158:@0.026565:0.967627:0.050760:0.967627:0.050760:0.951847:0.026565:0.951847:0.000000:0.000000:0.000000
1:@0.258110:0.152809:0.263803:0.152809:0.263803:0.142282:0.258110:0.142282:0.000000
2:@0.236473:0.124142:0.242166:0.124142:0.242166:0.113614:0.236473:0.113614:0.000000
1:@0.284909:0.189324:0.290602:0.189324:0.290602:0.178797:0.284909:0.178797:0.000000
0:@0.239151:0.189324:0.244843:0.189324:0.244843:0.178797:0.239151:0.178797:0.000000
–1:@0.205561:0.189324:0.217996:0.189324:0.217996:0.178797:0.205561:0.178797:0.000000:0.000000
–2:@0.167570:0.189324:0.180005:0.189324:0.180005:0.178797:0.167570:0.178797:0.000000:0.000000
2:@0.322888:0.189324:0.328581:0.189324:0.328581:0.178797:0.322888:0.178797:0.000000
–1:@0.231287:0.209627:0.243722:0.209627:0.243722:0.199100:0.231287:0.199100:0.000000:0.000000
–3:@0.231287:0.240258:0.243722:0.240258:0.243722:0.229731:0.231287:0.229731:0.000000:0.000000
–5:@0.231287:0.268346:0.243722:0.268346:0.243722:0.257819:0.231287:0.257819:0.000000:0.000000
A:@0.159839:0.153669:0.167075:0.153669:0.167075:0.143159:0.159839:0.143159:0.000000
B:@0.296440:0.121472:0.302470:0.121472:0.302470:0.110962:0.296440:0.110962:0.000000
C:@0.334005:0.269408:0.340409:0.269408:0.340409:0.258899:0.334005:0.258899:0.000000
x:@0.354595:0.185217:0.359842:0.185217:0.359842:0.174690:0.354595:0.174690:0.000000
y:@0.236738:0.098682:0.241900:0.098682:0.241900:0.088155:0.236738:0.088155:0.000000
p:@0.302154:0.305837:0.313634:0.305837:0.313634:0.295813:0.302154:0.295813:0.000000
 :@0.313634:0.306545:0.316516:0.306545:0.316516:0.295068:0.313634:0.295068:0.000000
Figura 3.24.:@0.316516:0.306545:0.370994:0.306545:0.370994:0.295068:0.316516:0.295068:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–2:@0.166751:0.878488:0.179304:0.878488:0.179304:0.867705:0.166751:0.867705:0.000000:0.000000
–1:@0.205902:0.878488:0.218455:0.878488:0.218455:0.867705:0.205902:0.867705:0.000000:0.000000
1:@0.287596:0.878488:0.293350:0.878488:0.293350:0.867705:0.287596:0.867705:0.000000
2:@0.326746:0.878488:0.332501:0.878488:0.332501:0.867705:0.326746:0.867705:0.000000
x:@0.354500:0.876184:0.359509:0.876184:0.359509:0.865354:0.354500:0.865354:0.000000
1:@0.239720:0.839301:0.245475:0.839301:0.245475:0.828517:0.239720:0.828517:0.000000
0:@0.241100:0.875894:0.246854:0.875894:0.246854:0.865111:0.241100:0.865111:0.000000
y:@0.240006:0.789862:0.245176:0.789862:0.245176:0.779032:0.240006:0.779032:0.000000
2:@0.239720:0.809927:0.245475:0.809927:0.245475:0.799143:0.239720:0.799143:0.000000
B:@0.296193:0.812984:0.302656:0.812984:0.302656:0.802135:0.296193:0.802135:0.000000
A:@0.168873:0.834233:0.176753:0.834233:0.176753:0.823384:0.168873:0.823384:0.000000
p:@0.302154:0.907796:0.313634:0.907796:0.313634:0.897772:0.302154:0.897772:0.000000
 Figura 3.25.:@0.313634:0.908504:0.370994:0.908504:0.370994:0.897028:0.313634:0.897028:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Distancia entre dos puntos:@0.404236:0.097328:0.619152:0.097328:0.619152:0.079645:0.404236:0.079645:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.404236:0.121627:0.484320:0.121627:0.484320:0.104681:0.404236:0.104681:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.404236:0.147523:0.442035:0.147523:0.442035:0.131025:0.404236:0.131025:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.445680:0.147260:0.456736:0.147260:0.456736:0.131105:0.445680:0.131105:0.000000
a bB:@0.479886:0.147260:0.523504:0.147260:0.523504:0.131105:0.479886:0.131105:0.000000:0.000000:0.000000:0.000000
cd:@0.547712:0.147260:0.569653:0.147260:0.569653:0.131105:0.547712:0.131105:0.000000:0.000000
(, ),:@0.474028:0.147147:0.510369:0.147147:0.510369:0.130963:0.474028:0.130963:0.000000:0.000000:0.000000:0.000000:0.000000
(, ):@0.541873:0.147147:0.575436:0.147147:0.575436:0.130963:0.541873:0.130963:0.000000:0.000000:0.000000:0.000000
2:@0.606469:0.139264:0.611293:0.139264:0.611293:0.129897:0.606469:0.129897:0.000000
=:@0.460060:0.147771:0.470435:0.147771:0.470435:0.131800:0.460060:0.131800:0.000000
=:@0.527905:0.147771:0.538281:0.147771:0.538281:0.131800:0.527905:0.131800:0.000000
∈:@0.578440:0.147771:0.591914:0.147771:0.591914:0.131800:0.578440:0.131800:0.000000
. Se llama distancia de :@0.612070:0.147529:0.770351:0.147529:0.770351:0.131031:0.612070:0.131031:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Aa B:@0.774067:0.147644:0.810999:0.147644:0.810999:0.131175:0.774067:0.131175:0.000000:0.000000:0.000000:0.000000
, que  :@0.812139:0.147529:0.854330:0.147529:0.854330:0.131031:0.812139:0.131031:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se nota :@0.404236:0.166759:0.460452:0.166759:0.460452:0.150261:0.404236:0.150261:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.473643:0.171485:0.515391:0.171485:0.515391:0.145598:0.473643:0.145598:0.000000:0.000000:0.000000
dA B:@0.463434:0.166881:0.507224:0.166881:0.507224:0.150412:0.463434:0.150412:0.000000:0.000000:0.000000:0.000000
,:@0.494217:0.166765:0.496972:0.166765:0.496972:0.150268:0.494217:0.150268:0.000000
,  al número real no negativo :@0.517142:0.166765:0.723098:0.166765:0.723098:0.150268:0.517142:0.150268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.417429:0.193236:0.459177:0.193236:0.459177:0.167350:0.417429:0.167350:0.000000:0.000000:0.000000
=:@0.462032:0.189153:0.472609:0.189153:0.472609:0.172872:0.462032:0.172872:0.000000
−:@0.496632:0.189153:0.507209:0.189153:0.507209:0.172872:0.496632:0.172872:0.000000
=:@0.529094:0.189153:0.539671:0.189153:0.539671:0.172872:0.529094:0.172872:0.000000
−:@0.573481:0.189153:0.584058:0.189153:0.584058:0.172872:0.573481:0.172872:0.000000
+:@0.610085:0.189153:0.620662:0.189153:0.620662:0.172872:0.610085:0.172872:0.000000
−:@0.640659:0.189153:0.651236:0.189153:0.651236:0.172872:0.640659:0.172872:0.000000
dA B:@0.407222:0.188632:0.451012:0.188632:0.451012:0.172163:0.407222:0.172163:0.000000:0.000000:0.000000:0.000000
A B:@0.482915:0.188632:0.519115:0.188632:0.519115:0.172163:0.482915:0.172163:0.000000:0.000000:0.000000
a c:@0.562173:0.188632:0.594384:0.188632:0.594384:0.172163:0.562173:0.172163:0.000000:0.000000:0.000000
b d:@0.628927:0.188632:0.663527:0.188632:0.663527:0.172163:0.628927:0.172163:0.000000:0.000000:0.000000
,:@0.437989:0.188517:0.440744:0.188517:0.440744:0.172019:0.437989:0.172019:0.000000
(:@0.556201:0.188517:0.562153:0.188517:0.562153:0.172019:0.556201:0.172019:0.000000
):@0.594307:0.188517:0.600260:0.188517:0.600260:0.172019:0.594307:0.172019:0.000000
(:@0.623359:0.188517:0.629312:0.188517:0.629312:0.172019:0.623359:0.172019:0.000000
).:@0.663480:0.188517:0.681358:0.188517:0.681358:0.172019:0.663480:0.172019:0.000000:0.000000
2:@0.600606:0.180481:0.605524:0.180481:0.605524:0.170932:0.600606:0.170932:0.000000
2:@0.669763:0.180481:0.674680:0.180481:0.674680:0.170932:0.669763:0.170932:0.000000
Ejercicio resuelto:@0.404236:0.213371:0.522215:0.213371:0.522215:0.196584:0.404236:0.196584:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los vértices de un triángulo son los vértices :@0.404236:0.239354:0.730777:0.239354:0.730777:0.222856:0.404236:0.222856:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.763662:0.242296:0.770078:0.242296:0.770078:0.220317:0.763662:0.220317:0.000000
):@0.800632:0.242296:0.807048:0.242296:0.807048:0.220317:0.800632:0.220317:0.000000
−:@0.771201:0.239997:0.781777:0.239997:0.781777:0.223716:0.771201:0.223716:0.000000
=:@0.750780:0.239361:0.761587:0.239361:0.761587:0.222863:0.750780:0.222863:0.000000
2,1 ,   =1,2 , :@0.781623:0.239361:0.895912:0.239361:0.895912:0.222863:0.781623:0.222863:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.736697:0.239476:0.747967:0.239476:0.747967:0.223007:0.736697:0.223007:0.000000
( ):@0.849942:0.242296:0.884465:0.242296:0.884465:0.220317:0.849942:0.220317:0.000000:0.000000:0.000000
B:@0.823982:0.239476:0.833171:0.239476:0.833171:0.223007:0.823982:0.223007:0.000000
(:@0.433762:0.261532:0.440178:0.261532:0.440178:0.239553:0.433762:0.239553:0.000000
):@0.473083:0.261532:0.479498:0.261532:0.479498:0.239553:0.473083:0.239553:0.000000
−:@0.453550:0.259233:0.464127:0.259233:0.464127:0.242953:0.453550:0.242953:0.000000
=2,3 .  Primero, determinemos el perímetro del triángulo (figura :@0.420876:0.258597:0.895859:0.258597:0.895859:0.242100:0.420876:0.242100:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.406813:0.258713:0.416850:0.258713:0.416850:0.242244:0.406813:0.242244:0.000000
3.24.). Para el efecto, calculemos las longitudes de cada uno de los :@0.404233:0.275948:0.895952:0.275948:0.895952:0.259450:0.404233:0.259450:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lados del triángulo. Tenemos::@0.404233:0.293299:0.609716:0.293299:0.609716:0.276801:0.404233:0.276801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.460933:0.315471:0.467348:0.315471:0.467348:0.293492:0.460933:0.293492:0.000000
) ( ) (:@0.497903:0.315471:0.575503:0.315471:0.575503:0.293492:0.497903:0.293492:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
):@0.617675:0.315471:0.624090:0.315471:0.624090:0.293492:0.617675:0.293492:0.000000
−:@0.421669:0.313172:0.432245:0.313172:0.432245:0.296891:0.421669:0.296891:0.000000
−:@0.468464:0.313172:0.479041:0.313172:0.479041:0.296891:0.468464:0.296891:0.000000
−:@0.506374:0.313172:0.516950:0.313172:0.516950:0.296891:0.506374:0.296891:0.000000
− −:@0.576634:0.313172:0.610292:0.313172:0.610292:0.296891:0.576634:0.296891:0.000000:0.000000:0.000000
AB:@0.407949:0.312651:0.444148:0.312651:0.444148:0.296182:0.407949:0.296182:0.000000:0.000000
=:@0.448059:0.312535:0.458867:0.312535:0.458867:0.296038:0.448059:0.296038:0.000000
2,1:@0.478902:0.312535:0.498861:0.312535:0.498861:0.296038:0.478902:0.296038:0.000000:0.000000:0.000000
1,2=:@0.525582:0.312535:0.567022:0.312535:0.567022:0.296038:0.525582:0.296038:0.000000:0.000000:0.000000:0.000000
3, 1,  :@0.587038:0.312535:0.636211:0.312535:0.636211:0.296038:0.587038:0.296038:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.693902:0.315471:0.700317:0.315471:0.700317:0.293492:0.693902:0.293492:0.000000
) (:@0.730872:0.315471:0.758633:0.315471:0.758633:0.293492:0.730872:0.293492:0.000000:0.000000:0.000000
) (:@0.791538:0.315471:0.819665:0.315471:0.819665:0.293492:0.791538:0.293492:0.000000:0.000000:0.000000
):@0.853399:0.315471:0.859814:0.315471:0.859814:0.293492:0.853399:0.293492:0.000000
−:@0.653644:0.313172:0.664221:0.313172:0.664221:0.296891:0.653644:0.296891:0.000000
−:@0.701441:0.313172:0.712018:0.313172:0.712018:0.296891:0.701441:0.296891:0.000000
−:@0.739336:0.313172:0.749913:0.313172:0.749913:0.296891:0.739336:0.296891:0.000000
−:@0.772010:0.313172:0.782587:0.313172:0.782587:0.296891:0.772010:0.296891:0.000000
−:@0.820790:0.313172:0.831366:0.313172:0.831366:0.296891:0.820790:0.296891:0.000000
AC:@0.639908:0.312651:0.676955:0.312651:0.676955:0.296182:0.639908:0.296182:0.000000:0.000000
=:@0.681001:0.312535:0.691809:0.312535:0.691809:0.296038:0.681001:0.296038:0.000000
2,1:@0.711845:0.312535:0.731803:0.312535:0.731803:0.296038:0.711845:0.296038:0.000000:0.000000:0.000000
2, 3=:@0.759314:0.312535:0.811157:0.312535:0.811157:0.296038:0.759314:0.296038:0.000000:0.000000:0.000000:0.000000:0.000000
4,4,:@0.831193:0.312535:0.864347:0.312535:0.864347:0.296038:0.831193:0.296038:0.000000:0.000000:0.000000:0.000000
( ) (:@0.459780:0.334707:0.515669:0.334707:0.515669:0.312728:0.459780:0.312728:0.000000:0.000000:0.000000:0.000000:0.000000
) (:@0.548574:0.334707:0.576710:0.334707:0.576710:0.312728:0.548574:0.312728:0.000000:0.000000:0.000000
):@0.609191:0.334707:0.615606:0.334707:0.615606:0.312728:0.609191:0.312728:0.000000
−:@0.419523:0.332408:0.430099:0.332408:0.430099:0.316128:0.419523:0.316128:0.000000
−:@0.496372:0.332408:0.506948:0.332408:0.506948:0.316128:0.496372:0.316128:0.000000
−:@0.529042:0.332408:0.539618:0.332408:0.539618:0.316128:0.529042:0.316128:0.000000
−:@0.577840:0.332408:0.588417:0.332408:0.588417:0.316128:0.577840:0.316128:0.000000
BC:@0.406801:0.331888:0.442866:0.331888:0.442866:0.315419:0.406801:0.315419:0.000000:0.000000
=1,2:@0.446911:0.331772:0.486867:0.331772:0.486867:0.315275:0.446911:0.315275:0.000000:0.000000:0.000000:0.000000
2, 3=:@0.516382:0.331772:0.568225:0.331772:0.568225:0.315275:0.516382:0.315275:0.000000:0.000000:0.000000:0.000000:0.000000
1,5,:@0.588260:0.331772:0.620118:0.331772:0.620118:0.315275:0.588260:0.315275:0.000000:0.000000:0.000000:0.000000
y de la definición de distancia entre dos puntos, obtenemos::@0.404236:0.356251:0.830917:0.356251:0.830917:0.339753:0.404236:0.339753:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.415214:0.388592:0.456962:0.388592:0.456962:0.362705:0.415214:0.362705:0.000000:0.000000:0.000000
−:@0.493218:0.384508:0.503795:0.384508:0.503795:0.368228:0.493218:0.368228:0.000000
+:@0.563324:0.384508:0.573901:0.384508:0.573901:0.368228:0.563324:0.368228:0.000000
dA B:@0.405003:0.383988:0.448793:0.383988:0.448793:0.367519:0.405003:0.367519:0.000000:0.000000:0.000000:0.000000
A B:@0.479501:0.383988:0.515701:0.383988:0.515701:0.367519:0.479501:0.367519:0.000000:0.000000:0.000000
,:@0.435788:0.383872:0.438543:0.383872:0.438543:0.367375:0.435788:0.367375:0.000000
=:@0.459408:0.383872:0.470215:0.383872:0.470215:0.367375:0.459408:0.367375:0.000000
=9 1= 10 , :@0.525256:0.383872:0.639479:0.383872:0.639479:0.367375:0.525256:0.367375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.650279:0.388592:0.693028:0.388592:0.693028:0.362705:0.650279:0.362705:0.000000:0.000000:0.000000
−:@0.729276:0.384508:0.739853:0.384508:0.739853:0.368228:0.729276:0.368228:0.000000
+:@0.807590:0.384508:0.818166:0.384508:0.818166:0.368228:0.807590:0.368228:0.000000
dA C:@0.640078:0.383988:0.684716:0.383988:0.684716:0.367519:0.640078:0.367519:0.000000:0.000000:0.000000:0.000000
A C:@0.715559:0.383988:0.752606:0.383988:0.752606:0.367519:0.715559:0.367519:0.000000:0.000000:0.000000
,:@0.670845:0.383872:0.673600:0.383872:0.673600:0.367375:0.670845:0.367375:0.000000
=:@0.695446:0.383872:0.706254:0.383872:0.706254:0.367375:0.695446:0.367375:0.000000
=1616= 42 ,:@0.762297:0.383872:0.891391:0.383872:0.891391:0.367375:0.762297:0.367375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.415214:0.416213:0.455825:0.416213:0.455825:0.390327:0.415214:0.390327:0.000000:0.000000:0.000000
−:@0.489920:0.412130:0.500496:0.412130:0.500496:0.395849:0.489920:0.395849:0.000000
+:@0.557830:0.412130:0.568406:0.412130:0.568406:0.395849:0.557830:0.395849:0.000000
dB C:@0.404998:0.411610:0.447498:0.411610:0.447498:0.395141:0.404998:0.395141:0.000000:0.000000:0.000000:0.000000
B C:@0.477205:0.411610:0.513250:0.411610:0.513250:0.395141:0.477205:0.395141:0.000000:0.000000:0.000000
,:@0.433646:0.411494:0.436401:0.411494:0.436401:0.394996:0.433646:0.394996:0.000000
=:@0.458248:0.411494:0.469055:0.411494:0.469055:0.394996:0.458248:0.394996:0.000000
=1 25 =26.:@0.522960:0.411494:0.640501:0.411494:0.640501:0.394996:0.522960:0.394996:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Consecuentemente, el perímetro   es :@0.404236:0.435974:0.673867:0.435974:0.673867:0.419476:0.404236:0.419476:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.641944:0.436089:0.651211:0.436089:0.651211:0.419620:0.641944:0.419620:0.000000
( ) ( ) ( ):@0.443971:0.461187:0.621057:0.461187:0.621057:0.435301:0.443971:0.435301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.487789:0.457104:0.498365:0.457104:0.498365:0.440823:0.487789:0.440823:0.000000
+:@0.556527:0.457104:0.567104:0.457104:0.567104:0.440823:0.556527:0.440823:0.000000
+:@0.670289:0.457104:0.680865:0.457104:0.680865:0.440823:0.670289:0.440823:0.000000
+:@0.718606:0.457104:0.729182:0.457104:0.729182:0.440823:0.718606:0.440823:0.000000
pd AB:@0.407954:0.456583:0.477559:0.456583:0.477559:0.440114:0.407954:0.440114:0.000000:0.000000:0.000000:0.000000:0.000000
dA C:@0.501506:0.456583:0.546143:0.456583:0.546143:0.440114:0.501506:0.440114:0.000000:0.000000:0.000000:0.000000
d BC:@0.570244:0.456583:0.612724:0.456583:0.612724:0.440114:0.570244:0.440114:0.000000:0.000000:0.000000:0.000000
=:@0.420033:0.456468:0.430841:0.456468:0.430841:0.439970:0.420033:0.439970:0.000000
,:@0.464536:0.456468:0.467291:0.456468:0.467291:0.439970:0.464536:0.439970:0.000000
,:@0.532272:0.456468:0.535027:0.456468:0.535027:0.439970:0.532272:0.439970:0.000000
,:@0.598872:0.456468:0.601627:0.456468:0.601627:0.439970:0.598872:0.439970:0.000000
=104 2:@0.623474:0.456468:0.714275:0.456468:0.714275:0.439970:0.623474:0.439970:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
26.:@0.744946:0.456468:0.766792:0.456468:0.766792:0.439970:0.744946:0.439970:0.000000:0.000000:0.000000
Ortogonalidad :@0.404236:0.491309:0.527525:0.491309:0.527525:0.473627:0.404236:0.473627:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.404236:0.515607:0.484320:0.515607:0.484320:0.498661:0.404236:0.498661:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i):@0.404236:0.541720:0.414774:0.541720:0.414774:0.525006:0.404236:0.525006:0.000000:0.000000
   Sean :@0.414774:0.541503:0.465488:0.541503:0.465488:0.525006:0.414774:0.525006:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.468800:0.540045:0.497686:0.540045:0.497686:0.524868:0.468800:0.524868:0.000000:0.000000
,:@0.480145:0.539938:0.482684:0.539938:0.482684:0.524735:0.480145:0.524735:0.000000
2:@0.535910:0.532533:0.540442:0.532533:0.540442:0.523733:0.535910:0.523733:0.000000
∈:@0.505563:0.540525:0.518222:0.540525:0.518222:0.525521:0.505563:0.525521:0.000000
. Se dice que   es ortogonal o perpendicular a  , :@0.541100:0.541509:0.895912:0.541509:0.895912:0.525011:0.541100:0.525011:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.636394:0.541625:0.647664:0.541625:0.647664:0.525156:0.636394:0.525156:0.000000
B:@0.879131:0.541625:0.888321:0.541625:0.888321:0.525156:0.879131:0.525156:0.000000
 :@0.891770:0.541509:0.895912:0.541509:0.895912:0.525011:0.891770:0.525011:0.000000
que se escribe :@0.427690:0.560739:0.531604:0.560739:0.531604:0.544242:0.427690:0.544242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
⊥:@0.549821:0.561382:0.562498:0.561382:0.562498:0.545101:0.549821:0.545101:0.000000
A:@0.535314:0.560861:0.546585:0.560861:0.546585:0.544392:0.535314:0.544392:0.000000
B:@0.566312:0.560861:0.575502:0.560861:0.575502:0.544392:0.566312:0.544392:0.000000
 si y solo si  .:@0.578510:0.560746:0.674762:0.560746:0.674762:0.544248:0.578510:0.544248:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.687246:0.561382:0.697823:0.561382:0.697823:0.545101:0.687246:0.545101:0.000000
0.:@0.701753:0.560746:0.713835:0.560746:0.713835:0.544248:0.701753:0.544248:0.000000:0.000000
AB:@0.660429:0.560861:0.683913:0.560861:0.683913:0.544392:0.660429:0.544392:0.000000:0.000000
ii):@0.404242:0.587321:0.419038:0.587321:0.419038:0.570607:0.404242:0.570607:0.000000:0.000000:0.000000
   Sean :@0.419038:0.587104:0.465494:0.587104:0.465494:0.570607:0.419038:0.570607:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.484401:0.587747:0.498138:0.587747:0.498138:0.571467:0.484401:0.571467:0.000000
2:@0.512827:0.579074:0.517744:0.579074:0.517744:0.569525:0.512827:0.569525:0.000000
A:@0.470318:0.587227:0.481588:0.587227:0.481588:0.570758:0.470318:0.570758:0.000000
 y S:@0.521885:0.587111:0.548163:0.587111:0.548163:0.570613:0.521885:0.570613:0.000000:0.000000:0.000000:0.000000
:@0.548163:0.586894:0.564211:0.586894:0.564211:0.572247:0.548163:0.572247:0.000000
R:@0.564211:0.586142:0.578120:0.586142:0.578120:0.572696:0.564211:0.572696:0.000000
2:@0.578111:0.580758:0.583064:0.580758:0.583064:0.571140:0.578111:0.571140:0.000000
 con :@0.583065:0.587111:0.619418:0.587111:0.619418:0.570613:0.583065:0.570613:0.000000:0.000000:0.000000:0.000000:0.000000
≠∅:@0.634766:0.587747:0.664704:0.587747:0.664704:0.571467:0.634766:0.571467:0.000000:0.000000
S:@0.623881:0.587227:0.631761:0.587227:0.631761:0.570758:0.623881:0.570758:0.000000
. Se dice que :@0.665058:0.587111:0.760438:0.587111:0.760438:0.570613:0.665058:0.570613:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.765257:0.587227:0.776527:0.587227:0.776527:0.570758:0.765257:0.570758:0.000000
 es ortogonal al :@0.779967:0.587111:0.895923:0.587111:0.895923:0.570613:0.779967:0.570613:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
conjunto  , que se escribe :@0.427683:0.607600:0.615881:0.607600:0.615881:0.591102:0.427683:0.591102:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.497192:0.607715:0.505071:0.607715:0.505071:0.591246:0.497192:0.591246:0.000000
⊥:@0.634106:0.608241:0.646782:0.608241:0.646782:0.591961:0.634106:0.591961:0.000000
A:@0.619599:0.607721:0.630869:0.607721:0.630869:0.591252:0.619599:0.591252:0.000000
S:@0.651387:0.607721:0.659266:0.607721:0.659266:0.591252:0.651387:0.591252:0.000000
, si y solo si :@0.658844:0.607605:0.739814:0.607605:0.739814:0.591107:0.658844:0.591107:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
⋅:@0.756166:0.607936:0.760911:0.607936:0.760911:0.591895:0.756166:0.591895:0.000000
∀ ∈:@0.801248:0.607936:0.841088:0.607936:0.841088:0.591895:0.801248:0.591895:0.000000:0.000000:0.000000
AB:@0.743483:0.607423:0.771216:0.607423:0.771216:0.591197:0.743483:0.591197:0.000000:0.000000
BS:@0.814658:0.607423:0.849186:0.607423:0.849186:0.591197:0.814658:0.591197:0.000000:0.000000
=0:@0.775044:0.607310:0.796930:0.607310:0.796930:0.591054:0.775044:0.591054:0.000000:0.000000
.:@0.849505:0.607605:0.852260:0.607605:0.852260:0.591107:0.849505:0.591107:0.000000
iii):@0.404227:0.632301:0.423280:0.632301:0.423280:0.615587:0.404227:0.615587:0.000000:0.000000:0.000000:0.000000
  Sean  ∙    dos subconjuntos no vacíos de  . Se dice que   es orto-:@0.423280:0.632084:0.891767:0.632084:0.891767:0.615586:0.423280:0.615587:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R  S:@0.464604:0.632200:0.491325:0.632200:0.491325:0.615731:0.464604:0.615731:0.000000:0.000000:0.000000:0.000000
R:@0.717341:0.631115:0.731251:0.631115:0.731251:0.617669:0.717341:0.617669:0.000000
2:@0.731323:0.625731:0.736277:0.625731:0.736277:0.616112:0.731323:0.616112:0.000000
R:@0.824760:0.632199:0.834335:0.632199:0.834335:0.615730:0.824760:0.615730:0.000000
gonal a  , que se escribe :@0.427686:0.651314:0.601129:0.651314:0.601129:0.634816:0.427686:0.634816:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.482611:0.651430:0.490491:0.651430:0.490491:0.634961:0.482611:0.634961:0.000000
⊥:@0.616559:0.651956:0.629236:0.651956:0.629236:0.635676:0.616559:0.635676:0.000000
R:@0.604056:0.651436:0.613631:0.651436:0.613631:0.634967:0.604056:0.634967:0.000000
S:@0.633840:0.651436:0.641720:0.651436:0.641720:0.634967:0.633840:0.634967:0.000000
, si y solo si :@0.641840:0.651320:0.722581:0.651320:0.722581:0.634823:0.641840:0.634823:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
⋅:@0.739107:0.651956:0.743923:0.651956:0.743923:0.635676:0.739107:0.635676:0.000000
∀ ∈∀ ∈:@0.784862:0.651956:0.881265:0.651956:0.881265:0.635676:0.784862:0.635676:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=0:@0.758275:0.651320:0.780488:0.651320:0.780488:0.634823:0.758275:0.634823:0.000000:0.000000
,:@0.836589:0.651320:0.839344:0.651320:0.839344:0.634823:0.836589:0.634823:0.000000
AB:@0.726237:0.651436:0.754384:0.651436:0.754384:0.634967:0.726237:0.634967:0.000000:0.000000
AR BS:@0.798482:0.651436:0.889480:0.651436:0.889480:0.634967:0.798482:0.634967:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.889015:0.651320:0.891770:0.651320:0.891770:0.634823:0.889015:0.634823:0.000000
iv):@0.404244:0.676016:0.423047:0.676016:0.423047:0.659302:0.404244:0.659302:0.000000:0.000000:0.000000
  Sea :@0.423047:0.675799:0.455959:0.675799:0.455959:0.659302:0.423047:0.659302:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S :@0.456376:0.675915:0.468397:0.675915:0.468397:0.659446:0.456376:0.659446:0.000000:0.000000
:@0.468802:0.675582:0.484850:0.675582:0.484850:0.660935:0.468802:0.660935:0.000000
 :@0.484850:0.675799:0.488992:0.675799:0.488992:0.659302:0.484850:0.659302:0.000000
R:@0.489396:0.674831:0.503306:0.674831:0.503306:0.661384:0.489396:0.661384:0.000000
2:@0.503303:0.669447:0.508256:0.669447:0.508256:0.659829:0.503303:0.659829:0.000000
 con :@0.508257:0.675799:0.543898:0.675799:0.543898:0.659301:0.508257:0.659301:0.000000:0.000000:0.000000:0.000000:0.000000
≠∅:@0.558554:0.676435:0.588492:0.676435:0.588492:0.660154:0.558554:0.660154:0.000000:0.000000
S:@0.547669:0.675914:0.555549:0.675914:0.555549:0.659446:0.547669:0.659446:0.000000
. Se dice que   es un conjunto ortogonal si        :@0.588389:0.675799:0.895891:0.675799:0.895891:0.659301:0.588389:0.659301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.682037:0.675914:0.689916:0.675914:0.689916:0.659446:0.682037:0.659446:0.000000
AB:@0.431313:0.694647:0.458343:0.694647:0.458343:0.678590:0.431313:0.678590:0.000000:0.000000
AB S:@0.502165:0.694647:0.555435:0.694647:0.555435:0.678590:0.502165:0.678590:0.000000:0.000000:0.000000:0.000000
=0:@0.462306:0.694535:0.484114:0.694535:0.484114:0.678449:0.462306:0.678449:0.000000:0.000000
,:@0.514168:0.694535:0.516854:0.694535:0.516854:0.678449:0.514168:0.678449:0.000000
⋅:@0.443673:0.695155:0.448369:0.695155:0.448369:0.679281:0.443673:0.679281:0.000000
∀:@0.488904:0.695155:0.502296:0.695155:0.502296:0.679281:0.488904:0.679281:0.000000
∈:@0.533872:0.695155:0.547264:0.695155:0.547264:0.679281:0.533872:0.679281:0.000000
 con :@0.558358:0.695035:0.593594:0.695035:0.593594:0.678538:0.558358:0.678538:0.000000:0.000000:0.000000:0.000000:0.000000
A ≠ B.:@0.593594:0.695151:0.635939:0.695151:0.635939:0.678682:0.593594:0.678682:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v):@0.404236:0.719731:0.418859:0.719731:0.418859:0.703017:0.404236:0.703017:0.000000:0.000000
   Sea :@0.418859:0.719514:0.455952:0.719514:0.455952:0.703017:0.418859:0.703017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S :@0.454596:0.719630:0.466617:0.719630:0.466617:0.703161:0.454596:0.703161:0.000000:0.000000
:@0.465249:0.719297:0.481297:0.719297:0.481297:0.704651:0.465249:0.704651:0.000000
   con  :@0.481297:0.719514:0.539577:0.719515:0.539577:0.703017:0.481297:0.703017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.484071:0.718546:0.497981:0.718546:0.497981:0.705099:0.484071:0.705099:0.000000
2:@0.497981:0.713162:0.502934:0.713162:0.502934:0.703544:0.497981:0.703544:0.000000
≠∅:@0.552460:0.721409:0.582398:0.721409:0.582398:0.705128:0.552460:0.705128:0.000000:0.000000
S:@0.541575:0.720888:0.549454:0.720888:0.549454:0.704419:0.541575:0.704419:0.000000
. El complemento ortogonal de   se nota con :@0.582379:0.719515:0.895879:0.719515:0.895879:0.703017:0.582379:0.703017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.800651:0.719631:0.808530:0.719631:0.808530:0.703162:0.800651:0.703162:0.000000
⊥:@0.439155:0.731083:0.446492:0.731083:0.446492:0.721660:0.439155:0.721660:0.000000
S:@0.431040:0.738867:0.438920:0.738867:0.438920:0.722399:0.431040:0.722399:0.000000
 y se define como el conjunto :@0.451143:0.738752:0.654156:0.738752:0.654156:0.722254:0.451143:0.722254:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
{:@0.690427:0.743961:0.699675:0.743961:0.699675:0.717261:0.690427:0.717261:0.000000
}:@0.876067:0.743961:0.885315:0.743961:0.885315:0.717261:0.876067:0.717261:0.000000
=:@0.676764:0.739388:0.687341:0.739388:0.687341:0.723107:0.676764:0.723107:0.000000
∈:@0.714775:0.739388:0.728511:0.739388:0.728511:0.723107:0.714775:0.723107:0.000000
⋅=:@0.772724:0.739388:0.802875:0.739388:0.802875:0.723107:0.772724:0.723107:0.000000:0.000000
∀∈:@0.827804:0.739388:0.868242:0.739388:0.868242:0.723107:0.827804:0.723107:0.000000:0.000000
⊥:@0.663676:0.731083:0.671013:0.731083:0.671013:0.721660:0.663676:0.721660:0.000000
|:@0.751835:0.738752:0.756844:0.738752:0.756844:0.722254:0.751835:0.722254:0.000000
0:@0.806799:0.738752:0.815295:0.738752:0.815295:0.722254:0.806799:0.722254:0.000000
. :@0.886326:0.738752:0.895913:0.738752:0.895913:0.722254:0.886326:0.722254:0.000000:0.000000
2:@0.743197:0.730715:0.748115:0.730715:0.748115:0.721166:0.743197:0.721166:0.000000
S:@0.655562:0.738867:0.663442:0.738867:0.663442:0.722399:0.655562:0.722399:0.000000
A:@0.700682:0.738867:0.711952:0.738867:0.711952:0.722399:0.700682:0.722399:0.000000
AB:@0.759845:0.738867:0.787992:0.738867:0.787992:0.722399:0.759845:0.722399:0.000000:0.000000
BS:@0.841408:0.738867:0.876452:0.738867:0.876452:0.722399:0.841408:0.722399:0.000000:0.000000
Ejercicios resueltos:@0.404245:0.763607:0.534900:0.763607:0.534900:0.746820:0.404245:0.746820:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.404245:0.789806:0.416517:0.789806:0.416517:0.773092:0.404245:0.773092:0.000000:0.000000
   Sean :@0.416517:0.789589:0.465497:0.789589:0.465497:0.773092:0.416517:0.773092:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.469050:0.788870:0.479850:0.788870:0.479850:0.773088:0.469050:0.773088:0.000000
B:@0.553645:0.788870:0.562451:0.788870:0.562451:0.773088:0.553645:0.773088:0.000000
=:@0.482696:0.788759:0.493054:0.788759:0.493054:0.772949:0.482696:0.772949:0.000000
2,1 ,:@0.512402:0.788759:0.546835:0.788759:0.546835:0.772949:0.512402:0.772949:0.000000:0.000000:0.000000:0.000000:0.000000
= 1, 2:@0.566313:0.788759:0.610290:0.788759:0.610290:0.772949:0.566313:0.772949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.495188:0.791572:0.501336:0.791572:0.501336:0.770509:0.495188:0.770509:0.000000
):@0.536120:0.791572:0.542268:0.791572:0.542268:0.770509:0.536120:0.770509:0.000000
(:@0.578821:0.791572:0.584969:0.791572:0.584969:0.770509:0.578821:0.770509:0.000000
):@0.611278:0.791572:0.617426:0.791572:0.617426:0.770509:0.611278:0.770509:0.000000
−:@0.502414:0.789369:0.512549:0.789369:0.512549:0.773767:0.502414:0.773767:0.000000
 (figura 3.25.).:@0.619610:0.789594:0.713933:0.789594:0.713933:0.773097:0.619610:0.773097:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Entonces:@0.427690:0.817211:0.492689:0.817211:0.492689:0.800713:0.427690:0.800713:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
⊥:@0.515050:0.817852:0.527726:0.817852:0.527726:0.801572:0.515050:0.801572:0.000000
A:@0.500543:0.817332:0.511813:0.817332:0.511813:0.800863:0.500543:0.800863:0.000000
B:@0.531541:0.817332:0.540731:0.817332:0.540731:0.800863:0.531541:0.800863:0.000000
, pues :@0.541076:0.817216:0.585830:0.817216:0.585830:0.800718:0.541076:0.800718:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
⋅:@0.602424:0.816595:0.607240:0.816595:0.607240:0.800314:0.602424:0.800314:0.000000
− +:@0.635310:0.816595:0.667598:0.816595:0.667598:0.800314:0.635310:0.800314:0.000000:0.000000:0.000000
AB:@0.589535:0.816074:0.617682:0.816074:0.617682:0.799606:0.589535:0.799606:0.000000:0.000000
=2 2= 0.  :@0.621573:0.815959:0.713939:0.817216:0.713939:0.800718:0.621573:0.799461:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.:@0.404230:0.845050:0.416502:0.845050:0.416502:0.828335:0.404230:0.828335:0.000000:0.000000
   Sean  =:@0.416502:0.844833:0.493882:0.844839:0.493882:0.828341:0.416502:0.828335:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.495957:0.847774:0.502373:0.847774:0.502373:0.825795:0.495957:0.825795:0.000000
):@0.538418:0.847774:0.544833:0.847774:0.544833:0.825795:0.538418:0.825795:0.000000
−:@0.503496:0.845475:0.514072:0.845475:0.514072:0.829194:0.503496:0.829194:0.000000
A:@0.468992:0.844955:0.480262:0.844955:0.480262:0.828486:0.468992:0.828486:0.000000
2,1  y  ={ 1, 2|:@0.513918:0.844839:0.649347:0.846096:0.649347:0.829599:0.513918:0.828341:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.603106:0.849031:0.609521:0.849031:0.609521:0.827052:0.603106:0.827052:0.000000
):@0.636723:0.849031:0.643139:0.849031:0.643139:0.827052:0.636723:0.827052:0.000000
∈:@0.660483:0.846732:0.674219:0.846732:0.674219:0.830452:0.660483:0.830452:0.000000
}. Entonces, :@0.688543:0.846096:0.773347:0.844839:0.773347:0.828341:0.688543:0.829599:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.566406:0.846212:0.574286:0.846212:0.574286:0.829743:0.566406:0.829743:0.000000
t:@0.596094:0.846212:0.601758:0.846212:0.601758:0.829743:0.596094:0.829743:0.000000
t:@0.651212:0.846212:0.656876:0.846212:0.656876:0.829743:0.651212:0.829743:0.000000
⊥:@0.791361:0.845475:0.804037:0.845475:0.804037:0.829194:0.791361:0.829194:0.000000
A:@0.776854:0.844955:0.788124:0.844955:0.788124:0.828486:0.776854:0.828486:0.000000
S:@0.808642:0.844955:0.816521:0.844955:0.816521:0.828486:0.808642:0.828486:0.000000
. En efecto, :@0.816263:0.844839:0.895904:0.844839:0.895904:0.828341:0.816263:0.828341:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sea :@0.427683:0.864069:0.454173:0.864069:0.454173:0.847572:0.427683:0.847572:0.000000:0.000000:0.000000:0.000000
B S,:@0.453941:0.864185:0.489852:0.864185:0.489852:0.847716:0.453941:0.847716:0.000000:0.000000:0.000000:0.000000
:@0.463131:0.863853:0.479179:0.863853:0.479179:0.849206:0.463131:0.849206:0.000000
 entonces   es de la forma :@0.489852:0.864069:0.677765:0.864069:0.677765:0.847572:0.489852:0.847572:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.562386:0.864185:0.571575:0.864185:0.571575:0.847716:0.562386:0.847716:0.000000
( ) (:@0.714670:0.867011:0.771599:0.867011:0.771599:0.845032:0.714670:0.845032:0.000000:0.000000:0.000000:0.000000:0.000000
):@0.799475:0.867011:0.805891:0.867011:0.805891:0.845032:0.799475:0.845032:0.000000
=:@0.693572:0.864712:0.704148:0.864712:0.704148:0.848431:0.693572:0.848431:0.000000
=:@0.751522:0.864712:0.762098:0.864712:0.762098:0.848431:0.751522:0.848431:0.000000
∈:@0.822033:0.864712:0.835769:0.864712:0.835769:0.848431:0.822033:0.848431:0.000000
Bt:@0.680048:0.864191:0.713299:0.864191:0.713299:0.847723:0.680048:0.847723:0.000000:0.000000
tt t:@0.772290:0.864191:0.818430:0.864191:0.818430:0.847723:0.772290:0.847723:0.000000:0.000000:0.000000:0.000000
1,2:@0.720986:0.864076:0.741215:0.864076:0.741215:0.847578:0.720986:0.847578:0.000000:0.000000:0.000000
,2:@0.779784:0.864076:0.792112:0.864076:0.792112:0.847578:0.779784:0.847578:0.000000:0.000000
.  Lue-:@0.850524:0.864076:0.891776:0.864076:0.891776:0.847578:0.850524:0.847578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
go, :@0.427695:0.883306:0.452143:0.883306:0.452143:0.866808:0.427695:0.866808:0.000000:0.000000:0.000000:0.000000
( ):@0.500772:0.886248:0.534679:0.886248:0.534679:0.864268:0.500772:0.864268:0.000000:0.000000:0.000000
⋅:@0.468733:0.883949:0.473549:0.883949:0.473549:0.867668:0.468733:0.867668:0.000000
−:@0.508304:0.883949:0.518880:0.883949:0.518880:0.867668:0.508304:0.867668:0.000000
+:@0.544176:0.883949:0.554752:0.883949:0.554752:0.867668:0.544176:0.867668:0.000000
AB:@0.455864:0.883428:0.484010:0.883428:0.484010:0.866959:0.455864:0.866959:0.000000:0.000000
t:@0.535275:0.883428:0.540939:0.883428:0.540939:0.866959:0.535275:0.866959:0.000000
t:@0.566215:0.883428:0.571879:0.883428:0.571879:0.866959:0.566215:0.866959:0.000000
=:@0.487902:0.883312:0.498710:0.883312:0.498710:0.866815:0.487902:0.866815:0.000000
2:@0.518746:0.883312:0.527241:0.883312:0.527241:0.866815:0.518746:0.866815:0.000000
2= 0.  Así, :@0.557469:0.883312:0.637836:0.883312:0.637836:0.866815:0.557469:0.866815:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
⋅:@0.654430:0.883949:0.659246:0.883949:0.659246:0.867668:0.654430:0.867668:0.000000
∀ ∈:@0.700185:0.883949:0.740623:0.883949:0.740623:0.867668:0.700185:0.867668:0.000000:0.000000:0.000000
AB:@0.641561:0.883428:0.669707:0.883428:0.669707:0.866959:0.641561:0.866959:0.000000:0.000000
BS:@0.713797:0.883428:0.748841:0.883428:0.748841:0.866959:0.713797:0.866959:0.000000:0.000000
=0:@0.673591:0.883312:0.695804:0.883312:0.695804:0.866815:0.673591:0.866815:0.000000:0.000000
.:@0.748918:0.883312:0.751673:0.883312:0.751673:0.866815:0.748918:0.866815:0.000000
Nótese que el conjunto   es un subespacio de R , que se identi-:@0.428770:0.906293:0.891772:0.906292:0.891772:0.889794:0.428770:0.889795:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.605300:0.906409:0.613179:0.906409:0.613179:0.889940:0.605300:0.889940:0.000000
2:@0.779954:0.899940:0.784907:0.899940:0.784907:0.890322:0.779954:0.890322:0.000000
fica con una recta que pasa por el origen y es paralela al vector :@0.428770:0.923643:0.895912:0.923643:0.895912:0.907145:0.428770:0.907145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.457301:0.945815:0.491824:0.945815:0.491824:0.923836:0.457301:0.923836:0.000000:0.000000:0.000000
B:@0.431335:0.942996:0.440524:0.942996:0.440524:0.926527:0.431335:0.926527:0.000000
=1,2 , llamado vector director de la recta.:@0.444416:0.942880:0.747359:0.942880:0.747359:0.926382:0.444416:0.926382:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.199644:0.396116:0.297267:0.396116:0.297267:0.380643:0.199644:0.380643:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.199644:0.408684:0.283707:0.408684:0.283707:0.393211:0.199644:0.393211:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Teorema:@0.199880:0.433581:0.261004:0.433581:0.261004:0.418109:0.199880:0.418109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.153337:0.452142:0.187849:0.452142:0.187849:0.437079:0.153337:0.437079:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.236908:0.453100:0.250644:0.453100:0.250644:0.436820:0.236908:0.436820:0.000000
AB C:@0.191577:0.452580:0.232863:0.452580:0.232863:0.436111:0.191577:0.436111:0.000000:0.000000:0.000000:0.000000
,,:@0.203868:0.452464:0.221746:0.452464:0.221746:0.435967:0.203868:0.435967:0.000000:0.000000
2:@0.265335:0.444429:0.270253:0.444429:0.270253:0.434880:0.265335:0.434880:0.000000
. La distancia :@0.269924:0.452144:0.355761:0.452144:0.355761:0.437081:0.269924:0.437081:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entre dos puntos de   verifica :@0.153337:0.467986:0.358812:0.467986:0.358812:0.452923:0.153337:0.452923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.287899:0.467101:0.300599:0.467101:0.300599:0.454824:0.287899:0.454824:0.000000
2:@0.300604:0.462186:0.305127:0.462186:0.305127:0.453405:0.300604:0.453405:0.000000
las propiedades siguientes::@0.153343:0.483828:0.324140:0.483828:0.324140:0.468765:0.153343:0.468765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i)  :@0.153343:0.503010:0.170423:0.503010:0.170423:0.487749:0.153343:0.487749:0.000000:0.000000:0.000000:0.000000
( ):@0.183615:0.507853:0.225363:0.507853:0.225363:0.481967:0.183615:0.481967:0.000000:0.000000:0.000000
≥:@0.228219:0.503770:0.238795:0.503770:0.238795:0.487489:0.228219:0.487489:0.000000
dA B:@0.173409:0.503249:0.217199:0.503249:0.217199:0.486780:0.173409:0.486780:0.000000:0.000000:0.000000:0.000000
,:@0.204189:0.503134:0.206944:0.503134:0.206944:0.486636:0.204189:0.486636:0.000000
0.:@0.242296:0.503134:0.253484:0.503134:0.253484:0.486636:0.242296:0.486636:0.000000:0.000000
ii) :@0.153344:0.527342:0.170582:0.527342:0.170582:0.512081:0.153344:0.512081:0.000000:0.000000:0.000000:0.000000
( ):@0.183775:0.532184:0.225522:0.532184:0.225522:0.506298:0.183775:0.506298:0.000000:0.000000:0.000000
dA B:@0.173566:0.527580:0.217359:0.527580:0.217359:0.511112:0.173566:0.511112:0.000000:0.000000:0.000000:0.000000
A B:@0.280626:0.527580:0.317192:0.527580:0.317192:0.511112:0.280626:0.511112:0.000000:0.000000:0.000000
, ,:@0.204355:0.527465:0.205503:0.527465:0.205503:0.510967:0.204355:0.510967:0.000000:0.000000:0.000000
=0:@0.227974:0.527465:0.250168:0.527465:0.250168:0.510967:0.227974:0.510967:0.000000:0.000000
= .:@0.294709:0.527465:0.321334:0.527465:0.321334:0.510967:0.294709:0.510967:0.000000:0.000000:0.000000
 :@0.250992:0.527342:0.254721:0.527342:0.254721:0.512081:0.250992:0.512081:0.000000
⇔:@0.254721:0.527646:0.273050:0.527646:0.273050:0.510444:0.254721:0.510444:0.000000
 :@0.273050:0.527342:0.276779:0.527342:0.276779:0.512081:0.273050:0.512081:0.000000
(:@0.182175:0.532184:0.188590:0.532184:0.188590:0.506298:0.182175:0.506298:0.000000
):@0.217507:0.532184:0.223923:0.532184:0.223923:0.506298:0.217507:0.506298:0.000000
dA:@0.171966:0.527580:0.201711:0.527580:0.201711:0.511112:0.171966:0.511112:0.000000:0.000000
B:@0.206566:0.527580:0.215756:0.527580:0.215756:0.511112:0.206566:0.511112:0.000000
A:@0.279023:0.527580:0.290293:0.527580:0.290293:0.511112:0.279023:0.511112:0.000000
B:@0.306404:0.527580:0.315593:0.527580:0.315593:0.511112:0.306404:0.511112:0.000000
=:@0.226368:0.527465:0.237175:0.527465:0.237175:0.510967:0.226368:0.510967:0.000000
0:@0.240065:0.527465:0.248561:0.527465:0.248561:0.510967:0.240065:0.510967:0.000000
=:@0.293102:0.527465:0.303910:0.527465:0.303910:0.510967:0.293102:0.510967:0.000000
.:@0.316980:0.527465:0.319735:0.527465:0.319735:0.510967:0.316980:0.510967:0.000000
iii):@0.153344:0.552931:0.170740:0.552931:0.170740:0.537670:0.153344:0.537670:0.000000:0.000000:0.000000:0.000000
( ) ( ):@0.183932:0.556516:0.293783:0.556516:0.293783:0.530629:0.183932:0.530629:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dA B:@0.173723:0.551912:0.217513:0.551912:0.217513:0.535443:0.173723:0.535443:0.000000:0.000000:0.000000:0.000000
d BA:@0.241826:0.551912:0.286714:0.551912:0.286714:0.535443:0.241826:0.535443:0.000000:0.000000:0.000000:0.000000
,:@0.204509:0.551796:0.207264:0.551796:0.207264:0.535298:0.204509:0.535298:0.000000
=:@0.228128:0.551796:0.238936:0.551796:0.238936:0.535298:0.228128:0.535298:0.000000
,:@0.270468:0.551796:0.273223:0.551796:0.273223:0.535298:0.270468:0.535298:0.000000
.:@0.294820:0.551796:0.297575:0.551796:0.297575:0.535298:0.294820:0.535298:0.000000
 :@0.301408:0.552931:0.305137:0.552931:0.305137:0.537670:0.301408:0.537670:0.000000
iv):@0.153336:0.577261:0.170503:0.577261:0.170503:0.562000:0.153336:0.562000:0.000000:0.000000:0.000000
( ) ( ) ( ):@0.183600:0.582104:0.360438:0.582104:0.360438:0.556218:0.183600:0.556218:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
≤:@0.227852:0.578021:0.238345:0.578021:0.238345:0.561740:0.227852:0.561740:0.000000
+:@0.296412:0.578021:0.306905:0.578021:0.306905:0.561740:0.296412:0.561740:0.000000
dA B:@0.173474:0.577500:0.216919:0.577500:0.216919:0.561032:0.173474:0.561032:0.000000:0.000000:0.000000:0.000000
d AC:@0.241824:0.577500:0.286110:0.577500:0.286110:0.561032:0.241824:0.561032:0.000000:0.000000:0.000000:0.000000
dC B:@0.310021:0.577500:0.352319:0.577500:0.352319:0.561032:0.310021:0.561032:0.000000:0.000000:0.000000:0.000000
,:@0.203998:0.577385:0.206731:0.577385:0.206731:0.560887:0.203998:0.560887:0.000000
,:@0.272348:0.577385:0.275081:0.577385:0.275081:0.560887:0.272348:0.560887:0.000000
,:@0.339398:0.577385:0.342131:0.577385:0.342131:0.560887:0.339398:0.560887:0.000000
 :@0.359985:0.577262:0.363714:0.577262:0.363714:0.562001:0.359985:0.562001:0.000000
  :@0.361497:0.577064:0.365279:0.577064:0.365279:0.562001:0.361497:0.562001:0.000000:0.000000
(desigualdad triangular).:@0.153337:0.598253:0.309802:0.598253:0.309802:0.583190:0.153337:0.583190:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El espacio  , provisto de la :@0.153337:0.619441:0.335154:0.619440:0.335154:0.604377:0.153337:0.604378:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.220512:0.618557:0.233212:0.618557:0.233212:0.606279:0.220512:0.606279:0.000000
2:@0.233218:0.613640:0.237740:0.613640:0.237740:0.604858:0.233218:0.604858:0.000000
métrica o distancia  , se llama :@0.153344:0.635282:0.350245:0.635282:0.350245:0.620219:0.153344:0.620219:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.280008:0.635388:0.288381:0.635388:0.288381:0.620351:0.280008:0.620351:0.000000
espacio métrico y se escribe :@0.153344:0.651124:0.337525:0.651124:0.337525:0.636061:0.153344:0.636061:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d d:@0.188891:0.670546:0.200435:0.670685:0.200435:0.654216:0.188891:0.654077:0.000000:0.000000:0.000000
( (:@0.155909:0.670430:0.164235:0.670570:0.164235:0.654072:0.155909:0.653932:0.000000:0.000000:0.000000
, ) , ):@0.184652:0.670430:0.206326:0.670570:0.206326:0.654072:0.184652:0.653932:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2 2:@0.176588:0.662394:0.183879:0.662534:0.183879:0.652985:0.176588:0.652845:0.000000:0.000000:0.000000
,      . :@0.181836:0.670109:0.213340:0.670109:0.213340:0.655046:0.181836:0.655046:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000