109:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000
Pensamiento espacial, métrico y variacional:@0.538113:0.043660:0.926913:0.043660:0.926913:0.024915:0.538113:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Evaluación formativa:@0.131433:0.098522:0.446328:0.098522:0.446328:0.067281:0.131433:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.  Verifica la siguiente demostración.:@0.073089:0.136699:0.360041:0.136699:0.360041:0.120194:0.073089:0.120194:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.073089:0.171045:0.077080:0.171045:0.077080:0.155488:0.073089:0.155488:0.000000
Probemos que   ·  ( , 1)    ( ,  ). Esto equivale a probar que se verifican las dos inclusiones siguientes::@0.103215:0.171045:0.831640:0.171045:0.831640:0.155488:0.103215:0.155488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r C:@0.212506:0.171045:0.238385:0.171045:0.238385:0.155763:0.212506:0.155763:0.000000:0.000000:0.000000
5:@0.274980:0.170496:0.290162:0.170496:0.290162:0.156916:0.274980:0.156916:0.000000
C:@0.293989:0.171045:0.303794:0.171045:0.303794:0.155763:0.293989:0.155763:0.000000
r:@0.322797:0.171045:0.328028:0.171045:0.328028:0.155763:0.322797:0.155763:0.000000
r C:@0.103215:0.205390:0.129097:0.205390:0.129097:0.190108:0.103215:0.190108:0.000000:0.000000:0.000000
 ·  ( , 1)    ( ,  ), y  ( ,  )     ·  ( , 1). :@0.108375:0.205390:0.369391:0.205390:0.369391:0.189833:0.108375:0.189833:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,:@0.165592:0.205253:0.180774:0.205253:0.180774:0.191344:0.165592:0.191344:0.000000
C:@0.184601:0.205390:0.194406:0.205390:0.194406:0.190108:0.184601:0.190108:0.000000
r:@0.213421:0.205390:0.218652:0.205390:0.218652:0.190108:0.213421:0.190108:0.000000
C:@0.242180:0.205390:0.251985:0.205390:0.251985:0.190108:0.242180:0.190108:0.000000
r:@0.270925:0.205390:0.276156:0.205390:0.276156:0.190108:0.270925:0.190108:0.000000
,:@0.284740:0.205253:0.299921:0.205253:0.299921:0.191344:0.284740:0.191344:0.000000
r C:@0.303749:0.205390:0.329628:0.205390:0.329628:0.190108:0.303749:0.190108:0.000000:0.000000:0.000000
 :@0.073089:0.239737:0.077080:0.239737:0.077080:0.224180:0.073089:0.224180:0.000000
Comencemos con la inclusión:@0.103215:0.239737:0.320231:0.239737:0.320231:0.224180:0.103215:0.224180:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r C:@0.103215:0.274083:0.129097:0.274083:0.129097:0.258801:0.103215:0.258801:0.000000:0.000000:0.000000
 ·  ( , 1)    ( ,  ). Sea     ( ,  )     ·  ( , 1).:@0.108375:0.274083:0.415786:0.274083:0.415786:0.258526:0.108375:0.258526:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,:@0.165666:0.273946:0.180848:0.273946:0.180848:0.260036:0.165666:0.260036:0.000000
C:@0.184675:0.274083:0.194480:0.274083:0.194480:0.258801:0.184675:0.258801:0.000000
r:@0.213572:0.274083:0.218802:0.274083:0.218802:0.258801:0.213572:0.258801:0.000000
5:@0.271749:0.273534:0.286930:0.273534:0.286930:0.259954:0.271749:0.259954:0.000000
x y:@0.295496:0.274083:0.322170:0.274083:0.322170:0.258801:0.295496:0.258801:0.000000:0.000000:0.000000
1:@0.302633:0.277223:0.307818:0.277223:0.307818:0.268153:0.302633:0.268153:0.000000
1:@0.321925:0.277223:0.327110:0.277223:0.327110:0.268153:0.321925:0.268153:0.000000
[:@0.335726:0.273796:0.350217:0.273796:0.350217:0.260519:0.335726:0.260519:0.000000
r C:@0.354049:0.274083:0.379928:0.274083:0.379928:0.258801:0.354049:0.258801:0.000000:0.000000:0.000000
 :@0.073089:0.308428:0.077080:0.308428:0.077080:0.292871:0.073089:0.292871:0.000000
Por la definición del conjunto   ·  ( , 1), existe:@0.103215:0.308428:0.424511:0.308428:0.424511:0.292871:0.103215:0.292871:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r C:@0.317668:0.308428:0.343548:0.308428:0.343548:0.293146:0.317668:0.293146:0.000000:0.000000:0.000000
 :@0.073089:0.342775:0.076369:0.342775:0.076369:0.327492:0.073089:0.327492:0.000000
   ( ,  )    ( , 1), tal que        .:@0.110376:0.342775:0.355038:0.342775:0.355038:0.327218:0.110376:0.327218:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.114287:0.342226:0.129469:0.342226:0.129469:0.328646:0.114287:0.328646:0.000000
x y:@0.138034:0.342775:0.164709:0.342775:0.164709:0.327492:0.138034:0.327492:0.000000:0.000000:0.000000
2:@0.145172:0.345915:0.150357:0.345915:0.150357:0.336845:0.145172:0.336845:0.000000
2:@0.164465:0.345915:0.169650:0.345915:0.169650:0.336845:0.164465:0.336845:0.000000
[:@0.178265:0.342488:0.192756:0.342488:0.192756:0.329211:0.178265:0.329211:0.000000
C:@0.196588:0.342775:0.206393:0.342775:0.206393:0.327492:0.196588:0.327492:0.000000
5:@0.311485:0.342226:0.326667:0.342226:0.326667:0.328646:0.311485:0.328646:0.000000
r:@0.330494:0.342775:0.335724:0.342775:0.335724:0.327492:0.330494:0.327492:0.000000
1:@0.346728:0.345915:0.351913:0.345915:0.351913:0.336845:0.346728:0.336845:0.000000
 :@0.073089:0.377120:0.077080:0.377120:0.077080:0.361563:0.073089:0.361563:0.000000
Esto es, ( ,  )    ( ,  ).:@0.103215:0.377120:0.272975:0.377120:0.272975:0.361563:0.103215:0.361563:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.164341:0.377120:0.191010:0.377120:0.191010:0.361838:0.164341:0.361838:0.000000:0.000000:0.000000
1:@0.171473:0.380261:0.176658:0.380261:0.176658:0.371192:0.171473:0.371192:0.000000
1:@0.190767:0.380261:0.195952:0.380261:0.195952:0.371192:0.190767:0.371192:0.000000
5:@0.204561:0.376571:0.219743:0.376571:0.219743:0.362991:0.204561:0.362991:0.000000
r x y:@0.223570:0.377120:0.260152:0.377120:0.260152:0.361838:0.223570:0.361838:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.240615:0.380261:0.245801:0.380261:0.245801:0.371192:0.240615:0.371192:0.000000
2:@0.259908:0.380261:0.265093:0.380261:0.265093:0.371192:0.259908:0.371192:0.000000
 :@0.073089:0.411467:0.077080:0.411467:0.077080:0.395909:0.073089:0.395909:0.000000
Considerando la definición del producto de números reales por vectores y la de igualdad de elementos de  , se tienen :@0.103215:0.411467:0.930970:0.411467:0.930970:0.395909:0.103215:0.395909:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.839407:0.410615:0.852565:0.410615:0.852565:0.397845:0.839407:0.397845:0.000000
2:@0.852248:0.405462:0.857433:0.405462:0.857433:0.396393:0.852248:0.396393:0.000000
las siguientes igualdades: :@0.103216:0.427944:0.283965:0.427944:0.283965:0.412387:0.103216:0.412387:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  )    ( ,  ) :@0.103215:0.481864:0.217415:0.481864:0.217415:0.466307:0.103215:0.466307:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.107959:0.481864:0.134629:0.481864:0.134629:0.466582:0.107959:0.466582:0.000000:0.000000:0.000000
1:@0.115093:0.485005:0.120278:0.485005:0.120278:0.475936:0.115093:0.475936:0.000000
1:@0.134386:0.485005:0.139571:0.485005:0.139571:0.475936:0.134386:0.475936:0.000000
5:@0.148181:0.481315:0.163363:0.481315:0.163363:0.467735:0.148181:0.467735:0.000000
r x y:@0.167190:0.481864:0.203771:0.481864:0.203771:0.466582:0.167190:0.466582:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.184236:0.485005:0.189421:0.485005:0.189421:0.475936:0.184236:0.475936:0.000000
2:@0.203528:0.485005:0.208713:0.485005:0.208713:0.475936:0.203528:0.475936:0.000000
 :@0.232930:0.481864:0.236793:0.481864:0.236793:0.465360:0.232930:0.465360:0.000000
x:@0.250408:0.475513:0.258202:0.475513:0.258202:0.459376:0.250408:0.459376:0.000000
1:@0.258009:0.478829:0.263484:0.478829:0.263484:0.469252:0.258009:0.469252:0.000000
    ,:@0.263484:0.475513:0.310314:0.475513:0.310314:0.459086:0.263484:0.459086:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.267698:0.474933:0.283729:0.474933:0.283729:0.460594:0.267698:0.460594:0.000000
rx:@0.287943:0.475513:0.301491:0.475513:0.301491:0.459376:0.287943:0.459376:0.000000:0.000000
2:@0.301490:0.478829:0.306965:0.478829:0.306965:0.469252:0.301490:0.469252:0.000000
y:@0.250407:0.492911:0.258220:0.492911:0.258220:0.476774:0.250407:0.476774:0.000000
1:@0.258029:0.496227:0.263504:0.496227:0.263504:0.486650:0.258029:0.486650:0.000000
    ,:@0.263502:0.492911:0.310486:0.492911:0.310486:0.476484:0.263502:0.476484:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.267717:0.492331:0.283747:0.492331:0.283747:0.477992:0.267717:0.477992:0.000000
ry:@0.287961:0.492911:0.301663:0.492911:0.301663:0.476774:0.287961:0.476774:0.000000:0.000000
2:@0.301662:0.496227:0.307137:0.496227:0.307137:0.486650:0.301662:0.486650:0.000000
x:@0.347357:0.467944:0.355151:0.467944:0.355151:0.451808:0.347357:0.451808:0.000000
2:@0.354950:0.471264:0.360425:0.471264:0.360425:0.461687:0.354950:0.461687:0.000000
        :@0.360425:0.467948:0.405956:0.467948:0.405956:0.451521:0.360425:0.451521:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.364639:0.467368:0.380670:0.467368:0.380670:0.453029:0.364639:0.453029:0.000000
y:@0.347358:0.496061:0.355171:0.496061:0.355171:0.479924:0.347358:0.479924:0.000000
2:@0.354970:0.499384:0.360445:0.499384:0.360445:0.489807:0.354970:0.489807:0.000000
        .:@0.360443:0.496068:0.409323:0.496068:0.409323:0.479641:0.360443:0.479641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.364658:0.495488:0.380688:0.495488:0.380688:0.481149:0.364658:0.481149:0.000000
x:@0.383807:0.463417:0.391601:0.463417:0.391601:0.447280:0.383807:0.447280:0.000000
1:@0.391600:0.465472:0.397075:0.465472:0.397075:0.455895:0.391600:0.455895:0.000000
r:@0.387679:0.479807:0.393202:0.479807:0.393202:0.463670:0.387679:0.463670:0.000000
x:@0.383807:0.491491:0.391601:0.491491:0.391601:0.475354:0.383807:0.475354:0.000000
1:@0.391600:0.493546:0.397075:0.493546:0.397075:0.483970:0.391600:0.483970:0.000000
r:@0.387679:0.507881:0.393202:0.507881:0.393202:0.491744:0.387679:0.491744:0.000000
 :@0.073089:0.541226:0.077080:0.541226:0.077080:0.525669:0.073089:0.525669:0.000000
Puesto que     ( ,  )    ( , 1), por la definición del conjunto  ( , 1) se tiene:@0.103215:0.541226:0.649163:0.541226:0.649163:0.525669:0.103215:0.525669:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.199139:0.540677:0.214320:0.540677:0.214320:0.527097:0.199139:0.527097:0.000000
x y:@0.222886:0.541226:0.249561:0.541226:0.249561:0.525944:0.222886:0.525944:0.000000:0.000000:0.000000
2:@0.230025:0.544368:0.235210:0.544368:0.235210:0.535298:0.230025:0.535298:0.000000
2:@0.249317:0.544368:0.254502:0.544368:0.254502:0.535298:0.249317:0.535298:0.000000
[:@0.263117:0.540939:0.277609:0.540939:0.277609:0.527662:0.263117:0.527662:0.000000
C:@0.281440:0.541226:0.291245:0.541226:0.291245:0.525944:0.281440:0.525944:0.000000
C:@0.546745:0.541226:0.556550:0.541226:0.556550:0.525944:0.546745:0.525944:0.000000
x:@0.103215:0.584939:0.110596:0.584939:0.110596:0.569656:0.103215:0.569656:0.000000
2:@0.110343:0.588080:0.115528:0.588080:0.115528:0.579010:0.110343:0.579010:0.000000
2:@0.115486:0.578938:0.120671:0.578938:0.120671:0.569868:0.115486:0.569868:0.000000
       1 y, en consecuencia, :@0.120514:0.584939:0.339202:0.584939:0.339202:0.569382:0.120514:0.569382:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.124432:0.584389:0.139614:0.584389:0.139614:0.570810:0.124432:0.570810:0.000000
y:@0.143441:0.584939:0.150840:0.584939:0.150840:0.569656:0.143441:0.569656:0.000000
2:@0.150579:0.588080:0.155764:0.588080:0.155764:0.579010:0.150579:0.579010:0.000000
2:@0.155722:0.578938:0.160907:0.578938:0.160907:0.569868:0.155722:0.569868:0.000000
5:@0.164668:0.584389:0.179850:0.584389:0.179850:0.570810:0.164668:0.570810:0.000000
x:@0.347053:0.579123:0.354508:0.579123:0.354508:0.563688:0.347053:0.563688:0.000000
₁:@0.354508:0.579123:0.358373:0.579123:0.358373:0.563411:0.354508:0.563411:0.000000
r:@0.348917:0.591642:0.354200:0.591642:0.354200:0.576207:0.348917:0.576207:0.000000
1:@0.379662:0.586182:0.394995:0.586182:0.394995:0.572466:0.379662:0.572466:0.000000
5:@0.435142:0.586182:0.450475:0.586182:0.450475:0.572466:0.435142:0.572466:0.000000
( ) ( ):@0.339698:0.592923:0.424971:0.592923:0.424971:0.562446:0.339698:0.562446:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
₂:@0.367144:0.575112:0.372408:0.575112:0.372408:0.559399:0.367144:0.559399:0.000000
y:@0.405173:0.579119:0.412646:0.579119:0.412646:0.563684:0.405173:0.563684:0.000000
₁:@0.412646:0.579119:0.416512:0.579119:0.416512:0.563407:0.412646:0.563407:0.000000
r:@0.407040:0.591642:0.412323:0.591642:0.412323:0.576207:0.407040:0.576207:0.000000
₂:@0.425269:0.575112:0.430533:0.575112:0.430533:0.559399:0.425269:0.559399:0.000000
1,:@0.459310:0.584833:0.471496:0.584833:0.471496:0.569120:0.459310:0.569120:0.000000:0.000000
 :@0.474287:0.584939:0.478279:0.584939:0.478279:0.569382:0.474287:0.569382:0.000000
 :@0.073089:0.626432:0.077080:0.626432:0.077080:0.610875:0.073089:0.610875:0.000000
de donde          , o sea,     ( ,  )    ( ,  ).:@0.103215:0.626432:0.455423:0.626432:0.455423:0.610875:0.103215:0.610875:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.177360:0.626432:0.184741:0.626432:0.184741:0.611150:0.177360:0.611150:0.000000
1:@0.184493:0.629574:0.189679:0.629574:0.189679:0.620504:0.184493:0.620504:0.000000
2:@0.189636:0.620432:0.194821:0.620432:0.194821:0.611362:0.189636:0.611362:0.000000
1:@0.198583:0.625883:0.213764:0.625883:0.213764:0.612303:0.198583:0.612303:0.000000
y:@0.217591:0.626432:0.224991:0.626432:0.224991:0.611150:0.217591:0.611150:0.000000
1:@0.224728:0.629574:0.229913:0.629574:0.229913:0.620504:0.224728:0.620504:0.000000
2:@0.229871:0.620432:0.235056:0.620432:0.235056:0.611362:0.229871:0.611362:0.000000
5:@0.238818:0.625883:0.253999:0.625883:0.253999:0.612303:0.238818:0.612303:0.000000
r:@0.257826:0.626432:0.263057:0.626432:0.263057:0.611150:0.257826:0.611150:0.000000
2:@0.262977:0.620428:0.268162:0.620428:0.268162:0.611358:0.262977:0.611358:0.000000
5:@0.331141:0.625883:0.346322:0.625883:0.346322:0.612303:0.331141:0.612303:0.000000
x y:@0.354888:0.626432:0.381563:0.626432:0.381563:0.611150:0.354888:0.611150:0.000000:0.000000:0.000000
1:@0.362026:0.629574:0.367211:0.629574:0.367211:0.620504:0.362026:0.620504:0.000000
1:@0.381319:0.629574:0.386504:0.629574:0.386504:0.620504:0.381319:0.620504:0.000000
[:@0.395119:0.626145:0.409611:0.626145:0.409611:0.612868:0.395119:0.612868:0.000000
C:@0.413442:0.626432:0.423247:0.626432:0.423247:0.611150:0.413442:0.611150:0.000000
r:@0.442337:0.626432:0.447568:0.626432:0.447568:0.611150:0.442337:0.611150:0.000000
Así,      ·  ( , 1)        ( , 1). Es decir, :@0.103215:0.660778:0.384163:0.660778:0.384163:0.645221:0.103215:0.645221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.143022:0.660490:0.157513:0.660490:0.157513:0.647213:0.143022:0.647213:0.000000
r C:@0.161345:0.660778:0.187224:0.660778:0.187224:0.645495:0.161345:0.645495:0.000000:0.000000:0.000000
[:@0.255234:0.660490:0.269726:0.660490:0.269726:0.647213:0.255234:0.647213:0.000000
C:@0.273557:0.660778:0.283362:0.660778:0.283362:0.645495:0.273557:0.645495:0.000000
r C:@0.103215:0.695124:0.131994:0.695124:0.131994:0.679842:0.103215:0.679842:0.000000:0.000000:0.000000
    ( , 1)    ( ,  ).:@0.108375:0.695124:0.229542:0.695124:0.229542:0.679567:0.108375:0.679567:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
?:@0.112293:0.694575:0.118362:0.694575:0.118362:0.680995:0.112293:0.680995:0.000000
,:@0.168553:0.694987:0.183734:0.694987:0.183734:0.681077:0.168553:0.681077:0.000000
C:@0.187561:0.695124:0.197366:0.695124:0.197366:0.679842:0.187561:0.679842:0.000000
r:@0.216457:0.695124:0.221687:0.695124:0.221687:0.679842:0.216457:0.679842:0.000000
 :@0.073089:0.729469:0.077080:0.729469:0.077080:0.713912:0.073089:0.713912:0.000000
Probemos que  ( ,  )        ( , 1).:@0.103215:0.729469:0.338868:0.729469:0.338868:0.713912:0.103215:0.713912:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.212506:0.729469:0.222311:0.729469:0.222311:0.714187:0.212506:0.714187:0.000000
r:@0.241409:0.729469:0.246639:0.729469:0.246639:0.714187:0.241409:0.714187:0.000000
,:@0.255223:0.729332:0.270405:0.729332:0.270405:0.715423:0.255223:0.715423:0.000000
r C:@0.274232:0.729469:0.303009:0.729469:0.303009:0.714187:0.274232:0.714187:0.000000:0.000000:0.000000
?:@0.283308:0.728920:0.289377:0.728920:0.289377:0.715340:0.283308:0.715340:0.000000
Sea    ( ,  )    ( ,  ), por lo que   satisface la ecuación cartesiana de la circunferencia:@0.103215:0.763816:0.720639:0.763816:0.720639:0.748259:0.103215:0.748259:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.143621:0.763267:0.158802:0.763267:0.158802:0.749687:0.143621:0.749687:0.000000
a b:@0.167368:0.763816:0.192446:0.763816:0.192446:0.748533:0.167368:0.748533:0.000000:0.000000:0.000000
[:@0.200874:0.763529:0.215366:0.763529:0.215366:0.750252:0.200874:0.750252:0.000000
C:@0.219197:0.763816:0.229002:0.763816:0.229002:0.748533:0.219197:0.748533:0.000000
r:@0.248092:0.763816:0.253323:0.763816:0.253323:0.748533:0.248092:0.748533:0.000000
a:@0.103215:0.800042:0.112382:0.800042:0.112382:0.784760:0.103215:0.784760:0.000000
2:@0.112311:0.794038:0.117496:0.794038:0.117496:0.784968:0.112311:0.784968:0.000000
        . Se definen      ,      .:@0.117450:0.800042:0.368257:0.800042:0.368257:0.784485:0.117450:0.784485:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.121368:0.799493:0.136550:0.799493:0.136550:0.785913:0.121368:0.785913:0.000000
b:@0.140377:0.800042:0.149544:0.800042:0.149544:0.784760:0.140377:0.784760:0.000000
2:@0.149464:0.794038:0.154650:0.794038:0.154650:0.784968:0.149464:0.784968:0.000000
5:@0.158522:0.799493:0.173703:0.799493:0.173703:0.785913:0.158522:0.785913:0.000000
r:@0.177530:0.800042:0.182761:0.800042:0.182761:0.784760:0.177530:0.784760:0.000000
2:@0.182681:0.794038:0.187866:0.794038:0.187866:0.784968:0.182681:0.784968:0.000000
x:@0.275027:0.800042:0.282408:0.800042:0.282408:0.784760:0.275027:0.784760:0.000000
5:@0.286253:0.799493:0.301435:0.799493:0.301435:0.785913:0.286253:0.785913:0.000000
a:@0.306646:0.794764:0.315904:0.794764:0.315904:0.779328:0.306646:0.779328:0.000000
r:@0.307347:0.806854:0.312630:0.806854:0.312630:0.791419:0.307347:0.791419:0.000000
y:@0.323548:0.800042:0.330948:0.800042:0.330948:0.784760:0.323548:0.784760:0.000000
5:@0.334793:0.799493:0.349975:0.799493:0.349975:0.785913:0.334793:0.785913:0.000000
b:@0.355186:0.795446:0.364444:0.795446:0.364444:0.780010:0.355186:0.780010:0.000000
r:@0.355885:0.807536:0.361168:0.807536:0.361168:0.792101:0.355885:0.792101:0.000000
Entonces,     ,      . Reemplazando en la ecuación precedente, se obtiene:@0.103215:0.834387:0.665700:0.834387:0.665700:0.818830:0.103215:0.818830:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.176388:0.834387:0.185555:0.834387:0.185555:0.819105:0.176388:0.819105:0.000000
5:@0.189400:0.833838:0.204582:0.833838:0.204582:0.820258:0.189400:0.820258:0.000000
rx b:@0.208409:0.834387:0.237277:0.834387:0.237277:0.819105:0.208409:0.819105:0.000000:0.000000:0.000000:0.000000
5:@0.241123:0.833838:0.256304:0.833838:0.256304:0.820258:0.241123:0.820258:0.000000
ry:@0.260131:0.834387:0.273035:0.834387:0.273035:0.819105:0.260131:0.819105:0.000000:0.000000
( )    ( )         (     )    , y como     0, la aplicación de la ley cancelativa da lugar a la ecuación cartesiana :@0.103215:0.868734:0.931359:0.868734:0.931359:0.853177:0.103215:0.853177:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rx:@0.107960:0.868734:0.120717:0.868734:0.120717:0.853451:0.107960:0.853451:0.000000:0.000000
2:@0.125409:0.862730:0.130594:0.862730:0.130594:0.853660:0.125409:0.853660:0.000000
1:@0.134648:0.868184:0.149829:0.868184:0.149829:0.854605:0.134648:0.854605:0.000000
ry:@0.158577:0.868734:0.171480:0.868734:0.171480:0.853451:0.158577:0.853451:0.000000:0.000000
2:@0.176173:0.862730:0.181358:0.862730:0.181358:0.853660:0.176173:0.853660:0.000000
5:@0.185411:0.868184:0.200593:0.868184:0.200593:0.854605:0.185411:0.854605:0.000000
r:@0.204602:0.868734:0.209833:0.868734:0.209833:0.853451:0.204602:0.853451:0.000000
2:@0.209757:0.862730:0.214942:0.862730:0.214942:0.853660:0.209757:0.853660:0.000000
r x:@0.238688:0.868734:0.263517:0.868734:0.263517:0.853451:0.238688:0.853451:0.000000:0.000000:0.000000
2 :@0.243852:0.862730:0.251321:0.862730:0.251321:0.853660:0.243852:0.853660:0.000000:0.000000
2:@0.263261:0.862730:0.268447:0.862730:0.268447:0.853660:0.263261:0.853660:0.000000
1:@0.272394:0.868184:0.287575:0.868184:0.287575:0.854605:0.272394:0.854605:0.000000
y:@0.291585:0.868734:0.298984:0.868734:0.298984:0.853451:0.291585:0.853451:0.000000
2:@0.298727:0.862730:0.303912:0.862730:0.303912:0.853660:0.298727:0.853660:0.000000
5:@0.312598:0.868184:0.327780:0.868184:0.327780:0.854605:0.312598:0.854605:0.000000
r:@0.331789:0.868734:0.337020:0.868734:0.337020:0.853451:0.331789:0.853451:0.000000
2:@0.336954:0.862730:0.342139:0.862730:0.342139:0.853660:0.336954:0.853660:0.000000
r:@0.407539:0.868734:0.412770:0.868734:0.412770:0.853451:0.407539:0.853451:0.000000
.:@0.416797:0.868184:0.431979:0.868184:0.431979:0.854605:0.416797:0.854605:0.000000
de la circunferencia :@0.103218:0.885211:0.246703:0.885211:0.246703:0.869654:0.103218:0.869654:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000