Informe de Matemática

 

AC DH_GRBMAC, IMEIG_VMY BCYHIMY X ICYMY FG C_AHICIHÙE

FGFHICVMRHC

C eugstrms pcfrgs, quhgegs sme nugrzc, kmtmr y kmthvm pcrc auidcr pmr eugstrcs kgtcs y csphrcihmegs,, pmr sus imesglms, pmr sus ãehkms, pmr su vcagetëc0 rrgimemigk csphrcihmegs gimemigkms ms su henhehtm gsnugrzm pmr gfuicrems y nmrkcrems imkm sgrgs fg bhge, pmr ams vcamrgs qug shgkprg ems dce heiuaicfm, csë khskm pcrc eugstrm prmngsmr qug ime su imemihkhgetm ems hestruyg c sgr prmngshmecags ime ac vmauetcf pagec fg sgrvhr c ac smihgfcf.

 

CJRCFGIHKHGEVM

C Fhms pmrqug gs ga irgcfmr fg eugstrm kuefm y pcfrg fg emsmtrms, gs quhge ems fc ac ng y ac gspgrcezc pcrc vhvhr ge ue kuefm kglmr y ems juëc ge ga ickhem fga bhge.

 

ËEFHIG

H. RGYWKGE..................................................................................................................................7 HH. CBYVRCIV.................................................................................................................................7 HHH. HEVRMFWIIHÙE.......................................................................................................................> H^. MBLGVH^MY...............................................................................................................................: 7.3 MBLGVH^M JGEGRCA............................................................................................................4 7.2 MBLGVH^MY GY_GIËNHIMY.....................................................................................................4 DHYVMRHC......................................................................................................................................8 FGNHEHIHÙE FG AC DH_ÈRBMAC...................................................................................................3? GAGKGEVMY FG AC DH_ÈRBMAC..................................................................................................3? RGACIHÙE FG AC DH_ÈRBMAC IME AC IMEYVRWIIHÙE..............................................................3> IMEIAWYHMEGY..........................................................................................................................3: RGIMKGEFCIHMEGY..................................................................................................................34 RGNGRGEIHCY..............................................................................................................................38

 

H. RGYWKGE

Ga shjuhgetg trcbclm surjhù c pcrthr fg ac egigshfcf fg fcr c imemigr ac hkpmrtceihc y su cpahicihùe fg ac dhpèrbmac ge ga ickpm fg ac hejgehgrëc, cpahicefm ge ga fgscrrmaam fg ams  prmbagkcs kctgkãthims kctgkãthims qug dci dcigg usm fg ac tg tgmrëc mrëc prgsgetcfc ggee ac henmrkcihùe fga iursm iursm fg kctgkãthic HHH. Gstg henmrkg thtuacfm< ‑Ac Dhpèrbmac‛ thgeg pmr mblgthvms< ‑Fgnhehr acs prheihpcags pcrtgs fg ac sgiihùe iùehic Dhpèrbmac‛ kgfhcetg ac fgsirhpihùe fg sus prheihpcags imeigptms, imeigptms, tgehgefm ams imkm mblgthvms gspgiënhims0 fgnhehr igetrm, vèrthigs, nmims glgs kcymr y kgemr, y gxigetrhihfcf fg ac dhpèrbmac0 cfgkãs fg ac hfgethnhicihùe fg iucaquhgr iùehic c trcvès fg ac fhsirhkhecetg fg uec giucihùe jgegrca fg sgjuefm jrcfm. Fgscrrmaaãefmsg fg kcegrc fgsirhpthvc ime, ga trcbclm imeiauyù< ‑Ac prheihpca rczùe fg gstufhm fg acs sgiihmegs iùehics iùehics gs pmr su nmrkc fg cfgiucrsg c eugvcs gstruiturcs ge eugstrc icrrgrc‛.

 

HH. CBYVRCIV

Vdg nmaamwhej wmr` crmsg nrmk tdg eggf tm pubahihzg tdg hkpmrtceig cef hts cppahicthme mn dypgrbmac he tdg nhgaf mn gejheggrhej, cppayhej ht he tdg fgvgampkget mn kctdgkcthica  prmbagks tdct kc`gs kc`gs usg mn tdg tdgmry prgsgetgf he tdg henmrkcthme mn tdg k kctdgkcthis ctdgkcthis imursg HHH. Vdg nmaamwhej rgpmrt gethtagf< "Vdg Dypgrbmac" chks tm< "Fgnheg tdg kche pcrts mn tdg imehica sgithme Dypgrbmac" by fgsirhbhej hts kche imeigpts, dcvhej tdgk cs spgihnhi mblgithvgs0 fgnheg igetgr, vgrthigs, kclmr cef khemr cxhs nmih, cef giigetrhihty mn tdg dypgrbmac0 he cffhthme tm tdg hfgethnhicthme mn cey imehi tdrmujd tdg fhsirhkhecet mn c jgegrca gqucthme mn tdg sgimef fgjrgg. Fgvgamphej he c fgsirhpthvg wcy whtd, tdg wmr` imeiaufgf< "Vdg kche rgcsme nmr stufyhej imehi sgithmes hs bgicusg mn tdghr wcy mn cfcpthej tm egw struiturgs he mur icrggr".

 

HHH. HEVRMFWIIHÙE

Ga prgsgetg henmrkg dc shfm fgscrrmaacfm ime ga prmpùshtm fg gxpahicr ac giucihùe fg ac dhpèrbmac pcrc pmfgr glgrihihms imthfhcems, ge fhidm trcbclm gxpahicrgkms su fgnhehihùe,  pcrtgs qug ac imkpmege, imkpmege, imk imkmm sg jgegrc jgegrc,, dhstmrhc, glgkpams fg glgrihihms y ac rgac rgacihùe ihùe qug gstc thgeg ime ac hejgehgrëc ihvha. Vckbhèe geimetrcrgkms cajuecs iacshnhicihmegs, iacshnhicihmegs,  prmigfhkhgetms,, thpms fg dhpèrbmac  prmigfhkhgetms dhpèrbmacss y cajuecs rgj rgjacs acs qug fgbg fgbgkms kms uthahzcr ca kmkgetm fg su imestruiihùe. Ime ga fgscrrmaam fg fhidm henmrkg gspgrckms nmrtcagigr ac imkprgeshùe fg gstg tgkc, yc qug gs kuy hkpmrtcetgs pcrc eugstrc icrrgrc prmngshmeca.

 

H^. MBLGVH^MY

7.3 MBLGVH^M JGEGRCA 

Gxpahicr ams imeigptms bãshims fg ac dhpèrbmac

7.2 MBLGVH^MY GY_GIËNHIMY



Geueihcr ams gagkgetms fg ac dhpèrbmac



Fgscrrmaacr glgrihihms fg cpahicihùe



Rgacihmecr ga gkpagm fg ac dhpèrbmac ge ac hejgehgrëc ihvha

 

DHYVMRHC

Ygjüe ac trcfhihùe acs sgiihmegs nugrme fgsiubhgrtcs pmr Kgegikm, ge su gstufhm fga  prmbagkc fg ac fupahicihùe fupahicihùe fga iiubm ubm fmefg fg fgkmstrù kmstrù ac gxhstgei gxhstgeihc hc fg uec rgsmau rgsmauihùe ihùe kgfhcetg ue imrtg fg uec pcrãbmac ime uec dhpèrbmac, am iuca pmstgrhmrkgetg gs imenhrkcfm pmr _rmiam y Grctùstgegs. Yhe gkbcrjm, ga prhkgrm ge uscr ga tèrkhem dhpèrbmac nug Cpmamehm ge su mbrc trctcfm Iùehics, imeshfgrcfc imeshfgrcfc mbrc iukbrg smbrg ga tgkc fg acs kctgkãthics jrhgjcs, fmefg sg fgscrrmaac ga gstufhm fg acs tcejgetgs c sgiihmegs iùehics. (Bugecs Vcrgcs, Vcrgcs, 2?32). Fgsicrtgs gxckhec ime fgtcaag ue aujcr jgmkètrhim smam uec vgz, y gs ge imegxhùe ime ga prmbagkc fga aujcr fg acs trgs y iuctrm rgitcs fg _cppus fga qug mbthgeg ac giucihùe y2; cy-bxy+ix-fx2. Giucihùe Giucihùe jgegrca fg uec iùehic qug pcsc pmr ga mrhjge fg immrfgecfcs. immrfgecfc s. _mr mtrm acfm, Fgsicrtgs prgsgetc imefhihmegs smbrg ams imgnhihgetgs pcrc qug ac iùehic sgc uec rgitc, uec pcrãbmac, èa scbëc qug, gahjhgefm cfgiucfckgetg ga mrhjge fg immrfgecfcs imkm ams glgs, pmfëc rgfuihrsg ac giucihùe c ac nmrkc kãs sgeihaac, pgrm ga dgidm gs qug em fc ehejuec fg acs nmrkcs iùehics. Bugecs Vcrgcs (2?32)

 

FGNHEHIHÙE FG AC DH_ÈRBMAC

Ac dhpèrbmac tckbhèe sg fgnheg imkm uec iùehic (sg ags fhig c acs iurvcs fg acs fhngrgetgs hetgrsgiihmegs hetgrsgiihmegs getrg ue imem y ue pacem qug em pcsc pmr su vèrthig). Yhgefm uec fg acs hetgrsgiihmegs fga imem ime ue pacem qug em pcsg pmr su vèrthig y qug nmrkg ue ãejuam ime ga glg fga imem kgemr qug ga ãejuam qug nmrkc ime ga glg jgegrctrhz j fga imem. Ac dhpèrbmac gs uec iurvc pacec cbhgrtc, ime fms rckcs. Yg rgcahzc ubhicefm ams puetms fga pacem iuyc fhngrgeihc fg fhstceihcs c mtrms fms nhlms, aackcfms nmims, gs imestcetg. GAGKGEVMY FG AC DH_ÈRBMAC Gagkgetms fg ac dhpèrbmac< 3. Nmims< Yme ams puetms nlms N y N'. 2. Glg prheihpca m rgca< Gs ac rgitc qug pcsc pmr ams mims. 9. Glg sgiuefcrhm m hkcjhecrhm< Gs ac kgfhctrhz fga sgjkgetm NN'. 6. Igetrm< Gs ga puetm fg hetgrsgiihùe fg ams glgs. 7. ^èrigs< Ams puetms C y C' sme ams puetms fg hetgrsgiihùe fg ac dhpèrbmac ime ga glg mica. Ams puetms B y B' sg mbgege imkm hetgrsgiihùe fga glg hkcjhecrhm ime ac ihriuegrgeihc qug geg pmr igetrm uem fg ams vèrigs y fg rcfhm i. >. Rcfhms vgitmrgs< Yme ams sgjkgetms qug vce fgsfg ue puetm fg ac dhpèrbmac c ams mims< _N y _N'. :. Fhstceihc mica< Gs ga sgjkgetm fg amejhtuf 2i. 4. Glg kcymr< Gs ga sgjkgetm fg amejhtuf 2c. 8. Glg kgemr< Gs ga sgjkgetm fg amejhtuf 2b. 3?. Glgs fg shkgtrëc< Yme acs rgitcs qug imegege ca glg rgca m ca glg hkcjhecrhm. 33. Csëetmtcs< Yme acs rgitcs fg giucihmegs. 32. Rgacihùe getrg ams sgkhglgs.

 

GIWCIHMEGY

 

C_AHICIHÙE FG AC DH_ÈRBMAC Acs bcsgs fg ue pugetg fgsirhbge uec dhpèrbmac, ac pcrtg kãs cejmstc khfg 2 kgtrms y su gxigetrhihfcf gs 3.7. Geimetrcr ac giucihùe fg ac dhpèrbmac

Nmim ; 2I N ; 2(3,7) ^2 (-3,?)

 

N; 9

^3 (3,?) N ; 2(-I,?)

^(c,?) 2k

^(-c,?) c;3 g ;3,7 I  ;½ c

Geimetrcefm ‑b‛

 ;3,7

I2 ; c2 + b2 (3,7)2 ; (3)2 + b2

I  3

;½

 ;3,7

(2,27) ’ 3 ; b2 3.27;b ∜ 3.27

 ;3,7

3,33 ; b

i;½

Gi. Dhpèrbmac 2

 x

2

c  x

2

 x

−

2

2

b

  x

;3

2

 −  ;3 3 ( 3,33 )2 2

 x

2

−

  x

2

 ;3 ( 3,29 )2

N ; 2(-I,?)

 

Ictgfrca fg Brcshahc. Brcsha, 38:?

 

Ac ictgfrca fg Brcshahc geg 6? kgtrms fg caturc y icpcihfcf pcrc 6 kha pgrsmecs. Ac bcsg fga gfhnihm gs ihriuacr y fg uems >? kgtrms fg fhãkgtrm. Ac imestruiihùe iugetc ime 3> phacrgs mrkcefm ue fhãkgtrm fg 2? kgtrms ge sus iurvcturcs. Ycbhgefm qug ac caturc dcstc acs iurvcturcs iurvcturcs fg ams phacrgs gs fg 2: k y ime fhstceihc getrg ams mims fg 6?k. Icaiuag ac gxigetrhihfcf y ac giucihùe fg ac dhpèrbmag.

^3(c,?) ; (-3?,?) ^2(-c,?) ; (-3?,?) N (I,?) ; (2?,?) N (-I,?) ; (-2?,?) i ; 2?

g;

i

2

I  2? ;2 ; c 3?

2

2

;c +b

2

2

( 2??) ;( 3?) + b 2

6??−3?? ;b

2

2

 ϊ 2 − y 2 ;3 c b

2

9?? ;b 9?? ??; b ∜ 9

2

 ϊ 

  y

2

 −  ;3 ( 3? ) ( 3:,92)2 2

3:,92;b

2

c ;3?

 

RGACIHÙE FG AC DH_ÈRBMAC IME AC IMEYVRWIIHÙE Dce kcricfm uec eugvc tgefgeihc ge ga kmefm fg ac crquhtgiturc, amjrcefm uec bgaagzc pcriuacr. Cfgkãs fg mtmrjcr gxigagetgs prmphgfcfgs iucefm sg trctc fg rggxhùe fg auz. Gstg fhsgóm rgprgsgetc uec njurc fg pcrcbmamhfg dhpgrbùahic shkhacr cüe egeücr, gstm imeshstg ge imestruhr uec supgrnihg gejgefrcfc pmr ga fgspaczckhgetm fg pcrãbmac jgegrctrhz qug sg fgsahzc fg ime fhrgiihùe pcrcagackgetg c am acrjm fg mtrc pcrãbmac mrkcefm uec fhrgitrhz fg iurvcturc mpugstc shtucfc ge su pacem fg shkgtrëc. uec fg acs icrcitgrësics fg gstg fhsgóm gs, sgr imkm ga dhpgrbmamhfg fg uec dmlc (supgrnihg fg rgvmauihùe jgegrcfc pmr ac rmtcihùe fg uec dhpèrbmac cargfgfmr fg uem fg sus glgs fg shkgtrëc). _mr mtrm acfm sh rgacihmeckms ga fhsgóm fg dhpèrbmacs ge imestruiihmegs ihvhags, sgrëc ge ams pugetgs, ime gstruiturcs fg crims, fmefg sg trcesngrg ga pgsm prmphm fga pugetg y acs smbrg icrjcs fg usm dcihc ams cpmyms kgfhcetg ac imkprgeshùe fga crim pcrcbùahim, ga iuca gs trcesmrkcfm ge ue gkpulg dmrhzmetca fglcefm ac icrjc c acs imaukecs ime fhrgiihùe vgrica.

 

IMEIAWYHMEGY



Ge gstg trcbclm sg hevgsthjcrme imeigptms bãshims y ac dhstmrhc fg ac dhpèrbmac, ime ga nhe fg gxpahicr ams imeigptms bãshims fg ac dhpèrbmac rgacihmeãefmams fg nmrkc fhrgitc ime ac vhfc fhcrhc y csë pmfgr cpahicrams ge ac hejgehgrëc ihvha.



Ca geueihcr ams gagkgetms fg ac dhpèrbmac ge acs jrãnhics kmstrcfcs, ncihahtce ac hfgethnhicihùe fg ams gagkgetms pcrc ac cpahicihùe fg acs nùrkuacs ca kmkgetm fg fgscrrmaacr ams glgrihihms fg cpahicihùe.



Ge imeiaushùe, ac dhpèrbmac thgeg uec hkpmrtcetg rgacihùe ime ga gkpagm ge ac hejgehgrëc ihvha yc qug mtmrjc ue eugvm fhsgóm c acs henrcgstruiturcs, cfgkãs fg fcr aukhemshfcf am qug cyufc ca cdmrrm fg gegrjëc.

 

RGIMKGEFCIHMEGY



Ime rgspgitm ca trcbclm fgscrrmaacfm gs hkpmrtcetg pgescr y cecahzcr cajuems icsms fg cpahicihùe fg dhpèrbmac, ac iuca gs kuy hkpmrtcetg ge ac gesgócezc fg acs kctgkãthics gs fg kuidc uthahfcf, pcrc amjrcr am gstcbagihfm gs rgimkgefcbag qug ams caukems sg imeigetrge,  prcithquge pcrc pmfgr pmfgr getgefg getgefgrr ga tgkc c ac pgrngii pgrngiihùe. hùe.



Ge gstg trcbclm dgkms pmfhfm ckpahcr eugstrms imemihkhgetms cigric fg acs sgiihmegs iùehics, imemigr kglmr acs iùehics, imkm pmr glgkpam dhpèrbmac.



 Imkm shjuhgetg rgimkgefcihùe sg prmpmeg pmegram ge prãithic ga tgkc  pcrc csë em tgegr tgegr fhnhiuatcf pcrc ge getgefgr. tgefgr.



Vckbhèe, cprgefhkms qug ac dhpèrbmac0 gs fg kuidc hkpmrtceihc ge eugstrc vhfc pmrqug thgeg fhngrgetgs cpahicihmegs prãithics. _mr glgkpam, jrcihcs c gaacs sg dce pmfhfm fgscrrmaacr fhngrgetgs cpcrctms, imestruiihmegss qug dce bgegnhihcfm y ncihahtcfm eugstrcs vhfcs. imestruiihmeg

 

RGNGRGEIHCY Bugecs Vcrgcs. (26 fg Mitubrg fg 2?32). Mbtgehfm fg

dps