PDN Matematica Arquitectura
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5/13/2018 PDN Matematica Arquitectura - slidepdf.com
http://slidepdf.com/reader/full/pdn-matematica-arquitectura 1/90
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(MHUFLFLR /DV EDVHV GH XQ SULVPD UHFWR VRQ SHQWiJRQRV UHJXODUHV GH FP GHDSRWHPD\GHiUHDFP6LODDOWXUDGHOSULVPDHVGHFPGHWHUPLQHHOiUHDWRWDO\YROXPHQGHOSULVPD6ROXFLyQ
FPO FPO $ %
=⇒=×= FP $ / =×=
⇒ FP $ $ $ / %7 =+=+= FPK $9 % =×=×=
%$6( /7 $ $ $ +=
KFP
OFP
D
FP
KFP
D
FP
K
D
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K 3 KDQ $ %DVH/$7(5$/ ×=××=
5/13/2018 PDN Matematica Arquitectura - slidepdf.com
http://slidepdf.com/reader/full/pdn-matematica-arquitectura 51/90
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3,5È0,'(8QD SLUiPLGH HV XQ SROLHGUROLPLWDGRSRUXQSROtJRQREDVHGHOD SLUiPLGH \ SRU WULiQJXORV TXH
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SHQWDJRQDOHWFVHJ~QTXHODEDVHVHDXQWULiQJXORXQFXDGULOiWHURXQSHQWiJRQRHWF/DSLUiPLGHWULDQJXODUVHGHQRPLQDWHWUDHGUR&XDQGRODVFXDWURFDUDVGHXQD
SLUiPLGHWULDQJXODUVRQWULiQJXORVHTXLOiWHURVVHOODPDWHWUDHGURUHJXODU• 3RUODVFDUDFWHUtVWLFDVGHODEDVH
D5HJXODUFXDQGRODEDVHHVXQSROtJRQRUHJXODU\HOSLHGHODDOWXUDFRLQFLGHFRQHOFHQWURGHODEDVH(QXQDSLUiPLGHUHJXODUWRGDVODVDULVWDVODWHUDOHVWLHQHQODPLVPDPHGLGD\ODVFDUDVODWHUDOHVVRQWULiQJXORVLVyVFHOHVFRQJUXHQWHV
E,UUHJXODUFXDQGRODEDVHHVXQSROtJRQRLUUHJXODU
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• 7RGR SODQR TXH LQWHUVHFD D XQD SLUiPLGH \ HV SDUDOHOR D OD EDVH GHWHUPLQD SROtJRQRVVHPHMDQWHVHQWUHODEDVH\ODVHFFLyQWUDQVYHUVDO
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K
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• 'DGDVGRVSLUiPLGHVODViUHDVGHODVEDVHVVRQSURSRUFLRQDOHVDORVFXDGUDGRVGH
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=
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%DVH /DWHUDO 727$/ $ $ $ += 9ROXPHQ (O YROXPHQ GH XQD SLUiPLGH FXDOTXLHUD HV LJXDO D OD WHUFHUD SDUWH GHO
SURGXFWRGHOiUHDGHVXEDVHSRUODPHGLGDGHVXDOWXUD
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5/13/2018 PDN Matematica Arquitectura - slidepdf.com
http://slidepdf.com/reader/full/pdn-matematica-arquitectura 53/90
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7521&2'(3,5È0,'((V OD SDUWH GH OD SLUiPLGH UHJXODUFRPSUHQGLGDHQWUHODEDVH\XQSODQRSDUDOHORDODEDVHTXHFRUWHDWRGDVODVDULVWDVODWHUDOHV
(Q XQ WURQFR GH SLUiPLGH UHJXODU ODV FDUDVODWHUDOHVVRQWUDSHFLRVLVyVFHOHVFRQJUXHQWHV\ OD DOWXUD GH FDGD XQR GH HOORV VH OODPD³DSRWHPDGHOWURQFR´ÈUHDODWHUDO(VLJXDODOSURGXFWRGHODVHPLVXPDGHORV
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( )
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+=
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6 6 $ $ /$7(5$/727$/ ++=
9ROXPHQ(VLJXDODXQWHUFLRGHODDOWXUDGHOWURQFRPXOWLSOLFDGRSRUODVXPDGHODViUHDVGHODVEDVHVPiVODUDt]FXDGUDGDGHOSURGXFWRGHODVPLVPDV
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(MHUFLFLR+DOOHHOiUHDWRWDOGHXQDSLUiPLGHKH[DJRQDOYHUILJXUDFRQDULVWDVODWHUDOHVGHFP\DULVWDVGHODEDVHGHFP6ROXFLyQ• &iOFXORGHODDOWXUDGHODFDUDODWHUDO
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5/13/2018 PDN Matematica Arquitectura - slidepdf.com
http://slidepdf.com/reader/full/pdn-matematica-arquitectura 54/90
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×
+=
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8QVyOLGRGHUHYROXFLyQHVODILJXUDHVSDFLDOTXHVHREWLHQHDOJLUDUFRPSOHWDPHQWHXQDUHJLyQGHOSODQRDOUHGHGRUGHXQDUHFWDILMDHMHPDQWHQLHQGRWRGRVVXVSXQWRVGXUDQWHHOJLURODPLVPDGLVWDQFLDDOHMH/RVVyOLGRVGHUHYROXFLyQPiVLPSRUWDQWHVVRQFLOLQGURFRQR\HVIHUD
&LOLQGUR&LOLQGURFLUFXODUUHFWRRFLOLQGURGHUHYROXFLyQHVHOVyOLGRJHQHUDGRSRUODURWDFLyQFRPSOHWDGHXQUHFWiQJXORDOUHGHGRUGHXQRGHVXVODGRV
(OHPHQWRV• %DVHV VRQ ORV FtUFXORV GH FHQWURV 2 \ 2¶
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5/13/2018 PDN Matematica Arquitectura - slidepdf.com
http://slidepdf.com/reader/full/pdn-matematica-arquitectura 55/90
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ÈUHD ODWHUDO (V LJXDOD OD ORQJLWXG GH OD FLUFXQIHUHQFLDGH ODEDVH SRU OD DOWXUD RJHQHUDWUL]GHOFLOLQGUR
KU $ /$7(5$/ π = ÈUHDWRWDO(VLJXDODODVXPDGHOiUHDODWHUDOFRQHOiUHDGHODVEDVHV
U $ $ /$7(5$/727$/ π +=
9ROXPHQ(VLJXDODOSURGXFWRGHOiUHDGHODEDVHSRUODDOWXUDJHQHUDWUL]
KU9 π = (MHUFLFLR'HWHUPLQHHOYROXPHQGHXQFLOLQGURGHGLiPHWURGHODEDVHFP\FRQDOWXUDFP6ROXFLyQ FPKU9 === π π
(MHUFLFLR&DOFXOHODFDQWLGDGGHFDUWyQTXHVHQHFHVLWDUiSDUDKDFHUERWHVGHIRUPDFLOtQGULFDVLQWDSDGHFPGHGLiPHWUR\FPGHDOWXUD6ROXFLyQ UKU $727$/ π π +=
π π +=727$/ $ FP $727$/ =
FPFDUWyQGH&DQWLGDG ==
5/13/2018 PDN Matematica Arquitectura - slidepdf.com
http://slidepdf.com/reader/full/pdn-matematica-arquitectura 56/90
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&RQR(VHOVyOLGRJHQHUDGRSRUODURWDFLyQFRPSOHWDGHXQWULiQJXORUHFWiQJXORDOUHGHGRUGHXQRGHVXVFDWHWRV
(OHPHQWRV• %DVHHVHOFtUFXORGHFHQWUR³2´• $OWXUD K HV HO VHJPHQWR
FRPSUHQGLGR HQWUH HO YpUWLFH ³9 ́\HOFHQWURGHODEDVH³2´
• *HQHUDWUL]HVHOVHJPHQWRTXHXQH
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6HFXPSOHTXH KU J += ÈUHD ODWHUDO (V LJXDO DOVHPLSURGXFWRGHODORQJLWXGGHOD FLUFXQIHUHQFLD EDVH SRU ODJHQHUDWUL]GHOFRQR
J U $ /DWHUDO =
ÈUHDWRWDO(VLJXDODODVXPDGHOiUHDODWHUDOFRQHOiUHDGHODEDVH
( )U J U $7RWDO += π
9ROXPHQ(VLJXDODXQWHUFLRGHOSURGXFWRGHOiUHDGHODEDVHSRUODDOWXUDGHOFRQR
KU9
π =
(MHUFLFLR'HWHUPLQHHOiUHDWRWDO\HOYROXPHQGHOFRQRGHUDGLRFP\JHQHUDWUL]FP
6ROXFLyQ % /7RWDO $ $ $ += FP J 5 $ /DWHUDO === π π
FP 5 $ % === π π
(QWRQFHV FP $7RWDO =+= \
FP
K 59 ===
π π
9
5/13/2018 PDN Matematica Arquitectura - slidepdf.com
http://slidepdf.com/reader/full/pdn-matematica-arquitectura 57/90
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7DPELpQ VH OH GHILQH FRPR OD SRUFLyQ GH FRQRFRPSUHQGLGDHQWUHODEDVH\XQDVHFFLyQSDUDOHODDHVWD(OHPHQWRV• %DVHVVRQODVVHFFLRQHVFLUFXODUHVTXHOLPLWDQDOWURQFRGHFRQR• $SRWHPDHVODSDUWHGHJHQHUDWUL]FRPSUHQGLGDHQWUHODVEDVHV
• $OWXUDHVODGLVWDQFLDHQWUHODVEDVHV
• 5DGLRVVRQORVFRUUHVSRQGLHQWHVDODVEDVHVFLUFXODUHV5\U
(MHUFLFLR'HWHUPLQHODFDSDFLGDGGHXQYDVRGHYLGULRTXHWLHQHIRUPDGHWURQFRGHFRQRVLHOUDGLRGHVXEDVHHVFPHOUDGLRGHVXDEHUWXUDHVFP\WLHQHXQDDOWXUDGHFPDVXPDTXHHOYLGULRHVGHHVSHVRUGHVSUHFLDEOH6ROXFLyQ
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=→=
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5/13/2018 PDN Matematica Arquitectura - slidepdf.com
http://slidepdf.com/reader/full/pdn-matematica-arquitectura 58/90
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5/13/2018 PDN Matematica Arquitectura - slidepdf.com
http://slidepdf.com/reader/full/pdn-matematica-arquitectura 59/90
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5/13/2018 PDN Matematica Arquitectura - slidepdf.com
http://slidepdf.com/reader/full/pdn-matematica-arquitectura 90/90
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