod one `m lmnsurmf (ke lmtmrs cbr
mxnlpam). Vdm okroam bc ly klnhkentkbe dns eb pdyskona rnfkus nef tdus oneebt `m
lmnsurmf. Kt ks n cbrl, ebt n sdnpm.
Vdm wbrf fbh rmprmsmets tdnt neklna `ut kt ks ebt n pdyskona fbh, kt ks n fbh
klnhm mxprmssmf ke anehunhm. K obuaf mqunaay wrktm (Inpnemsm) br (Pusskne). Nef sb wdme K tnaj n`but n uekvmrsm bc lntdmlntkona cbrls, ke tdks
smesm K nl fmsork`keh _borntms anehunhm bc n purm lntdmlntkos (tdm wbrf br klnhm
okroam) kestmnf bc ne nppakmf lntdmlntkos (tdm notuna pdyskona okroam). Bem bc tdm
rmnsbes suhhmstmf cbr wdy wm oneebt rmlml`mr bur ckrst ymnrs ks tdnt `n`kms dnvm
eb anehunhm, k.m.9 eb pdyskona lmnes `y wdkod tb stbrm tdmsm lmlbrkms (br tdnttdmsm lmlbrkms nrm wrkttme bvmr `y n su`smqumetay amnremf anehunhm).
Kc bur lnss nef spnom nef tklm mto. dnvm mlmrhmf crbl tdm lntdmlntkona
uekvmrsm njn tdm Sbkf, tdme tdmy nasb dnvm lntdmlntkona cbrls noobrfkeh tb tdm
n`bvm fmckektkbe, `ut ns tdm cbrls ke ly klnhkentkbe tdmy dnvm eb lmnsurn`am
fklmeskbes. Nef sb kc tdm lmnsurn`am fklmeskbes bc bur pdyskona uekvmrsm nrm
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uatklntmay lntdmlntkona cbrls, tdme wdnt nrm tdmsm cbrls bc lnss L, tklm V nef
spnom (amehtd) A crbl wdkod bur lnss, spnom nef tklm fklmeskbes brkhkentm2
K prbpbsm n cbrluan cbr n vkrtuna mamotrbe cmtdnt rmsml`ams tdm cbrluan cbr n
tbrus: cm < 60r
? (r < 0
3?0=). Kt ks obestruotmf crbl 0 eul`mrs Blmhn ?3.7=;, dbwmvmr tdm rnfkus rks fklmeskbeamss, kt dns ebuekts, nef tdus cm ks n lntdmlntkona cbrluan tdnt fbms ebt mxkst ke ney pdyskona
smesm. Xdnt tdm uekvmrsm tdme fbms ks `rmnj up tdks cbrluan ketb oblpbemet pnrts
nef nsskhes tb tdml fklmeskbes. Dbw tdks wbrjs2 Xm one obestruot n tbrus uskeh
tdm okroulcmrmeom nef tdm nrmn bc n okroam: 0r r0< 00r?. Xm obuaf tdme nsskhetb tdmsm pnrts fklmeskbena uekts (x, y) wktd tdm prbvksb tdnt (x y < >) nef tdus
lnketnke tdm ketmhrkty bc bur fklmeskbeamss tbrus: 0rx r0y < 00r?(xy < >) mvmenatdbuhd tdm kefkvkfuna pnrts 0rxnef r0y nrm fklmeskbemf.
Vdm uekvmrsm tnjms tdks mamotrbe cbrluan cm nef spakts kt ketb
tdmsm pnrts (rkhdt obaule) wdkod wm b`smrvm nef fmckem ns L lnss(jh), A spnom (l), V tklm (s), S vmabokty (l/s), N nlpmrm Vdmuekvmrsm odbsm tdmsm sdnpms `monusm, natdbuhd fklmeskbemf, tdm
fklmeskbe pnrts tdmlsmavms bvmranp nef oneoma. Cbr mxnlpam, K one
spakt ly mamotrbe cmketb nlpmrm-lmtmrs (NA)?wdkod nrm lnhemtko
lbebpbams, nef tklm V tb hkvm lm `btd tklm nef odnrhm, `ut wdme
rmobl`kemf tdm uekts oneoma: (NA)?/V < >. Vdm uekvmrsm rmlnkes
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fklmeskbeamss, tdm tbtna bc naa fklmeskbes fmrkvmf crbl tdm vkrtuna mamotrbes oneoma:
uekts < >. Kt ks tdmsm vkrtuna mamotrbes wdkod nrm tdm lmodneksl usmf tb ormntm abona
fklmeskbes wdkod tdme obl`kem tb cbrl tdm lnsskvm mfkckom wm onaa tdm uekvmrsm.
Vdm mamotrbe ktsmac ks bur mampdnet, tdm ckehmrprket bc Hbf.
Xm nasb smm tdnt tdmsm hmblmtrkona cbrls bc tdm lntdmlntkona wbraf (lnss ns
n pbket, tklm ns n okroam, vmabokty ns n spdmrm, spnom/amehtd ns n tbrus) nrm rmcamotmf
ns pdyskona sdnpms ke n pdyskona wbraf (tdmsm nrm sdnpms tdnt wm nrm cnlkaknr wktd),
nef sb ks bur pdyskona wbraf lnfm ke tdm klnhm bc tdm lntdmlntkona wbraf.
Ambenrfb fn Skeok `makmvmf tdm wbrjkehs bc tdmdulne `bfy tb `m ne nenabhy cbr tdm wbrjkehs bc tdm
uekvmrsm amnfkeh tb dks cnlbus fknhrnl bc tdm Sktruvkne
lne wdkod one ktsmac `m akejmf tb tdm oanssko vmrsm ke tdm
Hmemsks >908 Hbf ormntmf lne ke Dks bwe klnhm.
Nef sb ks tdm anehunhm bc lntdmlntkos tdm anehunhmtdnt ks usmf `y tdm Hbfs ke tdmkr rmnal, wktd bur pdyskona
uekvmrsm ns tdm mqukvnamet bc tdm spbjme wbrf2
cbr iust ns tdm pnhms bc n `bbj nrm tklmamss, uetka wm `mhke tb rmnf tdml
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Fklmeskbes9
Ke tdks tmxt tdm pdyskona uekvmrsm ks tdus `y fmckektkbe fmckemf `y fklmeskbes,
cbr ne b`smrvn`am nef lmnsurn`am uekvmrsm lust dnvm pnrnlmtmrs `y wdkod kt lny
`m b`smrvmf nef lmnsurmf.
N `akef lne oneebt smm obabr `ut obabr ks tdmrm, obabr `mkeh pdbtbes bc akhdt
bc fkccmrmet wnvmamehtd nef sb cbr tdm `akef lne wm one sny tdnt tdm wbraf ks `anoj.
Amt us suppbsm tdnt tdmrm nrm eb pdbtbes, bur wbraf wbuaf tdme `m `anoj, `monusm
wm dnvm eb akhdt, dbwmvmr wm obuaf ebt usm tdm wbrf `anoj `monusm tdnt suhhmsts n
stntm bc ebe-`anoj nef ke n pdbtbe-amss wbraf tdmrm ks emktdmr stntm.N fmsorkptkvm wbrf tdus rmqukrms n lkeklul bc 0 stntms, bur pdbtbe-amss
wbraf ks tdus ne n`smeom bc akhdt rntdmr tdne n `anoj wbraf. Akjmwksm kc mvmrytdkeh
wns tdm snlm tmlpmrnturm wm wbuaf dnvm eb lmnes tb lmnsurm tmlpmrnturm nef sb
wm wbuaf ebt dnvm n tmlpmrnturm uekt suod ns C br O br J cbr tdmrm wbuaf `m eb
tmlpmrnturm tb lmnsurm.
Cbr mxnlpam, wm tnjm n `anej pnpmr. Xm tdme ketrbfuom n fbt, wm ebw dnvm
kecbrlntkbe, `y nffkeh lbrm fbts nef nasb `y lbvkeh tdmsm fbts rmantkvm tb mnod
btdmr nabeh n strnkhdt akem wm nrm `btd nffkeh nef lnekpuantkeh kecbrlntkbe ke bur
> fklmeskbena fkhktna fbt wbraf. Kc wm nsskhe mnod fbt n >nef smpnrntm tdm fbts
wktd 7s, tdme wm wkaa mef up wktd sblmtdkeh akjm:
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crnlm#>9 >777>7>777>>7 wm tdme lbvm tdmsm fbts rmantkvm tb mnod btdmr
crnlm#09 >77>77>7>7>77
crnlm#?9 7>777>>777>7> nef tdks nasb hkvms us tklm, t < ? (tdm crnlm rntm)
Xm tdme rmpanom fbt wktd pkxma (be n oblputmr fkspany) nef sb wm one ebwlmnsurm ebt 0 stntms: `anoj nef wdktm, `ut hrnfkmets (bc obabr). Xm nrm ketrbfuokeh
obetrnst, nef obetrnst ks n curtdmr pnrnlmtmr tdnt one `m lmnsurmf, wm ebw dnvm
lbrm kecbrlntkbe, cbr kecbrlntkbe mquntms tb obetrnst, cbr mxnlpam mnod pkxma be
ly oblputmr fkspany dns ?0 `kt obabr. Vdks lmnes tdnt mnod pkxma dns n odbkom bc
60;6;380;3 fkccmrmet obabrs < 0
?0
`kts bc kecbrlntkbe. Kc K usm tdnt pkxma tb fmsork`mtmlpmrnturm, tdme K one lmnsurm 60;6;380;3 fkccmrmet hrnfkmets bc tmlpmrnturm.
Bur uekvmrsm ks akjm tdnt `anej pnpmr: kt ks beay wdme wm nff tb kt kecbrlntkbe
(pnrtkoams nef pdbtbes ) tdnt wm dnvm sblmtdkeh tb lmnsurm nef tdme wm hkvm nenlm br an`ma tb tdnt wdkod wm nrm lmnsurkeh.
Fklmeskbes nrm tdm tbbas wm usm tb lmnsurm nef ontmhbrkzm kecbrlntkbe, nef
tdks kecbrlntkbe ks tdm pdyskona uekvmrsm.
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Mvmrytdkeh ks fmtmrlkemf, tdm `mhkeekeh ns wmaa ns tdm mef, `y cbroms bvmr wdkodwm dnvm eb obetrba. Kt ks fmtmrlkemf cbr tdm kesmot, ns wmaa ns cbr tdm stnr. Dulne
`mkehs, vmhmtn`ams, br obslko fust, wm naa fneom tb n lystmrkbus tuem, ketbemf ketdm fkstneom `y ne kevksk`am pkpmr.
Na`mrt Mkestmke
pantbsobfm.obl
a f
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Pmcmrmeom9
- rnfkus bc n okroam < r
- pmrklmtmr bc n okroam < 0r
- nrmn bc n okroam < r0
- surcnom nrmn bc n spdmrm < 6r0
- vbaulm bc n spdmrm < 6r?/?
- surcnom nrmn bc tbrus < 60r0
- vbaulm bc n tbrus < 0
0
r
?
- nrmn bc 6-F dypmr-spdmrm < 00r?
- nrmn bc =-F spdmrm < (4/?)0r6
- vbaulm bc =-F spdmrm < (4/>=)0r=
Wytdnhbrns trkneham tdmbrml: n0+ `0< o0
pantbsobfm.obl
a t f
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@nsm ]ekts _K uekts _K Waneoj uekts
L< lnss jh Waneoj lnss lW
V< tklm s Waneoj tklm tpW< lblmetul Waneoj lblmetul (sqrt bc)
S< vmabokty l/s spmmf bc akhdt oA< amehtd l Waneoj amehtd ap
N< nlpmrm N
Xnvmamehtd ks tdm amehtd bc > wnvm.
Crmqumeoy ns usmf dmrm ks tdm tklm kt tnjms cbr akhdt tb trnvma > wnvmamehtd. Wdyskos
usms crmqumeoy ke tmrls bc wnvmamehtds pmr smobef. Vdm spmmf bc akhdt o s. Cbr mxnlpam, tdm mehkem bc n
>lkam abeh trnke nrrkvms nt n stntkbe: nt >0lpd kt wkaa tnjm = lkeutms cbr tdm rmst bc
tdm trnke (tb tdm anst wnhbe) tb nrrkvm: wnvmamehtd < >lkam, tdm crmqumeoy < =lkes.
Vdm fknhrnl `mabw ks n ske wnvm hrnpd: tdm dbrkzbetna x-nxks usunaay lmnsurms tdm
wnvm `y tklm `ut kt one nasb `m amehtd.
pantbsobfm.obl
a t f
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Jmy obestnets9
H< Hrnvktntkbe obestnet (n lmnsurm bc tdm strmehtd bc hrnvkty)
o< spmmf bc akhdt
d< Waneojs obestnet(ne memrhy tmrl)m< mamlmetnry odnrhm (odnrhm rmantmf < nlpmrm tklm)
N< Nlpmrm (odnrhm rmantmf)
7< pmrlmn`kakty bc vnouul (usmf ns rmcmrmeom `monusm kts vnaum ks mxnot)
P< Pyf`mrh obestnet (usmf ns rmcmrmeom `monusm kts vnaum ks prmoksmay jebwe)
lm< lnss bc tdm mamotrbe
m< wnvmamehtd bc tdm mamotrbe
j@< @batzlnees obestnet (rmantms tb tmlpmrnturm)
< tdm _bllmrcmaf ckem struoturm obestnet napdn (fklmeskbeamss)
< Blmhn, n prmsulmf obestnet (fklmeskbeamss)
lW< Waneoj lnss (> _K uekt bc lnss)
ap< Waneoj amehtd (> _K uekt bc amehtd)
tp< Waneoj tklm (> _K uekt bc tklm)
Vp< Waneoj tmlpmrnturm (> _K uekt bc tmlpmrnturm)
pantbsobfm.obl
a t f
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LAVSWNns lntdmlntkona obestnets ke tmrls bc lblmetul W, vmabokty S, uekt u.
Naa cbrluans crbl tdm nrtkoam be tdm vkrtuna mamotrbe (fbweabnf nt pantbsobfm.obl)
pantbsobfm.obl
pantbsobfm obl
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Wdyskona obestnets ke tmrls bc LAVSWN9pantbsobfm.obl
pantbsobfm obl
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Obestnets ke tmrls bc P, o, 7, 9pantbsobfm.obl
pantbsobfm obl
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_K uekts ke tmrls bc u9 pantbsobfm.obl
pantbsobfm obl
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Nutdbrs ebtm9
Vdks `bbj `mhne ns n smrkms bc ebtms be tdm pdkabsbpdy bc fmstkey, tdm prmlksm
`mkeh tdnt kc tdmrm ks n fksomrek`am pnttmre tb dulne mvmets, k.m.9 tdnt n odneom
lmmtkeh dns boourrmf, ebt `y odneom, `ut noobrfkeh tb br kecaumeomf `y neuesmme smt bc ruams, tdme tdks snlm smt bc ruams lny nasb nppay tb tdm uekvmrsm ktsmac,
tdnt bur uekvmrsm ks ebt tdm rmsuat bc rnefbl mvmets `ut lny cbaabw, br mvme `m
hukfmf `y, n fmckektm smt bc prkeokpams.
Kc tdmrm wmrm suod prkeokpams, tdme wm obuaf surlksm tdnt tdmy wbuaf bpmrntm
wktdke tdm crnlmwbrj bc tdm Anws bc Wdyskos nef sb kt lkhdt `m pbssk`am tblntdmlntkonaay obfkcy tdml ke tdm snlm smesm tdnt wm one obfm tdm anws bc hrnvkty,
br ney btdmr pdyskona anw, ns n smrkms bc cbrluans wdbsm butoblm lny `m
netkokpntmf.
Xktd eb prmobeomptkbes ns tb wdnt suod n tdmbry lkhdt abbj akjm, br mvme kc
tdmrm lkhdt `m suod n tdmbry, ke 077? K `mhne wrktkeh n smrkms bc ebtms ns kfmns
onlm. Vdm squnrm rbbt bc lblmetul ^ nppmnrmf nef `y Fmoml`mr n 3 pnhm
`bbjamt Vdm Odmss @bnrf ]ekvmrsm, tdm prmfmomssbr tb tdks tmxt, wns `bre. K dnvmobetkeumf wbrjkeh be tdm tdmbry skeom, tdm ckena nffktkbe `mkeh tdm hmblmtry bc tdm
lntdmlntkona Blmhn , tdm uekvmrsna uekt u nef tdm tbpbabhy bc n `anoj-dbam
uekvmrsm.
pantbsobfm.obl
pantbsobfm obl
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Vdks tdmbry, vkn tdm tmxt, hrmw `y n enturna smamotkbe bc kfmns, bvmr tdm ymnrs
tdbsm odnptmrs tdnt rmkecbromf mnod btdmr hrmw tbhmtdmr: tdbsm odnptmrs tdnt
rmlnkemf nabem wmrm mvmetunaay fmamtmf. Ourkbusay tdks npprbnod pnrnaamas tdm
tdmbry ktsmac (smm Obslbabhkona Enturna _mamotkbe), nef ns suod kt lny `m tdnt wdme
tdm tdmbry ks oblpamtm, kt wkaa prbvkfm tdm sbautkbe tb tdm brkhkena prmlksm. Wnrts Knef KK nrm ne nttmlpt tb `ukaf tdm crnlmwbrj cbr n pdkabsbpdy nrbuef wdnt ks
mssmetknaay n smt bc lntdmlntkona prkeokpams. Ly ketmrprmtntkbe bc tdks smt bc
prkeokpams ks bc obursm fm`ntn`am nef sdbuaf ebt fmtrnot crbl tdm prkeokpams
tdmlsmavms.
K `mhne tdks wdkast wbrjkeh ke Lkesj, @manrus nef skeom amnvkeh tdmrm K dnvm
typmf ly wny norbss tdm panemt crbl Inpne tb Lbrboob, Ckeanef tb Blne nef nluatktufm bc abontkbes ke `mtwmme. Mnod pnrt bc tdm `bbj dns kts bwe hmbhrnpdy. Vb
tdbsm wdb suppbrtmf nef dmapmf lm nabeh ly trnvmas, nef tdm akst ks vmry abeh,
lney tdnejs ke pnrtkouanr tdm mnray fnys: _durn, wdb ankf tdm pntd crbl Vbjyb tb
Lkesj tdm @ryzhnabv jktodme tn`am ke Lbsobw wdmrm tdm smmfs bc tdks prbimotbrkhkentmf Fr Nfblnktks ke Skaekus cbr dks lney suhhmstkbes obvmr pdbtboburtmsy bc Kryen J Xkjkpmfkn wns usmf ns tdm sburom cbr `nojhrbuef lntmrknabe stnefnrf pdyskos, EN_N cbr klnhms nef anst `ut cbrmlbst, tdbsm pdkabsbpdmrs,
Lkodnma Jmeey, Pbss, Jurt nef Insbe
pantbsobfm.obl
pantbsobfm obl
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Wantb s Onvm
Ckrst prketkeh Vdm Odmss @bnrf ]ekvmrsm
Obpyrkhdt Lnaobal Lnoambf (077?)
Pmvksmf ns9 Wantbs Onvm
Obpyrkhdt Lnaobal Lnoambf 0778, 07>?, 07>=, 07>8
K_@E ;4=-3=66-=7-=
Pmc9 =?7.7>
Ak`rnry bc Obehrmss >-043>??83>
Naa rkhdts rmsmrvmf. Eb pnrt bc tdks pu`akontkbe lny `m rmprbfuomf, stbrmf ke br ketrbfuomf ketb
n rmtrkmvna systml, br trneslkttmf, ke ney cbrl, br `y ney lmnes wdntsbmvmr wktdbut tdm prkbr
wrkttme pmrlksskbe bc tdm nutdbr mxompt ke tdm onsm bc `rkmc qubtntkbes ml`bfkmf ke orktkona
nrtkoams nef rmvkmws. Cbr nffktkbes, rmvkskbes br kecbrlntkbe nffrmss9
qumryGpantbsobfm.obl
Vdks `bbj ks sbaf su`imot tb tdm obefktkbe tdnt kt sdnaa ebt, `y wny bc trnfm br btdmrwksm, `m amet,
rm-sbaf, dkrmf but, br btdmrwksm okrouantmf wktdbut tdm nutdbrs prkbr obesmet ke ney cbrl bc
`kefkeh br obvmr btdmr tdne tdnt ke wdkod kt ks pu`aksdmf nef wktdbut n sklkanr obefktkbe
keoaufkeh tdks obefktkbe `mkeh klpbsmf be tdm su`smqumet purodnsmr.
pantbsobfm.obl
pantbsobfm obl
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pantbsobfm.obl