escher e a matemática

Transcrição

escher e a matemática
INTERFACE TECNOLÓGICA - v.5 - n.1 - 2008
ESCHER E A MATEMÁTICA
Adriana Batista da SILVA*
Cristina Aparecida ZAPATA**
Luciana Aparecida FERRAREZI***
RESUMO
O objetivo é mostrar a importância das obras de Escher, não só para os matemáticos, mas também sua
utilização na matemática de Horma prática, possibilitando ao aluno visualizar os conceitos matemáticos. Assim, a contribuição de Escher é signiſcativa principalmente por que identiſcamos de Horma
prática alguns conceitos matemáticos existentes em suas obras, que mostra que podemos utilizar
outros recursos para tornar as aulas mais atrativas, com exemplos suſcientemente claros, Hacilitando
o entendimento da matemática.
PALAVRAS-CHAVE: Escher. Matemática. Arte.
INTRODUÇÃO
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envolvida em suas obras e a divisão das obras principais. O presente artigo faz parte do trabalho de
conclusão de curso de $GULDQD%DWLVWDGD6LOYDFRPFDUiWHUGHSHVTXLVDELEOLRJUi¿FDHFDUDFWHUtVWLFD
principal de divulgação de suas obras.
1. A VIDA DE ESCHER
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pais eram Sarah Gleichman e Gorge Arnold Escher que era engenheiro civil.
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VHPDQDLVGHGHVHQKR(VFKHUQmRFRQVHJXLXRGLSORPD¿QDOSRUQmRREWHUERDVQRWDV
_______________________________
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INTERFACE TECNOLÓGICA - v.5 - n.1 - 2008
Figura - Auto retrato
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Decorativas.
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144
INTERFACE TECNOLÓGICA - v.5 - n.1 - 2008
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suas obras de grandes sucessos.
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escola secundária tinha um bom nome e também era seu país de origem.
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várias revistas internacionais como 7LPH e The Studio.
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Matemática.
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obras.
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WRGDVDVDSUHVHQWDo}HVWLYHUDPFDVDFKHLDHWDPEpPTXHDPDLRUSDUWHGDSODWpLDHUDFRPSRVWDGH
jovens.
(PODQoDUDPXP¿OPHVREUH(VFKHU¿OPHHVVHTXHIRLHQFRPHQGDGRSHOR ministro dos negócios
145
INTERFACE TECNOLÓGICA - v.5 - n.1 - 2008
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2. AS OBRAS DE ESCHER
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$SDUWLUGRDQRGH(VFKHUFRPHoDDVHLQWHUHVVDUSHODVUHJXODULGDGHVSHODVHVWUXWXUDVPDWHPiWLFDV
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3HORIDWRGDVREUDVQmRVHJXLUHPRSDGUmRTXHDVRFLHGDGHHVWDYDDFRVWXPDGDDDSUHFLDUDVREUDVGH
(VFKHUQRSULQFtSLRVRIUHUDPYiULDVFUtWLFDVHFKHJDUDPDWpVHUHPLJQRUDGDV$V~QLFDVSHVVRDVTXH
QRLQtFLRVHLQWHUHVVDUDPSHODVFULDo}HVIRUDPRV0DWHPiWLFRVRV)tVLFRVHDOJXPDVRXWUDVSHVVRDV
1DV REUDV PDWHPiWLFDV GH (VFKHU FHUFD GH REVHUYDPRV WUrV WHPDV GLIHUHQWHV D HVWUXWXUD GR
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2.1 A estrutura do espaço
Podemos observar que em algumas de suas obras Escher utiliza de vários espaços ao mesmo tempo.
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matemáticos abstratos.
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INTERFACE TECNOLÓGICA - v.5 - n.1 - 2008
- Sólidos geométricos abstratos
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esse que lhe possibilitou a criação de obras com a divisão regular de superfícies. A estrutura da
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&LFORVH$SUR[LPDomRDRLQ¿QLWR
- Metamorfose
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INTERFACE TECNOLÓGICA - v.5 - n.1 - 2008
- Figuras impossíveis
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tridimensional.
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dessa etapa com Em cima e em EDL[R
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INTERFACE TECNOLÓGICA - v.5 - n.1 - 2008
)LJXUD(PFLPDHHPEDL[R )LJXUD(VWUHODV
)RQWH(6&+(5S
)RQWH(6&+(5S
±3HUtRGRGDDSUR[LPDomRDRLQ¿QLWR
,QLFLRXFRPDJUDYXUDHPPDGHLUD&DGDYH]PDLVSHTXHQR, $~OWLPDJUDYXUDGHVVHSHUtRGR
IRL6HUSHQWHVTXDQGRMiHVWDYDGRHQWH2 iSLFHIRLFRP*DOHULDGH$UWHSRLVFRP
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GHiJXD
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INTERFACE TECNOLÓGICA - v.5 - n.1 - 2008
)LJXUD6HUSHQWHV
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CONCLUSÃO
(VFKHU IRL XP DUWLVWD FRP JUDQGH LPSRUWkQFLD SDUD D PDWHPiWLFD H SDUD D ItVLFD SRLV VXDV REUDV
DSRQWDPFRQFHLWRVTXHQHPVHPSUHVmRIiFHLVGHVHUHPLGHQWL¿FDGRV-iTXHRVFRQFHLWRVJHRPpWULFRV
QmRVmRIiFHLVGHVHUHPLGHQWL¿FDGRVHHPDOJXPDVREUDVGHDUWHHVVHVFRQFHLWRVVmREHPYLVXDLV
SRGHPRVXWLOL]iODVHPDXODVGHPDWHPiWLFDFRPRXPDIHUUDPHQWDH¿FLHQWH
$VREUDVGH(VFKHUPRVWUDPDEHOH]DGHVVHVFRQFHLWRVTXDQGRID]FRPTXH¿JXUDVTXHURWLQHLUDV
WRPDPIRUPDVPDWHPiWLFDVWUDQVIRUPDQGRDVHPEHODVHFRPSOH[DVREUDVDUWtVWLFDVTXHSRGHPVHU
XWLOL]DGDVFRPRDSOLFDo}HVSUiWLFDVSDUDDVVLPVHWRUQDUHPXPHORHQWUHDPDWHPiWLFDDDUWHHD
realidade.
ABSTRACT
7KH REMHFWLYH LV WR VKRZ WKH LPSRUWDQFH RI WKH ZRUNV RI (VFKHU QRW RQO\ IRU WKH PDWKHPDWLFLDQV
EXWDOVR\RXUXVHLQWKHPDWKHPDWLFVLQDSUDFWLFDOZD\PDNLQJSRVVLEOHWKHVWXGHQWWRYLVXDOL]HWKH
PDWKHPDWLFDOFRQFHSWV/LNHWKLVWKHFRQWULEXWLRQRI(VFKHULVPDLQO\VLJQL¿FDQWZK\ZHLGHQWL¿HG
LQDSUDFWLFDOZD\VRPHH[LVWHQWPDWKHPDWLFDOFRQFHSWVLQ\RXUZRUNVWKDWLWVKRZVWKDWZHFDQXVH
RWKHUUHVRXUFHVWRWXUQWKHPRVWDWWUDFWLYHFODVVHVZLWKH[DPSOHVVXI¿FLHQWO\FOHDUIDFLOLWDWLQJWKH
XQGHUVWDQGLQJRIWKHPDWKHPDWLFV
KEYWORDS: (VFKHU0DWKHPDWLFV$UW
153
INTERFACE TECNOLÓGICA - v.5 - n.1 - 2008
REFERÊNCIAS
(51(67%(VSHOKRPiJLFRGH0&(VFKHUHG637DVFKHQ
7$6&+(1%0&(VFKHUJUDYXUDHGHVHQKRHG+RODQGD7DVFKHQ
7$6&+(1%Caleidociclos de M. C. Escher.HG+RODQGD7DVFKHQ
154

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