Ficha 7 Matemática: Las transformaciones geométricas en el antiguo Perú

Cigdl 0 - Eltaeìtigl

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Jls trlosckrelgikoas àkeétrigls ao aj lotiùk Xarò< Gdlo Gdlo as jl giuflfajl fa nlrrk eìs `rlofa fa Leérigl pragkjkeniol, pkr jk qua su iepkrtlogil rlfigl ao vljkras dist÷rigks, astétigks, gujturljas y skgiljas. Xksaa uo ljtk `rlfk fa kr`loizlgi÷o asplgilj y lnlrgl ljrafafkr fa >8 me >. Aj

cao÷eaok faj Oiük qua ao <9>1 fastruy÷ fa struy÷ aj elòåcigk eurlj faj Xljlgik Sajlrfa, jks siseks y jl lgtuljeaota ajavlfl olpl craìtigl, suelfks l jl parsistaogil fa l`rigujtkras praglriks, gkostituyao jks priogipljas làotas gkotrl su prasarvlgi÷o. As pkr astk qua aj EIOGAVQ^> y aj IOG7 dlo ioigilfk jks trlnlbks fa gkosarvlgi÷o a iovasti`lgi÷o ao aj gkobuotk Sajlrfa.

Witulgi÷o prknjaeìtigl

Ao uol fa jls plrafas fa asta gkepjabk lrquitagt÷oigk, sa knsarvlo astls ciùrls qua siùao giartk krfao. Gultrk fa ajjls dlo sifk ratirlfls plrl flrjas elotaoieiaotk= sio aenlr`k, plrl ok kjviflr su pksigi÷o lj ekeaotk fa slglrjls, sa lokt÷ jk siùiaota2 ‚Fa faragdl l izquiarfl2 trlsjlgi÷o - rktlgi÷o - trlsjlgi÷o - rktlgi÷o ―. âspkofa jls siùiaotas praùotls2 <. »G÷ek sko jls ciùrls qua sa knsarvlo; [[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ [[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ [[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ [[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ [[[[[[[[[[[[[[[[[[[[[ [[[[[ >. »Viaoao jl eisel ckrel; »\ué puafas fagir fa sus pksigikoas; [[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ [[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ [[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ [[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ [[[[[[[[[[[[[[[[[[[[[ [[[[[ 7. »\ué siòicigl trlsjlflr y y rktlr ; < Lflptlfk fa @lnriajl y Jlurl

(>8<8). ‚Glpåtujk II―. Njk` Jks sagratks fa Gdlo Gdlo . Gkosujtl2 >1 fa

bujik fa >8<1. :dttp2//jkssagratksfagdlogdlo.njk`spkt.gke/? :dttp2//jkssagratksfagdlogdlo.njk`spkt.gke/? > 7

EIOGAVQ^2 Eioistarik fa Gkeargik Axtarikr y Vurisek IOG2 Iostitutk Olgikolj fa Gujturl

i

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[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ [[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ [[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ [[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ [[[[[[[[[[[[[[[[[[[[[ [[[[[ 6. Wa`òo jls loktlgikoas lj ekeaotk fa ratirlr jls ciùrls (fa faragdl l izquiarfl2 trlsjlgi÷o - rktlgi÷o - trlsjlgi÷o - rktlgi÷o), gkepjatl jls qua dlgao cljtl ao jl cktk.

Lpraofaeks Vrlosckrelgikoas àkeétrigls Jl trlsjlgi÷o. As uol trlosckrelgi÷o àkeétrigl qua sa raljizl ao aj pjlok. Ao astl

trlosckrelgi÷o, jls ciùrls skjk glenilo su pksigi÷o, as fagir, fa gir, skjk glenilo fa ju`lr. Wu kriaotlgi÷o, tlelük y ckrels sa elotiaoao. Abaepjk2 ao asta glsk, jl ciùrl LNG sa sa trlsjlfl tkelofk gkek racaraogil aj vagtkr (3, <), aj gulj iofigl qua jl ciùrl kriìolj fana ekvarsa 3 uoiflfas l jl faragdl y < uoiflf dlgil lrrinl plrl trlosckrelrsa ao jl ciùrl L’N’G’ .

Jls rktlgikoas k ìrks. Wko ekvieiaotks qua raljizlo jls ciùrls ljrafafkr fa uo

puotk cibk ao aj pjlok. Ao jls rktlgikoas, jls ciùrls gkosarvlo su ckrel, tlelük y

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Abaepjk2 sa lpragil qua jl ciùrl lzuj rktl 98¸ ljrafafkr faj puotk T plrl trlosckrelrsa ao jl ciùrl rkbl.

Jl racjaxi÷o. As jl ielào fa uo knbatk k sar vivk qua sa euastrl ao aj aspabk. Xlrl

kntaoar jl racjaxi÷o fa uol ciùrl, sa utijizl uol ragtl qua ragina aj okenra fa aba fa racjaxi÷o. L jl racjaxi÷o raspagtk fa uol ragtl tleniéo sa ja faokeiol sieatrål lxilj. Abaepjk2 aj triìoùjk varfa sa racjabl gko raspagtk l uo aba fa racjaxi÷o plrl gkovartirsa ao aj triìoùjk rkslfk.

Xkjå`koks raùjlras

Wa faokeiol pkjå`kok raùjlr l lquaj qua tiaoa tkfks sus jlfks y ìoùjks gko`ruaotas. Aj paråeatrk fa uo pkjå`kok raùjlr sa gljgujl eujtipjiglofk jl jkoìtuf fa uoks fa sus jlfks pkr aj oòeark fa jlfks qua tao`l. Xkr ktrl plrta, tleniéo pkfaeks gljgujlr aj ìral fa guljquiar pkjå`kok raùjlr fivifiéofkjk ao triìoùjks, tkfks gko uo vértiga gkeòo ao aj gaotrk faj pkjå`kok. Lj kntaoar aj ìral fa uok fa ajjks y eujtipjiglrjl pkr aj oòeark fa triìoùjks qua sa ckrelo, sa kntiaoa aj ìral tktlj. Xlrl gljgujlr aj ìral faj triìoùjk, nlstl gko gkokgar su nlsa (aj jlfk faj pkjå`kok) y su ljturl (aj lpktael faj pkjå`kok).

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L  o( L )

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= fkofa

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paråeatrk,

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jkoìtuf faj

Loljizleks <. Jl siùiaota ciùrl euastrl uo pkjå`kok irraùjlr uniglfk ao uok fa jks gulfrlotas faj pjlok glrtasilok2

»G÷ek quaflrì cioljeaota jl ciùrl si sa lpjiglo fks ekvieiaotks sugasivks2 aj prieark, uol racjaxi÷o raspagtk lj aba T , y jua`k uo racjaxi÷o gko raspagtk lj aba Y ; âskjugi÷o

Wlnaeks qua si gkosifarleks lj aba T gkek gkek aba fa racjaxi÷o, jl ciùrl taofrì qua racjablrsa dlgil lnlbk, gkek ao jl ciùrl <. Y si l asta rasujtlfk ja lpjigleks uol racjaxi÷o tkelofk gkek puotk aj aba Y , aj pkjå`kok raùjlr taofrì qua racjablrsa dlgil jl faragdl, y quaflrì gkek jl ciùrl >2





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raì÷o trlositlnja. Iofigl ao aj pjlok jks puotks fkofa fanarìo sar gkjkglfls jls gìelrls plrl guepjir gko asa prkp÷sitk, si astls fanao sar jl eaokr glotiflf pksinja. âskjugi÷o

Flfk qua jls gìelrls tiaoao uol vistl fa ìrk fa 738¸, astk quiara fagir qua flo uol vuajtl gkepjatl. Aotkogas nlstl gko gkjkglr skjk uol ao aj puotk fa nicurglgi÷o fa jl raì÷o gkjkralfl plrl taoar uol vistl fa tkfl jl zkol trlositlnja.

7. Wa fasal gkjkglr ao jl plraf uo aspabk ao ckrel daxl`kolj raùjlr qua tao`l gkek eafifl fa jlfk 7 fe. »Guìotk eafirì jl suparcigia fa figdk aspabk; âskjugi÷o

Aj aspabk tiaoa ckrel fa uo daxì`kok raùjlr. Dlgaeks uo paquaük nksquabk. Xlrl gkokgar jl suparcigia, pkfaeks fasgkepkoar aj daxì`kok raùjlr ao triìoùjks.

7 fe

Knsarvleks qua jks triìoùjks sko aquijìtarks= pkr tlotk, si fatareioleks aj ìral fa uok fa ajjks y jl eujtipjigleks pkr 3, kntaofraeks aj ìral faj daxì`kok. >

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<. Wa euastrl aj pjlok fa uo gaotrk gkeargilj fa uol skjl pjlotl. Jl plrta gkjkralfl raprasaotl jls ìrals pkr fkofa trlositl jl àota. Wa vlo l iostljlr gìelrls fa saùriflf plrl knsarvlr tkfl aj ìral trlositlnja. Astls gìelrls pkfrìo taoar uol vistl fa 738¸. Gkjkgl ao aj a j pjlok jks puotks fkofa sa fanarålo iostljlr jls gìelrls plrl qua salo jl eaokr glotiflf pksinja y qua gko astls sa puafl knsarvlr tkfl aj ìral trlositlnja. Ìral trlositlnja

Viaofls

>. »Guìj fa jls siùiaotas kpgikoas euastrl euastrl aj rasujtlfk fa rktlr jl ciùrl ao <48¸ saotifk dkrlrik ljrafafkr faj puotk 8;

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7. Ao uol tlral fa lrta, Flota raljiz÷ jl lepjilgi÷o fa jl siùiaota ciùrl.







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Wi jl lepjilgi÷o gkosistål ao fupjiglr jl ciùrl, finubl ao jl gulfrågujl jl ciùrl lepjilfl pkr Flota.

6. Ajaol astì fisaülofk aj blrfåo ragtloùjlr fa uo gkofkeioik. Ajjl dl pjlselfk su fisaük ao uol dkbl ao jl gulj < ge aquivlja l < e. Wi guaotl gko <88 e fa vljjls, asgrina varflfark k cljsk sa`òo gkrraspkofl2 I. II. III. IS.

Wa`òo aj fisaük fa Ajaol, aj blrfåo taofrì uol suparcigia fa 1>1 e >. Wi ajjl quiara lepjilr jl suparcigia faj blrfåo, oagaslrileaota fana gkeprlr eìs vljjlfk. Wi rafuga 1 e l uo jlfk y lueaotl 1 e lj ktrk, ok vlrål aj ìral faj blrfåo. Wi jl suparcigia faj blrfåo sa rafuga l jl eitlf, eitl f, tleniéo sa oagasitlrål jl eitlf fa jl jkoìtuf faj vljjlfk.

l. SSCC n. CSSS g.

CCCC

f. SCCC

Blrfåo

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Gkofkeioik






eìxiel jkoìtuf aotarl faj rlfik fa jl suparcigia faj blrfåo si asta tuviarl ckrel girgujlr; Gkosifarl ψ 5 7,<6. l. <1 e n. <3 e g.

18 e

f. <88 e 0. Aj siùiaota elpl gkrraspkofa l jl raf fa glrratarls qua uoa jks puanjks fa uo fistritk. Ao éj astì iofiglfk aj tiaepk ao eioutks qua faekrl ir fa uo ju`lr l ktrk. »Guìotks eioutks gkek eåoiek faekrl uol parskol plrl ir fa jls @lrfaoils l jks Blzeioas;

l. >4 eioutks. n. 77 eioutks. g.

>< eioutks.

f. >8 eioutks. 4. Gko raspagtk lj prknjael lotarikr, si Aroastk faekr÷ 7< eioutks ao

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n.

3 fe

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g. >6 7fe f. >6 fe>

>

<8. Ao jl pjlzl fa uol giuflf sa astì gkostruyaofk uol pijatl fa ckrel girgujlr. Wa vlo axtaofar 1 tunks qua irìo fasfa aj gaotrk fa jl pijatl dlstl 1 puotks ao aj nkrfa fa astl= ao ajjks sa iostljlrìo `ricks fistrinuifks l uol eisel fistlogil uoks fa ktrks. »Guìotk eafirì aj ìoùjk fa lnarturl aotra tunk y tunk; l. 73¸ n. 0>¸ g.

98¸

f. 738¸ <<. Knsarvl jls ciùrls L, N y G . »Guìj as aj krfao fa jls trlosckrelgikoas qua fanaeks acagtulr acagtulr l jl ciùrl L plrl qua sa gkoviartl ao jl ciùrl N, y jua`k astl ao jl ciùrl G ;

l. âcjaxi÷o y rktlgi÷o. n. âcjaxi÷o y trlsjlgi÷o. g. ^ktlgi÷o y trlsjlgi÷o. f. ^ktlgi÷o y racjaxi÷o.

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Gdristilo, jks > `rìcigks (gkek gårgujks) fanao sar iféotigks, pkr ask ‚gkepjaté― jl ciùrl fa uok gko uo plrgda. @rlgils (Jupa)

Waüljl qué ekvieiaotk sa ja lpjig÷ l jl raì÷o skenralfl plrl kntaoar su ielào. l. Qol racjaxi÷o tkelofk gkek aba aj saèaotk OW . n. Qol racjaxi÷o tkelofk gkek aba aj saèaotk J^ . g. Qol rktlgi÷o fa 78¸ gko gaotrk ao aj puotk J. f. Qol rktlgi÷o fa <>8¸ gko gaotrk ao aj puotk E . <7. Qol pjlzl tiaoa ckrel fa uo daxì`kok raùjlr. Xkr aj loivarslrik vlo l gkjkglr glfaoatls fa uol asquiol l ktrl, fa tlj eloarl qua jls glfaoatls sa grugao ao aj puotk gaotrk fa jl pjlzl. Wi jl pjlzl eifa <1 e ao glfl jlfk, »guìotl sarì jl jkoìtuf eåoiel fa jl glfaoatl qua uoa fks asquiols fa jl pjlzl; l. 98 e n. 38 e g. 78 e f. <1 e

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vlrijjl sio trlnlblr guyl jkoìtuf as 1,1 e, »guìotks triìoùjks eusigljas gkepjatks (triloùjk y vlrijjl) sa pkfrì kntaoar fa jl vlrijjl sio trlnlblr; l. 0 n. 0,4 g. 4 f. 9,9

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Ficha 7 Matemática: Las transformaciones geométricas en el antiguo Perú

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