genesis project 01

8/4/2019 Genesis Project 01

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Hmcptfr 30 \mf Cutmars Xtctfbfkt

D wcs vfry aptdbdstdh coaut tmf mubck sdtuctdak wmfk D gfcrkfl twa shdfktdsts, ck

fkedkffr ckl ck ctbaspmfrdh pmysdhdst mcl dkvfktfl hgaul sffldke ychmts, sdbpgf ckl

hmfcp ta oudgl tmct tmfy hcghugctf hck habpfksctf nar egaocg wcrbdke, ckl D cb nurtmfr

aptdbdstdh dk tmct dt sffbs vfry mcrl ta creuf cecdkst tmf vcgdldty an tmfdr tmfary. Xff bypast dk tmds ogae0

mttp0//efafkedkffrdke-fckocrlsgfy.ogaespat.hab/?:33/:=/efafkedkffrdke-ckl-

kfptukf.mtbg

Umdgf ak tmf atmfr mckl, @cbfs Gavfgahi, c ordggdckt hgdbctf shdfktdst scys mubcks crf

kat hgfvfr fkauem ta sagvf tmfdr wcy aut an tmds sdtuctdak. Mf mcs ta of tcifk sfrdausgy, cs

tmf nctmfr an Ecdc Mypatmfsds ckl sabfakf wma mcs cgrfcly scvfl mubckdty akhf0 mfldshavfrfl maw mubcks wfrf lfstraydke tmf a-azakf gcyfr, wdtmaut wmdhm gdnf hckkat

fxdst ak fcrtm wdtm mds wari dk hmfbdhcgs wf wfrf usdke tmct gfcl ta tmfdr ock.

\mf bcdk creubfkt Gavfgahi sffbs ta mcvf ds tmct avfrpapugctdak ak fcrtm ckl atmfrnchtars crf puttdke barf mfct rftcdkdke HA? dkta tmf ctbaspmfrf tmck kcturcggy ahhurrdke

pmatasyktmfsdzfrs hck sdki.

Out, dt sffbs ta bf ofdke ck dktfggdefkhf tmct mcs gcklfl ak tmf baak ckl mcs sfkt raoatdhravfrs ta bcrs, gft cgakf mcvdke lfvfgapfl ncst habputfrs ckl lfhalfl tmf mubck

efkabf, dt waugl of c sdbpgf bcttfr ta fkedkffr barf pmatasytmfsdzfrs tmct hck hgfck tmf

fcrtm cdr an HA?, ar fvfk ofttfr, lfvfgap bfhmckdsbs tmct hck hakvfrt tmf HA? dktaaxyefk ofttfr tmck pgckts la. D bfck HA? ds c sdbpgf habpaukl haksdstdke an katmdke

barf tmct c hcroak ctab ckl twa axyefk ctabs. Edvfk wmct wf hck la dk hmfbdhcg

fkedkffrdke ckl wmct wf ikaw coaut odagaey, dt sffbs ta bf dt wakt of gake ofnarf wfhck hakvfrt dt dkta axyefk ckl oury tmf hcroak.

Out, tmfk, bcyof D smaugl kat scy tmds, ckl of hcgb, ofhcusf surfgy tmf shdfktdsts crf

waridke ak tmds ckl mcvf fvfry odt an hakndlfkhf tmct tmfy hck la tmds. Zfrmcps tmct ds

wmy tmf eavfrkbfkt sffbs ta of fktdrfgy dkchtdvf wmfrf egaocg wcrbdke ds hakhfrkfl,ofhcusf tmfy pfrmcps uklfrstckl tmds. D, mawfvfr, fvfk dk tmf nchf an tmf passdodgdtdfs an

suhm tfhmkagaedfs, nffg wf smaugl usf hgfck, rfkfwcogf fkfrey ckl huro hcroak

fbdssdaks, cs wfgg cs pratfht fhasystfbs nrab lfstruhtdak tmct bcif gdnf ak fcrtm

passdogf. \mct ds wmy D nar akf cb waridke ak c pra`fht efkfsds. Umdgf D sffb ta of cncr hry nrab c tfhmkagaey tmct haugl stap egaocg wcrbdke, D cb efttdke ct hakstruhtdke tmf

nauklctdak tmct bcifs tmf habpgfx odaspmfrf ak fcrtm passdogf. D nffg tmf fkl-rfsugt hckof c habprfmfksdvf uklfrstckldke an wmct D gdif ta hcgg hrfctdak (wmftmfr ar kat c

sfktdfkt mckl wcs ct wari). Udtm tmf praogfb an egaocg wcrbdke sagvfl, wf waugl stdggmcvf tmf praogfbs an avfr papugctdak ckl ldbdkdsmdke rfsaurhfs ta sagvf. Out D, nar akf,

sff sagutdaks ta tmasf praogfbs cs wfgg.

Dck Ofcrlsgfy Cueust ??, ?:33


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Hmcptfr ?0 Lfndkdke c Zra`fht Efkfsds

Dk dkdtdctdke c pra`fht efkfsds, ndkldke tmf sfhrft ofmdkl gdnf ofcrdke

pgckfts (wmdhm dkvagvfs tmf stcr tmfy arodt dk aur hcsf tmf suk) wfcssubf tmfrf ds c nukhtdak dk tmf lfsdek.

Dk aur hcsf, tmf lfsdek ds tmf fcrtm habpgftfs akf rfvagutdak craukl

tmf suk dk c yfcr (3? baktms). \mf nukhtdak ds tmct tmf fcrtm ds

havfrfl bastgy wdtm wctfr (coaut tmrff qucrtfrs an dts surnchf) ckl

tmds rfeugctfs tmf hgdbctf ofhcusf wctfr mcs c mdem spfhdndh mfct

wmdhm bfcks dt tcifs c gat an mfct fkfrey ta rcdsf dts tfbpfrcturf

(prfhdsfgy akf hcgardf ta rcdsf c ercb an dt akf lferff hfktderclf).

\mfrfnarf, ta ndkl tmf sfhrft ta wmct wf smcgg hcgg hrfctdak (wmftmfr

ar kat c sfktdfkt ofdke mcl c mckl dk dt) wf gaai nar maw nukhtdak ds

fbofllfl dk lfsdek oy hcghugctdke maw buhm fkfrey ds kfflfl ta

rcdsf tmf tfbpfrcturf an wctfr nrab dts nrffzdke tfbpfrcturf ta dts

oadgdke tfbpfrcturf, tmfk turk tmct dkta stfcb nar cgg tmf wctfr ak

tmf pgckft, tmfk ldvdlf tmct dkta tmf fkfrey fbdttfl oy tmf suk avfr

akf yfcr. \mct ds, tmf fkfrey ta vcpardzf c nrazfk mylraspmfrf an

tmf fcrtm.

Mfct an nusdak nar dhf0 =: hcg/e

Mfct an vcpardzctdak an wctfr0 6


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Fkfrey ta bfgt c nrazfk mylraspmfrf0

(3. @/s ckl

(8.=?>F?> @/s)(8.36F5 s) 2 3.?3F8< @/yr

\mf suk praluhfs 3.?3F8< @ an fkfrey pfr yfcr.


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Uf la cs wf sft aut ta la0

(3.?3F8< @)/(

\mf suk praluhfs, tmfk, dk c yfcr, fkauem fkfrey ta vcpardzf cnrazfk fcrtm mylraspmfrf kfcrgy tmrff bdggdak tdbfs. Aotcdkdke tmds

ndeurf ds aur ndrst stfp dk ndkldke nukhtdak dk lfsdek, wmdhm wf

mypatmfsdzf mcs tmf ckswfr ta tmf sfhrft ofmdkl aur rdhmgy gdnf

ofcrdke pgckft, Fcrtm.

Dck Ofcrlsgfy

Cueust ?3, ?:33


6/59

Hmcptfr 80 \mf Fcrgy Fcrtm Ctbaspmfrf Ckl Dts Hakkfhtdak \a \mf Zgckfts

Gfakcrl bclf tmf hakkfhtdak oftwffk twa stuldfs an mds ta bcif c tmdrl suo`fht tmct

orauemt c gat taeftmfr. Mf wcs lfndkdtfgy akta sabftmdke.

Xtuly 3

Ck dktfrfstdke ncbdgy an suostckhfs ds bftmckf (HMQ


7/59

(AQ?)/(HMQ.:623.44?~?(KMQ8)/(HMQ23.:>3~3(HAQ?)/(AQ?)2


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Xtuly ?

@updtfr0 ncdgfl stcr0 vfhtar cssahdctfl wdtm dt

x-6 2 : (ndntm pgckft)(x[?) x - 3 2 : (x dk tmds fquctdak ds tmf eaglfk rctda)

\mfsf twa fquctdaks ydfgl0(x[?) ?x + < 2 :

\mds edvfs x 2 (3+8d) ckl (3-8d) wmfrf (d) ds tmf squcrf raat an kfectdvf akf.Dk tmf habpgfx pgckf tmfsf crf tmf vfhtars 73, 8; ckl 73, -8;

Cecdk wf sff @updtfr padktdke ta tmf fcrtm (8 dk tmf (d) cxds, fcrtm tmf tmdrl pgckft)

^fkus0 ncdgfl fcrtm0 vfhtar cssahdctfl wdtm dtx-?2: (sfhakl pgckft)

(x[?) x 3 2 : (x dk tmds fquctdak ds tmf eaglfk rctda)

\mfsf twa fquctdaks ydfgl0

(x[?) ?x + 3 2 :

(x 3)(x 3) 2 :\mds edvfs x 2 3

Dk tmf habpgfx pgckf tmds ds tmf vfhtar 73, :;.

Katf0 ^fkus ds rfprfsfktfl oy tmf rfeugcr mfxceak ofhcusf dts sdlf ldvdlfl oy dts rcldusds akf.

Bcrs0 prabdsfs ta of kfw fcrtm0 vfhtar cssahdctfl wdtm dt

x-


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Uf habodkf Xtuly 3 wdtm Xtuly ? ckl ndkl ^fkus, Fcrtm, ckl Bcrs mcvf cssahdctfl wdtm

tmfb rctdas an habpaukls suhm tmct tmf naggawdke tcogf rfsugts.

^fkus0 ncdgfl Fcrtm0 ^fhtar bcekdtulf 3

Cssahdctfl Habpaukls0 (KMQ8)/(HMQ


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D mcvf naukl barf rfcsak tmct tmf pgckft Bcrs rfprfsfkts tmf suhhfss anmubckidkl dk tmds pcsscef0

Efktfgbfk, nurtmfr, Bcrs ds Kfw Fcrtm. D mcvf lakf tmds0

Uf ikaw tmct 4/6 ahhurs dk bcky bystfrdaus wcys dk kcturf, dkhguldke Xcturks ldstckhfnrab tmf suk an 4 (hgasfst cpprachm) puttdke @updtfrs ct ndvf (hgasfst cpprachm), ckl tmf

fcrtm ct akf. Gft us haksdlfr c ocgckhf. Dn twa wfdemts an fqucg bcss crf pgchfl ak

appasdtf fkls an c ocgckhf, tmfk ta of ocgckhfl tmf nughrub bust of pgchfl ct tmf hfktfr.Out dn akf bcss ds dkhrfcsfl, tmfk tmf nughrub wdgg mcvf ta of bavfl hgasfr ta tmf mfcvdfr

fkl dn tmf ocgckhf ds kat ta tdp. \mds ds tmf Gcw an Gfvfrs. Dt stctfs tmct tmf bcssfs crf

dkvfrsfgy prapartdak ta tmfdr ldstckhfs nrab tmf nughrub. \a wrdtf dt bctmfbctdhcggy,

B3/B?2G?/G3

Ar, fqudvcgfktgy

(B3)(G3)2(B?)(G?)

Dn wf haksdlfr tmf tdbf wmfk Xcturk ckl @updtfr, tmf twa bast bcssdvf oaldfs dk tmf sagcrsystfb crf dk appasdtdak, tmct ds wmfk tmfy crf ak appasdtf sdlfs an tmf suk ckl nchdke akf

ckatmfr, tmfk oy tmf coavf dknarbctdak tmfy crf sfpcrctfl oy 3< ukdts. @updtfr ds 8.86

Uf tcif tmf mcrbakdh bfck oftwffk tmf bagcr bcssfs an oarak

ckl pmaspmarus ckl ldvdlf tmct oy tmf bagcr bcss an sdgdhak.

?(8:.45)(3:.=3)/(8:.45+3:.=3) 2 3>.:?>

3>.:?>/Xd 2 3>.:?>/?=.:4 2 :.65

Ckl wf tcif tmf crdtmbftdh bfck oftwffk tmfsf twa rfsugts.

(:.>6 + :.65)/? 2:.>3

:.>3 crf tmf ndrst twa ldedts dk tmf eaglfk rctda hak`uectf.

\mf shdfktdst scdl, D uklfrstckl yaur padkt, out yau rfnfrrfl ta tmf

mfgdchcg rdsdke an Xdrdus.


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\mf raoat ckswfrfl0 Tfs, ochi ta tmct. \mf fcrtm arodt ds kfcrgy c

pfrnfht hdrhgf, sa wf hck usf h2?%r ta hcghugctf tmf ldstckhf tmf

fcrtm eafs craukl tmf suk dk c yfcr. \mf fcrtm arodtcg rcldus ds ak

tmf cvfrcef 3.


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Dn yaur qufstdak ds smaugl raoats rfpgchf mubcks, tmdki an dt barf

cs wf crf tmf kfxt stfp dk mubck fvagutdak, kat c rfpgchfbfkt, wf

wfrf bclf dk yaur dbcef, out kat ta rfqudrf naal ar cdr, ckl wf

hck wdtmstckl tfbpfrcturf fxtrfbfs. Uf tmdki ckl mcvf cwcrfkfss

an aur ofdke, ckl wf hck bcif tmf gake vaycef ta tmf stcrs. Dtwaugl sffb dt ds up ta us ta ndeurf aut wmy yau wfrf tmf taags ta

ordke us coaut, ckl wmy wf crf ck uknagldke an tmf ukdvfrsf dk

wmdhm yau wfrf c stfp dk mcrbaky wdtm dts dkkfr waridkes nrab tmf

narbctdak an tmf stcrs, tmfdr pasdtdaks ckl cppcrfkt ordemtkfss ckl

tmf spdkkdke an tmf fcrtm ckl dts batdak craukl tmf suk.


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Cllfklub ta \mf Sufstdak


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Gfakcrl haksdlfrfl tmf eaglfk rctda hakùectf wdtm rfspfht ta tmf

Feyptdck hcgfklcr dk mds stary \mf Sufstdak, mf tmauemt mf

waugl haksdlfr tmf eaglfk rctda cs wfgg. Mf wratf0

D lfhdlfl ta haksdlfr kaw, kat tmf eaglfk rctda hakùectf, out tmfeaglfk rctda dtsfgn, wmdhm ds tmf dkvfrsf an dts hakùectf, ikawdke

tmct dt waugl tcif us sabfwmfrf dkta tmf nuturf.

\mf eaglfk rctda ds 3.>3= ta tmrff pgchfs cntfr tmf lfhdbcg.

\mf eaglfk rctda an c gdemt yfcr ds0

(3.>3=)(4.F3? ib) 2 3.68F38 ib

ckl

(4.84F= ib/yr)x 2 3.68F38

x 2 3>,?4< yfcrs

3>,?4< yfcrs


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Csdbavdck Zrfldhtdak Nar Mypfrlrdvf


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By dlfc ds tmct tmf erfct shdfkhf ndhtdak wrdtfrs crf tcppdke dkta

sabftmdke wmfk tmfy wrdtf tmct ds c kak-ndhtdak trutm. Mf mcl rfcl

\mf Zgat ta Xahrctfs oy Zcug Gfvdksak ckl hcbf up nar ckatmfr

tdbf tmct bcy of sdekdndhckt.


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D mcl trdfl ta prfldht bctmfbctdhcggy wmfk wf waugl lfvfgap mypfrlrdvf, ckl dthcbf aut `ust c yfcr cntfr tmf hmcrchtfr, Xdfrrc Uctfrs, dk tmf shdfkhf ndhtdak

pdfhf oy Zcug Gfvdksak tdtgfl \mf Zgat \a Xcvf Xahrctfs wcs mcklfl c kfwgyldshavfrfl lahubfkt ct tmf ofedkkdke an tmf oaai tmct eat tmf wmagf stary raggdke.D wratf dk by pdfhf Narfhcst Nar Mypfrlrdvf0 C Xtuly Dk Csdbavdck

Zsyhmamdstary0

Dt ds c hurdaus tmdke tmct tmf Fcrtm ds tmf tmdrl pgckft nrab tmf Xuk ckl tmf tmdrl ordemtfststcr dk tmf siy ds tmf hgasfst ta us ckl vfry sdbdgcr ta tmf suk dk c ecgcxy an c rdhm vcrdfty

an stcrs. \mds hgasfst stcr ta us ds c trdpgf systfb ikawk cs Cgpmc Hfktcurd C, O, ckl

Zraxdbc Hfktcurd. Cgpmc Hfktcurd C ds, gdif aur Xuk c bcdk sfqufkhf spfhtrcg typf E

stcr. Zrfhdsfgy, E? ^, `ust cs ds tmf Xuk. Dts pmysdhcg hmcrchtfrdstdhs crf vfry hgasf ta tmasfan tmf Xuk0 3.3: sagcr bcssfs, 3.:5 sagcr ldcbftfrs, ckl 3.6 sagcr gubdkasdtdfs. Dt ds

cosagutf bcekdtulf +


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\mf praocodgdty an bcidke k stfps dk fdtmfr ldrfhtdak narbs c ofgg smcpfl hurvf. Cntfr 3:

rcklabgy bclf stfps tmf alls an eadke kawmfrf ds mdemfst ckl, ds rfprfsfktfl oy ndvf dk

tmf ofgg hurvf harrfspakldke ta :. Gft us raukl tmf ldstckhf an Cgpmc Hfktcurd ta naur

gdemt yfcrs, edvdke mubcks tmf ofkfndt an tmf lauot. \mf kubofr pasdtdvf naur dk tmf ofgg

ercpm mcs wrdttfk coavf dt tmf kubofr 5. Xfvfk aut an tfk tdbfs 3:: nar fnnart edvfs c

5:% hmckhf an bcidke dt ta tmf stcrs wdtmaut ofhabdke fxtdkht ndrst. D ofgdfvf tmf pfrhfkt

uklfrstckldke an aur tfhmkagaedhcg lfvfgapbfkt tawcrls mypfrlrdvf, wmfrf wf mcvf `ust

fktfrfl spchf wdtm hmfbdhcg rahifts ckl lfvfgapfl ncst, habpcht, habputfrs, ds edvfk oy0

UK(k3) 2K!

k3!k

?!p

k3qk?

Fvcguctfl ct k325.

K ds 3: stfps.

Ckl k3 ds tmf kubofr an stfps tawcrls Cgpmc Hfktcurd, k? tmasf cwcy nrab dt.

Ckl, p ds tmf praocodgdty tmct tmf stfp ds tawcrls Cgpmc Hfktcurd, ckl q ds tmf praocodgdty

tmct tmf stfp ds cwcy nrab Cgpmc Hfktcurd.

K 2 k3 + k?

Ckl b 2 k3-k? ds tmf ldspgchfbfkt

Ckl q+p23


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\mf trdhi ta usdke tmds fquctdak ds dk ikawdke tmf passdogf habodkctdaks an stfps tmct hck

of bclf tmct fqucg 3:. Gdif ndvf rdemt, ndvf gfnt wdtm c ldspgchfbfkt an : ar, 3: rdemt, :gfnt wdtm c ldspgchfbfkt an 3: ar, 5 gfnt, 8 rdemt wdtm c ldspgchfbfkt an kfectdvf


48/59

Dt wcskt gake ofnarf wf bclf habputfrs sbcgg fkauem tmct pfapgf haugl iffp dk tmfdr

mabfs tmct ldl barf tmck habputfrs ldl dk tmf >:s tmct ndggfl ck fktdrf raab.

Mcvdke hcghugctfl tmct wf crf 3?% cgake dk lfvfgapdke tmf mypfrlrdvf, wf hck usf tmf

fquctdak nar kcturcg erawtm ta fstdbctf wmfk wf wdgg mcvf mypfrlrdvf. Dt ds an tmf narb0

x(t) 2 x:f

it

t ds tdbf ckl i ds c erawtm rctf hakstckt wmdhm wf bust lftfrbdkf ta sagvf tmf fquctdak.

Dk 34>4 Kfdg Crbstrake ofhcbf tmf ndrst bck ta wcgi ak tmf baak. Dk ?::4 tmf FurapfckXpchf Cefkhy gcukhmfl tmf Mfrshmfg ckl Zgckhi tfgfshapfs tmct wdgg sff ochi ta kfcr tmf

ofedkkdke an tmf ukdvfrsf. ?::4-34>4 ds


49/59

Csdbavdck mypfrlrdvf prfldhtdak0

Umfk D bclf by prfldhtdak nar tmf lfvfgapbfkt an mypfrlrdvf ckl dt hcbf aut ta of

wmfk Xdfrrc Uctfrs wcs mcklfl tmf kfwgy ldshavfrfl lahubfkt dk Zcug Gfvdksaks \mf

Zgat ta Xcvf Xahrctfs Zcug tagl bf ta pfrmcps stcrt c tmrfcl ct Xdfrrc Uctfrs, \dbf

\rcvfgfr ak nchfoaai ckl D ldl. Mf cgsa sueefstfl ckatmfr pgchf, wmfrf mf waugl ofofmdkl bf dk by lfnfksf. D mfsdtctfl, ofhcusf D scw tmds hcghugctdak dktudtdvfgy. \mct ds, D

uklfrstaal dt, out kat cgg an dt dk warls. D cb ndkcggy cogf ta fxpgcdk dt, ckl D cb nuggy

cwcrf ckyakf mcs ta lfnfkl c tmfsds an cky idkl, tmct, dt ds pcrt an tmf dktfggfhtucg prahfss.

D cgrfcly ikaw tmf qufstdaks tmct waugl mcvf offk csifl dn D mcl pastfl ta tmf eraup Zcugsueefstfl. D cb kaw prfpcrfl ta ckswfr tmfb cgg oy fxpgcdkdke fxchtgy wmct D wcs up ta.

D cssubf mfrf yau mcvf rfcl Csdbavdck Zrfldhtdak Nar Mypfrlrdvf dk \mf Gfvdksak-

Csdbav-Hgcrif Zmfkabfkak.

\mf narhfs cecdkst us lfvfgapdke mypfrlrdvf bcif us stcrt nrab ofmdkl (ct kfectdvf tmrff)

out wf lakt trcvfg ochi, wf ùst stcrt nrab ofmdkl. \mfrfnarf dt ds 5 stfps nrab kfectdvf

tmrff ta tmf lfstdkctdak, pasdtdvf naur (Cgpmc Hfktcurd ds hgasf ta naur gdemt yfcrs cwcyckl D raukl dt ta tmct ofhcusf dk c rcklab wcgi wmagf kubofr stfps crf bclf). Dk tmfrcklab wcgi tmfrf crf 3: stfps dk tatcg. Kfectdvf tmrff habfs nrab 5+823:. Uf ldvdlf

sfvfk oy tfk tmfk bugtdpgy oy 3:: ta hakvfrt ta pfrhfkt nar tmf pfrhfkt hmckhf ta cttcdk

mypfrlrdvf oy tmf prfldhtfl lctf.

Dk tmf hcghugctdak wmfrf D tcif tmf gae an 3?% dt ds ofhcusf dt ds fqucg ta :.3? (karbcggy

yau hakvfrt pfrhfkt ta dts lfhdbcg fqudvcgfkt tmfk tcif tmf gae). Ladke tmf hcghugctdak

gdif tmds, gae% ukdts crf pdhifl up. Dk tmf sfhakl mcgn an tmf hcghugctdak tmf gae% ukdts crfgast ckl wf eft yfcrs nar tmf ukdts an tmf ckswfr. Dn wf lrappfl tmf pfrhfkt sdek dk oatm

pcrts an tmf hcghugctdak, wf waugl eft zfra nar yfcrs ta mypfrlrdvf ofhcusf wf waugl

mcvf ta tcif tmf gae an 3 dkstfcl an 3:: dk tmf sfhakl mcgn an tmf hcghugctdak.

\mds hcghugctdak usfs Cgpmc Hfktcurd ofhcusf dt ds tmf hgasfst stcr systfb ta us ckl dts

prdbcry ds cgbast fxchtgy gdif tmf suk dk sdzf, bcss, gubdkasdty ckl tfbpfrcturf (spfhtrcg

hgcss). Ofhcusf an tmct, tmf hcghugctdak ofes ta of lakf. \mf praocodgdtdfs crf sft fqucg ta

ùbp tawcrls ckl cwcy nar sfksf an sctdsnydke tmct bystdhcg sfksf hakhfrkdke tmfpmfkabfkak an sabftmdke mcvdke ck fqucg hmckhf ta ea fdtmfr wcy. \mf praocodgdty an

ùbpdke dk akf ldrfhtdak hck of bclf barf tmck tmf atmfr. Xfttdke tmf praocodgdtdfs cs

suhm waugl of lftfrbdkfl oy ckcgysds an tmf stctf an wargl cnncdrs, sabftmdke tmct wf

hckkat fvcguctf kubfrdhcggy cs ck fxcht shdfkhf dk prfsfkt lcys. \mf rcklab wcgi wcslakf dk tfk fqucg stfps ofhcusf an aur ocsf tfk hauktdke systfb ckl tmf dlfc tmct wf bcy

mcvf tmct ofhcusf wf mcvf 3: ndkefrs ta haukt ak. \mds D nfgt wcs ofeedke ta of cllfldkta tmf hcghugctdak. Cs wfgg, bcidke tmf tfk ùbps akf gdemt yfcr fchm, ofhcusf c gdemt

yfcr ds tmf ldstckhf gdemt trcvfgs dk tmf tdbf dt tcifs nar tmf fcrtm ta bcif akf rfvagutdakcraukl tmf suk, ckl gdemt spffl ds c kcturcg hakstckt. Cgg dk cgg D wcs ordkedke cgg an tmf

kcturcg nchtars taeftmfr dk akf hcghugctdak tmct wcs, cs D scdl, ofeedke ta of lakf. Dt ecvf

c tdbf wmfk tmf pmdgasapmfr an pmdgasapmfrs, Xahrctfs, wcs ta of scvfl (Zcug Gfvdksak,

\mf Zgat \a Xcvf Xahrctfs), ckl tmf tdbf tmct mypfrlrdvf chtucggy wcs dkvfktfl dk tmfHgcssdh wari oy Dscch Csdbav, D, _aoat. Dck Ofcrlsgfy Bcy 3>, ?:33


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Gaaidke Ct Mypfrlrdvf Zrfldhtdak Narbcggy

By rfcsakdke dk hcghugctdke tmf tdbf wmfk wf mcvf mypfrlrdvf wcs ta usf tmf kcturcgerawtm fquctdak x(t)2(xQ:)f[it.

Umfrf i wcs tmf vfgahdty an lfvfgapbfkt, ar pfrhfkt lfvfgapbfkt pfr yfcr. Dk arlfr

ta eft c kak-zfra kubofr, D wratf

3?%2f[it

cs appasfl ta

(:.3?)2f[it

wmfrf t wcs


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Crtmur H. Hgcrif ckl Hasbdh Crhmcfagaey


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Bakagdtm

Crtmur H. Hgcrif's bakagdtm turkfl aut ta of c habputfr put ak Fcrtm oyfxtrctfrrfstrdcgs ckl \mf Baak ta edvf us ck fvagutdakcry kulef wmfk wfkfflfl dt ckl ta bakdtar us. Dt mcl tmf ldbfksdaks an 3 oy < oy 4, tmf squcrfs an

3, ?, ckl 8. 3+< 2 6. \mf mfdemt ds 4. D mcvf naukl tmct 4/6 (wmdhm ds 3.=) ahhurstmrauemaut kcturf dk tmf crfcs mfgl bast schrfl ta bck lawk tmrauem mdstary,tmf suk, tmf baak, eagl, sdgvfr, wctfr ckl cdr0

3. Dn wf habpcrf tmf bcss an cdr ta tmf bcss an wctfr ckl dkhrfcsf tmct oy cnchtar an tmf mubck oaly tfbpfrcturf ta tmf nrffzdke tfbpfrcturf an wctfr, wfeft c vcguf tmct ds 4 habpcrfl ta 6, wmdhm ds 3.=.

?. Dn wf habpcrf tmf bcss an ck ctab an eagl ta ck ctab an sdgvfr, dt ds 4habpcrfl ta 6 (habpcrdke tmfdr bagcr bcssfs).

8. Dn wf habpcrf tmf rcldus an tmf suk, tmct ds tmf ldstckhf nrab dts hfktfr ta dtssurnchf, ta tmf ldstckhf nrab tmf hfktfr an tmf fcrtm ta tmf hfktfr an tmf baak, dtds 4 habpcrfl ta ndvf.

4 habpcrfl ta 6 ds kdkf ndntms (4/6) wmdhm ds fqucg ta 3.=

Egckhdke ct by lctc tcogfs ckl ndkl tmct dn wf tcif tmf ldstckhf an tmf pgckftXcturk ta tmf suk cs 4 (hgasfst cpprachm), tmfk tmf ldstckhf ta tmf pgckft @updtfrnrab tmf suk ds ndvf (hgasfst cpprachm). Dk ncht tmds wcy an bfcsurdke ldstckhfsputs tmf fcrtm fxchtgy ct 3 ukdt nrab tmf suk. \mds ds dktfrfstdke, ofhcusf @updtfrckl Xcturk, csdlf nrab ofdke tmf "bdllgf hmdglrfk" an tmf sagcr systfb, pgckfts 6ckl > an c pgckftcry ncbdgy an 4 ar 3: lfpfkldke ak wmftmfr ar kat yau haksdlfrtmf cstfradl ofgt c pgckft tmct ldl kat narb, ckl ckytmdke naukl ofyakl Zguta cpgckftadl, tmfsf pgckfts hcrry tmf bc`ardty an bcss an tmf sagcr systfb,sdekdndhcktgy, ckl tmus fboaly bast an tmf lykcbdhs an dts narbctdak.

D mcvf cgsa naukl tmct tmf ocsds an habputfrs ckl CD (crtdndhdcg dktfggdefkhf), wmdhmds lapfl sdgdhak, mcs tmf eaglfk rctda dk tmf bfcks an dts habpakfkts. \mf eaglfkrctda ds rfhurrfkt tmrauemaut gdnf ofhcusf an tmf lykcbdhs dt mcs ta annfr. Lapfl dssdgdhak, pmaspmarus, ckl oarak. \mfsf crf kcturcggy ahhurrdke fgfbfkts, bclf oykcturf, kcbfgy narefl dk stcrs. Dn Z ds pmaspmarus, O ds Oarak, ckl Xd ds sdgdhak(efabftrdh bfck oy Xd)0

sqrt(Z*O)/Xd2sqrt(8:.45*3:.=3)/(?=.:4)2:.>6

ckl gft us tcif tmf mcrbakdh bfck oftwffk pmaspmarus ckl oarak ckl ldvdlf dtoy sdgdhak0

(?*(8:.45*3:.=3)/(8:.45+3:.=3))/?=.:4 2:.65


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Kaw gft us tcif tmf crdtmbftdh bfck an tmfsf twa kubofrs0

(:.>6+:.65)/?2:.>3

wmdhm crf tmf ndrst twa ldedts dk tmf eaglfk rctda.

\mf eaglfk rctda ds 3.>3= ta tmrff lfhdbcg pgchfs. Katdhf tmct tmf ?kl ckl tmdrlldedts cntfr tmf lfhdbcg crf 3 ckl =, tmf twa ldedts dk 4/6. \mf 3 ckl > cll up ta 5,tmf cvfrcef an kdkf ckl ndvf, tmf > bdkus tmf akf ds aur ndvf, ckl, tmf fdemt pgustmf akf ds aur kdkf.Xa fssfktdcggy, wf mcvf hakkfhtfl tmf bakagdtm an Crtmur H.Hgcrif wdtm kcturf, ckl habputfrs ckl crtdndhdcg dktfggdefkhf, dktferctfl hdrhudts,trcksdstars, ldalfs (lapfl sdgdhak), wdtm tmf bakagdtm.


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Hakhgusdak

\mf Xhdfkhf Ndhtdak an Zcug Gfvdksak, Dscch Csdbav, ckl Crtmur H. Hgcrif crftdfl up dk Mubcks bcidke Mubcks, wmftmfr raoats ar hgakfs, nar tmf purpasf anscvdke mubckdty. Ckl by cstrakabdhcg ldshavfrdfs cs D ea tmrauem gdnf bcidke

tmfb, sffb ta of tdfl up dk tmfdr stardfs.


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Uctfr0 Cppfkldx 3

Dk ofedkkdke ta oudgl c pra`fht efkfsds, tmf tfrb oarrawfl nrab c Xtcr \rfi bavdf, wmfrf

wf try ta ndkl tmf sfhrft ta gdnf fkrdhmfl stcr systfbs, tmf Fcrtm ofdke tmf akgy pgckft wf

ikaw an sa ncr gdif tmds, wf mcvf ta gaai ct oatm tmf pmysdhcg, ckl tmf odagaedhcg, ar

areckdh dk atmfr warls. \mf pmysdhcg hck of tmf tfbpfrcturf an tmf suk, tmf ldstckhf an tmffcrtm nrab tmf suk, tmf bcss an tmf fcrtm (wmdhm lftfrbdkfs tmf strfketm an dts ercvdty)

ckl tmf odagaedhcg hck of tmf hmfbdstry tmct bcifs gdnf passdogf, cs dk tmf hmfbdhcg

habpasdtdak an LKC, bftcoagdsb, mabfastcsds ar tmf struhturf an tmf nuklcbfktcg ukdts

an gdnf, tmf hfgg. Dt hck ea ofyakl tmds ta ochtfrdc dk tmf sadg tmct ndxfs kdtraefk nar pgckts tausf ckl maw tmf pmysdhcg dktfrchts wdtm gdnf ta suppart dt, ckl maw tmf vcrdaus papugctdaks

an areckdsbs dktfrcht taeftmfr ta suppart akf ckatmfr. \mfsf gcttfr hakhfpts waugl of tmf

stuly an fhasystfbs.

Ct tmf mfcrt an c pra`fht efkfsds, ds gdnf, ckl tmf sdkegf bast dbpartckt suostckhf ta bcif

gdnf cs wf ikaw dt passdogf, ds wctfr (M?A). \mfrfnarf katmdke hck of barf dbpartckt ta c

pra`fht efkfsds tmck uklfrstckldke wmct wctfr lafs tmct bcifs gdnf passdogf ckl maw dtlafs dt.

Gft us gaai ct tmf ndrst0

3. Uctfr Ds Xagvfkt0 Dt cggaws habpaukls ta sfpcrctf ckl tmfrfnarf nar rfchtdaks taahhur. \mf hfggs tmct bcif up gdnf crf cqufaus sagutdaks cs wfgg cs tmf ahfck. \mct

ds ta scy tmfy crf nugg an ldssagvfl habpaukls. \mf ldssagvfl suostckhfs dk tmf

ahfck crf kfhfsscry nar cquctdh areckdsbs ta tcif up.?. Uctfr Ds Hamfsdvf Ckl Clmfsdvf0 \mds cggaws vfssfgs prfsfkt dk oatm ckdbcgs

(ogaal vfssfgs, crtfrdfs, ckl vfdks) ckl pgckts (raats, trukis, stfbs) ta trckspart

ldssagvfl bctfrdcgs.8. Uctfr Mcs C Mdem Xurnchf \fksdak0 \mds cggaws sbcgg lfords ta rfst ak tap anwctfr wdtmaut sdkidke, pravdldke naal nar areckdsbs tmct gdvf kfcr dts surnchf.


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\mf Vkdvfrscgdty An Efkfsds0 Cppfkldx ?

Dt ds tmf cutmars ofgdfn tmct gdnf cs dt ds struhturfl ak fcrtm bcifs tmf aptdbub usf an tmf

kcturcggy ahhurrdke fgfbfkts pravdlfl oy tmf ukdvfrsf ckl cs suhm waugl of tmf scbf cs

ak fcrtm tmrauemaut tmf ukdvfrsf, nar tmf bast pcrt dn kat habpgftfgy fvfk tmauematmfr balfgs mcvf offk prfsfktfl.

Ck fxcbpgf an tmds ds tmct gdnf ak fcrtm ds hcroak ocsfl, ckl hcroak ds tmf gdemtfst, gfcst

habpgfx fgfbfkt mcvdke naur vcgfkhf fgfhtraks, wmdhm cggaws dt ta narb dk gake hmcdks.Ckatmfr fxcbpgf waugl of tmct bftmckf, cbbakdc, wctfr, ckl mylraefk ecs habodkfl

uklfr fkfrey narb cbdka chdls, tmf oudgldke ogahis an gdnf, ckl cgg an tmfsf, fxhfpt tmf

mylraefk, crf systfbs an trdckegfs wmdgf ofdke bclf an tmf gdemtfst fgfbfkts ct tmf tap an

tmf pfrdaldh tcogf an fgfbfkts ckl systfbs an trdckegfs crf tmf bast stcogf struhturfs.

Xuhm fxcbpgfs hck of nurtmfr rfgctfl, nar pmatasyktmfsds, ckl bftcoagdh nukhtdaks dk tmf

gdvdke hfggs an oatm pgckts ckl ckdbcgs ta tmf struhturf an fhasystfbs ak fcrtm tmct bcifgdnf passdogf. \mct ds, tmfrf ds c eaal hmckhf c pra`fht efkfsds nar fcrtm waugl cppgytmrauemaut tmf ukdvfrsf, ar, ct gfcst, tmrauemaut bast an tmf ukdvfrsf.

Dck Ofcrlsgfy

Cueust ?5, ?:33


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Areckdh Bcttfr0 Cppfkldx 8

\a hgcrdny c pra`fht efkfsds dt ds kfhfsscry ta lfndkf areckdh bcttfr sdkhf dt ds tmct tmdke

wmdhm ldstdkeudsmfs gdnf hmfbdstry nrab pmysdhcg hmfbdstry.

Areckdh bcttfr ds cky an c mylrahcroak sifgftcg hmcdk habodkfl wdtm c nukhtdakcg eraup.\mf mylrahcroaks hck ahhur dk hmcdks, orckhmfs, ar rdkes an hcroak lauogf ar sdkegf

oaklfl ta atmfr hcroak ctabs ckl sdkegf oaklfl ta mylraefk ctabs. \mf nukhtdakcg

eraup hck haksdst an cky an hcroak, mylraefk, kdtraefk, axyefk, pmaspmarus, ckl sugnur

ctabs bast an tmf tdbf.


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Fktry0 \apdh0 Bagcr Bcssfs0 Cppfkldx .::)(:.?3) + (3

\mf bcrtdck ctbaspmfrf ds bastgy hcroak ldaxdlf (HA?). \mds edvfs0

HA? 2 (3?.:3) + ?(3>.::) 2 M3?A> 2 >(3?.:3) + 3?(3.::=) + >(3>.::) 2 3=:.3>

Ckl wctfr (M?A) havfrs bast an fcrtm ckl ds fssfktdcg ta gdnf, dts bagcr bcss ds0

M?A 2 ?(3.::=) + (3>.::) 2 3=.:3>

3=:.3> ldvdlfl oy 3=.:3> ds coaut 3: ckl tmf fcrtm ds coaut 3: tdbfs cs bcssdvf cs bcrs.

\mct ds, eguhasf ds ta wctfr cs tmf fcrtm ds ta bcrs.


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genesis project 01

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