224:@0.054582:0.966558:0.078778:0.966558:0.078778:0.950778:0.054582:0.950778:0.000000:0.000000:0.000000
A + B:@0.333345:0.151031:0.358992:0.151031:0.358992:0.140324:0.333345:0.140324:0.000000:0.000000:0.000000:0.000000:0.000000
A – B:@0.218313:0.249658:0.243411:0.249658:0.243411:0.238950:0.218313:0.238950:0.000000:0.000000:0.000000:0.000000:0.000000
A – B:@0.249449:0.168788:0.274547:0.168788:0.274547:0.158080:0.249449:0.158080:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.272207:0.150642:0.279501:0.150642:0.279501:0.139934:0.272207:0.139934:0.000000
B:@0.317985:0.187401:0.323932:0.187401:0.323932:0.176694:0.317985:0.176694:0.000000
–B:@0.285415:0.261280:0.297855:0.261499:0.298187:0.250794:0.285747:0.250575:0.000000:0.000000
–B:@0.163212:0.253821:0.175651:0.254040:0.175983:0.243336:0.163543:0.243116:0.000000:0.000000
B:@0.213921:0.164696:0.219868:0.164696:0.219868:0.153988:0.213921:0.153988:0.000000
A:@0.252464:0.203462:0.259758:0.203462:0.259758:0.192754:0.252464:0.192754:0.000000
0:@0.203540:0.222086:0.208764:0.222086:0.208764:0.211378:0.203540:0.211378:0.000000
x:@0.351236:0.218560:0.356073:0.218560:0.356073:0.207852:0.351236:0.207852:0.000000
y:@0.191883:0.135520:0.196857:0.135520:0.196857:0.124813:0.191883:0.124813:0.000000
p:@0.298088:0.314611:0.309568:0.314611:0.309568:0.304586:0.298088:0.304586:0.000000
 :@0.309568:0.315319:0.312450:0.315319:0.312450:0.303842:0.309568:0.303842:0.000000
Figura 5.12.:@0.312450:0.315319:0.366929:0.315319:0.366929:0.303842:0.312450:0.303842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.404235:0.110490:0.442033:0.110490:0.442033:0.093992:0.404235:0.093992:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.444226:0.111679:0.469810:0.111679:0.469810:0.095211:0.444226:0.095211:0.000000:0.000000
AB:@0.449890:0.136664:0.485665:0.136664:0.485665:0.120195:0.449890:0.120195:0.000000:0.000000
AB:@0.520978:0.136664:0.556753:0.136664:0.556753:0.120195:0.520978:0.120195:0.000000:0.000000
A:@0.609983:0.136664:0.621253:0.136664:0.621253:0.120195:0.609983:0.120195:0.000000
B:@0.655313:0.136664:0.664503:0.136664:0.664503:0.120195:0.655313:0.120195:0.000000
AB:@0.449909:0.168531:0.485684:0.168531:0.485684:0.152063:0.449909:0.152063:0.000000:0.000000
AB:@0.521980:0.168531:0.557755:0.168531:0.557755:0.152063:0.521980:0.152063:0.000000:0.000000
AB:@0.577328:0.168531:0.613104:0.168531:0.613104:0.152063:0.577328:0.152063:0.000000:0.000000
AA:@0.457692:0.192605:0.488651:0.192605:0.488651:0.176137:0.457692:0.176137:0.000000:0.000000
AB:@0.519109:0.192605:0.546832:0.192605:0.546832:0.176137:0.519109:0.176137:0.000000:0.000000
BB:@0.567734:0.192605:0.593472:0.192605:0.593472:0.176137:0.567734:0.176137:0.000000:0.000000
A:@0.463356:0.216462:0.474626:0.216462:0.474626:0.199994:0.463356:0.199994:0.000000
A B:@0.518165:0.216462:0.545888:0.216462:0.545888:0.199994:0.518165:0.199994:0.000000:0.000000:0.000000
B:@0.572454:0.216462:0.581644:0.216462:0.581644:0.199994:0.572454:0.199994:0.000000
AB:@0.449909:0.244426:0.485684:0.244426:0.485684:0.227957:0.449909:0.227957:0.000000:0.000000
AB:@0.521980:0.244426:0.557755:0.244426:0.557755:0.227957:0.521980:0.227957:0.000000:0.000000
AB:@0.577328:0.244426:0.613104:0.244426:0.613104:0.227957:0.577328:0.227957:0.000000:0.000000
A:@0.463356:0.272404:0.474626:0.272404:0.474626:0.255935:0.463356:0.255935:0.000000
A B:@0.518165:0.272404:0.545888:0.272404:0.545888:0.255935:0.518165:0.255935:0.000000:0.000000:0.000000
B:@0.572454:0.272404:0.581644:0.272404:0.581644:0.255935:0.572454:0.255935:0.000000
AB:@0.449909:0.301524:0.485684:0.301524:0.485684:0.285055:0.449909:0.285055:0.000000:0.000000
AB:@0.520997:0.301524:0.556772:0.301524:0.556772:0.285055:0.520997:0.285055:0.000000:0.000000
A:@0.610002:0.301524:0.621272:0.301524:0.621272:0.285055:0.610002:0.285055:0.000000
B:@0.655333:0.301524:0.664522:0.301524:0.664522:0.285055:0.655333:0.285055:0.000000
,:@0.456555:0.111563:0.459310:0.111563:0.459310:0.095066:0.456555:0.095066:0.000000
=2:@0.572917:0.136548:0.594860:0.136548:0.594860:0.120051:0.572917:0.120051:0.000000:0.000000
.:@0.686041:0.136548:0.688796:0.136548:0.688796:0.120051:0.686041:0.120051:0.000000
=(:@0.501828:0.168416:0.521228:0.168416:0.521228:0.151918:0.501828:0.151918:0.000000:0.000000
)(:@0.557312:0.168416:0.576558:0.168416:0.576558:0.151918:0.557312:0.151918:0.000000:0.000000
):@0.612660:0.168416:0.618613:0.168416:0.618613:0.151918:0.612660:0.151918:0.000000
=:@0.443089:0.192490:0.453897:0.192490:0.453897:0.175992:0.443089:0.175992:0.000000
2(:@0.503967:0.192490:0.518358:0.192490:0.518358:0.175992:0.503967:0.175992:0.000000:0.000000
):@0.546389:0.192490:0.552341:0.192490:0.552341:0.175992:0.546389:0.175992:0.000000
=:@0.443089:0.216347:0.453897:0.216347:0.453897:0.199849:0.443089:0.199849:0.000000
2(:@0.503023:0.216347:0.517395:0.216347:0.517395:0.199849:0.503023:0.199849:0.000000:0.000000
):@0.545425:0.216347:0.551378:0.216347:0.551378:0.199849:0.545425:0.199849:0.000000
,:@0.592182:0.216347:0.594937:0.216347:0.594937:0.199849:0.592182:0.199849:0.000000
=(:@0.501828:0.244310:0.521228:0.244310:0.521228:0.227813:0.501828:0.227813:0.000000:0.000000
)(:@0.557312:0.244310:0.576558:0.244310:0.576558:0.227813:0.557312:0.227813:0.000000:0.000000
):@0.612660:0.244310:0.618613:0.244310:0.618613:0.227813:0.612660:0.227813:0.000000
=:@0.443089:0.272288:0.453897:0.272288:0.453897:0.255790:0.443089:0.255790:0.000000
2(:@0.503023:0.272288:0.517395:0.272288:0.517395:0.255790:0.503023:0.255790:0.000000:0.000000
):@0.545425:0.272288:0.551378:0.272288:0.551378:0.255790:0.545425:0.255790:0.000000
,:@0.592182:0.272288:0.594937:0.272288:0.594937:0.255790:0.592182:0.255790:0.000000
=2:@0.572897:0.301408:0.594840:0.301408:0.594840:0.284910:0.572897:0.284910:0.000000:0.000000
.:@0.686022:0.301408:0.688777:0.301408:0.688777:0.284910:0.686022:0.284910:0.000000
2:@0.501445:0.103638:0.506617:0.103638:0.506617:0.093596:0.501445:0.093596:0.000000
2:@0.493490:0.288725:0.498661:0.288725:0.498661:0.278683:0.493490:0.278683:0.000000
2:@0.564753:0.288725:0.569924:0.288725:0.569924:0.278683:0.564753:0.278683:0.000000
2:@0.493314:0.123863:0.498485:0.123863:0.498485:0.113821:0.493314:0.113821:0.000000
2:@0.568083:0.123863:0.573254:0.123863:0.573254:0.113821:0.568083:0.113821:0.000000
2:@0.628815:0.123753:0.633733:0.123753:0.633733:0.114204:0.628815:0.114204:0.000000
2:@0.672158:0.123753:0.677076:0.123753:0.677076:0.114204:0.672158:0.114204:0.000000
2:@0.493319:0.155728:0.498490:0.155728:0.498490:0.145686:0.493319:0.145686:0.000000
2:@0.482178:0.203659:0.487350:0.203659:0.487350:0.193617:0.482178:0.193617:0.000000
2:@0.594825:0.203659:0.599996:0.203659:0.599996:0.193617:0.594825:0.193617:0.000000
2:@0.493319:0.231638:0.498490:0.231638:0.498490:0.221596:0.493319:0.221596:0.000000
2:@0.482178:0.261869:0.487350:0.261869:0.487350:0.251827:0.482178:0.251827:0.000000
2:@0.589841:0.261869:0.595012:0.261869:0.595012:0.251827:0.589841:0.251827:0.000000
2:@0.628809:0.288722:0.633980:0.288722:0.633980:0.278680:0.628809:0.278680:0.000000
2:@0.674390:0.288722:0.679562:0.288722:0.679562:0.278680:0.674390:0.278680:0.000000
R:@0.486735:0.114643:0.500644:0.114643:0.500644:0.093302:0.486735:0.093302:0.000000
∈:@0.472876:0.112200:0.486612:0.112200:0.486612:0.095919:0.472876:0.095919:0.000000
+:@0.463378:0.137184:0.473955:0.137184:0.473955:0.120904:0.463378:0.120904:0.000000
+:@0.501080:0.137184:0.511656:0.137184:0.511656:0.120904:0.501080:0.120904:0.000000
−:@0.534466:0.137184:0.545043:0.137184:0.545043:0.120904:0.534466:0.120904:0.000000
+:@0.636552:0.137184:0.647129:0.137184:0.647129:0.120904:0.636552:0.120904:0.000000
+:@0.463378:0.169052:0.473955:0.169052:0.473955:0.152771:0.463378:0.152771:0.000000
+ ⋅:@0.535468:0.169052:0.569567:0.169052:0.569567:0.152771:0.535468:0.152771:0.000000:0.000000:0.000000
+:@0.590817:0.169052:0.601393:0.169052:0.601393:0.152771:0.590817:0.152771:0.000000
⋅+:@0.470352:0.193126:0.501446:0.193126:0.501446:0.176845:0.470352:0.176845:0.000000:0.000000
⋅+ ⋅:@0.531769:0.193126:0.583245:0.193126:0.583245:0.176845:0.531769:0.176845:0.000000:0.000000:0.000000:0.000000
+:@0.489925:0.216983:0.500502:0.216983:0.500502:0.200702:0.489925:0.200702:0.000000
⋅ +:@0.530806:0.216983:0.564269:0.216983:0.564269:0.200702:0.530806:0.200702:0.000000:0.000000:0.000000
−:@0.463397:0.244946:0.473974:0.244946:0.473974:0.228666:0.463397:0.228666:0.000000
− ⋅:@0.535487:0.244946:0.569587:0.244946:0.569587:0.228666:0.535487:0.228666:0.000000:0.000000:0.000000
−:@0.590836:0.244946:0.601412:0.244946:0.601412:0.228666:0.590836:0.228666:0.000000
−:@0.489925:0.272924:0.500502:0.272924:0.500502:0.256643:0.489925:0.256643:0.000000
⋅ +:@0.530806:0.272924:0.564269:0.272924:0.564269:0.256643:0.530806:0.256643:0.000000:0.000000:0.000000
+ ∈:@0.463397:0.302044:0.484049:0.302695:0.484049:0.286414:0.463397:0.285764:0.000000:0.000000:0.000000
+:@0.501099:0.302044:0.511676:0.302044:0.511676:0.285764:0.501099:0.285764:0.000000
−:@0.534486:0.302044:0.545062:0.302044:0.545062:0.285764:0.534486:0.285764:0.000000
+:@0.636571:0.302044:0.647148:0.302044:0.647148:0.285764:0.636571:0.285764:0.000000
. En la figura 5.12. se muestran los vectores  ,   y los :@0.508059:0.110490:0.895905:0.110490:0.895905:0.093992:0.508059:0.093992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B B:@0.819041:0.086642:0.826768:0.086642:0.826768:0.069457:0.819041:0.069457:0.000000:0.000000:0.000000
AB:@0.820287:0.112019:0.853115:0.112019:0.853115:0.094834:0.820287:0.094834:0.000000:0.000000
A A:@0.820287:0.137397:0.830186:0.137397:0.830186:0.120212:0.820287:0.120212:0.000000:0.000000:0.000000
B B:@0.819041:0.162774:0.826768:0.162774:0.826768:0.145589:0.819041:0.145589:0.000000:0.000000:0.000000
A A:@0.820287:0.188151:0.830186:0.188151:0.830186:0.170967:0.820287:0.170967:0.000000:0.000000:0.000000
AB:@0.820287:0.213529:0.853115:0.213529:0.853115:0.196344:0.820287:0.196344:0.000000:0.000000
AB:@0.820287:0.238906:0.858362:0.238906:0.858362:0.221721:0.820287:0.221721:0.000000:0.000000
BB:@0.819041:0.264283:0.846742:0.264283:0.846742:0.247099:0.819041:0.247099:0.000000:0.000000
B B:@0.819041:0.289661:0.826768:0.289661:0.826768:0.272476:0.819041:0.272476:0.000000:0.000000:0.000000
. .:@0.868876:0.086491:0.869889:0.086491:0.869889:0.069276:0.868876:0.069276:0.000000:0.000000:0.000000
.=0:@0.836530:0.111868:0.879209:0.111868:0.879209:0.094653:0.836530:0.094653:0.000000:0.000000:0.000000
, ,:@0.873057:0.137246:0.874071:0.137246:0.874071:0.120031:0.873057:0.120031:0.000000:0.000000:0.000000
=0.:@0.831585:0.162623:0.858221:0.162623:0.858221:0.145408:0.831585:0.145408:0.000000:0.000000:0.000000
.=0,:@0.836510:0.213393:0.883571:0.213393:0.883571:0.196178:0.836510:0.196178:0.000000:0.000000:0.000000:0.000000
= =:@0.834942:0.238770:0.844359:0.238770:0.844359:0.221555:0.834942:0.221555:0.000000:0.000000:0.000000
=0:@0.849697:0.264148:0.872796:0.264148:0.872796:0.246933:0.849697:0.246933:0.000000:0.000000
=0:@0.831585:0.289525:0.854683:0.289525:0.854683:0.272310:0.831585:0.272310:0.000000:0.000000
2 2:@0.861185:0.078140:0.864447:0.078140:0.864447:0.068188:0.861185:0.068188:0.000000:0.000000:0.000000
2 2:@0.864532:0.128905:0.867794:0.128905:0.867794:0.118953:0.864532:0.118953:0.000000:0.000000:0.000000
2 2:@0.864532:0.179670:0.867794:0.179670:0.867794:0.169718:0.864532:0.169718:0.000000:0.000000:0.000000
∈ ∈:@0.831605:0.087185:0.844077:0.087185:0.844077:0.070196:0.831605:0.070196:0.000000:0.000000:0.000000
∈ ∈:@0.834962:0.137955:0.847434:0.137955:0.847434:0.120966:0.834962:0.120966:0.000000:0.000000:0.000000
∈ ∈:@0.834962:0.188725:0.847434:0.188725:0.847434:0.171736:0.834962:0.171736:0.000000:0.000000:0.000000
⋅ ⋅:@0.830620:0.264872:0.833784:0.264872:0.833784:0.247883:0.830620:0.247883:0.000000:0.000000:0.000000
AB:@0.818426:0.112019:0.851254:0.112019:0.851254:0.094834:0.818426:0.094834:0.000000:0.000000
AB:@0.818426:0.213529:0.851254:0.213529:0.851254:0.196344:0.818426:0.196344:0.000000:0.000000
AB:@0.818426:0.238906:0.856501:0.238906:0.856501:0.221721:0.818426:0.221721:0.000000:0.000000
BB:@0.817179:0.264283:0.844881:0.264283:0.844881:0.247099:0.817179:0.247099:0.000000:0.000000
.=:@0.834669:0.111868:0.865527:0.111868:0.865527:0.094653:0.834669:0.094653:0.000000:0.000000
0:@0.868482:0.111868:0.877347:0.111868:0.877347:0.094653:0.868482:0.094653:0.000000
=0:@0.829724:0.162623:0.852822:0.162623:0.852822:0.145408:0.829724:0.145408:0.000000:0.000000
.:@0.853485:0.162623:0.856360:0.162623:0.856360:0.145408:0.853485:0.145408:0.000000
.=:@0.834649:0.213393:0.865507:0.213393:0.865507:0.196178:0.834649:0.196178:0.000000:0.000000
0,:@0.868462:0.213393:0.881710:0.213393:0.881710:0.196178:0.868462:0.196178:0.000000:0.000000
=0:@0.847836:0.264148:0.870935:0.264148:0.870935:0.246933:0.847836:0.246933:0.000000:0.000000
=0:@0.829724:0.289525:0.852822:0.289525:0.852822:0.272310:0.829724:0.272310:0.000000:0.000000
vectores :@0.404239:0.129937:0.468064:0.129937:0.468064:0.113439:0.404239:0.113439:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.471442:0.130275:0.507217:0.130275:0.507217:0.113806:0.471442:0.113806:0.000000:0.000000
AB:@0.471442:0.150228:0.507217:0.150228:0.507217:0.133759:0.471442:0.133759:0.000000:0.000000
+:@0.484947:0.130795:0.495523:0.130795:0.495523:0.114514:0.484947:0.114514:0.000000
−:@0.484947:0.150749:0.495523:0.150749:0.495523:0.134468:0.484947:0.134468:0.000000
 y :@0.511281:0.129944:0.527059:0.129944:0.527059:0.113446:0.511281:0.113446:0.000000:0.000000:0.000000
AB:@0.530435:0.110158:0.566211:0.110158:0.566211:0.093689:0.530435:0.093689:0.000000:0.000000
AB:@0.530435:0.130111:0.566211:0.130111:0.566211:0.113642:0.530435:0.113642:0.000000:0.000000
+:@0.543940:0.110678:0.554517:0.110678:0.554517:0.094398:0.543940:0.094398:0.000000
−:@0.543940:0.130632:0.554517:0.130632:0.554517:0.114351:0.543940:0.114351:0.000000
 que forman las diagonales del paralelogramo. :@0.570274:0.129944:0.895951:0.129944:0.895951:0.113446:0.570274:0.113446:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
También se muestran los vectores :@0.404227:0.149391:0.648815:0.149391:0.648815:0.132894:0.404227:0.132894:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.635786:0.129612:0.671562:0.129612:0.671562:0.113143:0.635786:0.113143:0.000000:0.000000
AB:@0.635786:0.149565:0.671562:0.149565:0.671562:0.133097:0.635786:0.133097:0.000000:0.000000
+:@0.649291:0.130133:0.659868:0.130133:0.659868:0.113852:0.649291:0.113852:0.000000
−:@0.649291:0.150086:0.659868:0.150086:0.659868:0.133805:0.649291:0.133805:0.000000
 y :@0.675702:0.149398:0.691808:0.149398:0.691808:0.132900:0.675702:0.132900:0.000000:0.000000:0.000000
AB:@0.695525:0.129612:0.731301:0.129612:0.731301:0.113143:0.695525:0.113143:0.000000:0.000000
AB:@0.695525:0.149565:0.731301:0.149565:0.731301:0.133097:0.695525:0.133097:0.000000:0.000000
+:@0.709030:0.130133:0.719607:0.130133:0.719607:0.113852:0.709030:0.113852:0.000000
−:@0.709030:0.150086:0.719607:0.150086:0.719607:0.133805:0.709030:0.133805:0.000000
.:@0.733597:0.149398:0.736352:0.149398:0.736352:0.132900:0.733597:0.132900:0.000000
Un resultado muy conocido de la geometría plana es el famoso teorema :@0.404238:0.184100:0.895933:0.184100:0.895933:0.167602:0.404238:0.167602:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de Pitágoras que enuncia lo siguiente: en todo triángulo rectángulo, la :@0.404238:0.201450:0.895978:0.201450:0.895978:0.184953:0.404238:0.184953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hipotenusa al cuadrado es igual a la suma de los cuadrados de los :@0.404238:0.218801:0.895995:0.218801:0.895995:0.202304:0.404238:0.202304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
catetos. Este resultado es extendido al espacio euclídeo  .:@0.404238:0.236152:0.820762:0.236152:0.820762:0.219654:0.404238:0.219654:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.799149:0.235183:0.813058:0.235183:0.813058:0.221736:0.799149:0.221736:0.000000
2:@0.813055:0.229800:0.818008:0.229800:0.818008:0.220182:0.813055:0.220182:0.000000
Teorema de Pitágoras:@0.404235:0.282943:0.577037:0.282943:0.577037:0.265260:0.404235:0.265260:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.404235:0.302241:0.442033:0.302241:0.442033:0.285743:0.404235:0.285743:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.441663:0.302174:0.467247:0.302174:0.467247:0.285705:0.441663:0.285705:0.000000:0.000000
AB:@0.447327:0.327159:0.483102:0.327159:0.483102:0.310690:0.447327:0.310690:0.000000:0.000000
AB:@0.518415:0.327159:0.554190:0.327159:0.554190:0.310690:0.518415:0.310690:0.000000:0.000000
A:@0.607419:0.327159:0.618690:0.327159:0.618690:0.310690:0.607419:0.310690:0.000000
B:@0.652750:0.327159:0.661940:0.327159:0.661940:0.310690:0.652750:0.310690:0.000000
AB:@0.447346:0.359026:0.483121:0.359026:0.483121:0.342558:0.447346:0.342558:0.000000:0.000000
AB:@0.519417:0.359026:0.555192:0.359026:0.555192:0.342558:0.519417:0.342558:0.000000:0.000000
AB:@0.574765:0.359026:0.610540:0.359026:0.610540:0.342558:0.574765:0.342558:0.000000:0.000000
AA:@0.455129:0.383100:0.486088:0.383100:0.486088:0.366631:0.455129:0.366631:0.000000:0.000000
AB:@0.516546:0.383100:0.544269:0.383100:0.544269:0.366631:0.516546:0.366631:0.000000:0.000000
BB:@0.565171:0.383100:0.590909:0.383100:0.590909:0.366631:0.565171:0.366631:0.000000:0.000000
A:@0.460793:0.406957:0.472063:0.406957:0.472063:0.390489:0.460793:0.390489:0.000000
A B:@0.515602:0.406957:0.543325:0.406957:0.543325:0.390489:0.515602:0.390489:0.000000:0.000000:0.000000
B:@0.569891:0.406957:0.579081:0.406957:0.579081:0.390489:0.569891:0.390489:0.000000
AB:@0.447346:0.434921:0.483121:0.434921:0.483121:0.418452:0.447346:0.418452:0.000000:0.000000
AB:@0.519417:0.434921:0.555192:0.434921:0.555192:0.418452:0.519417:0.418452:0.000000:0.000000
AB:@0.574765:0.434921:0.610540:0.434921:0.610540:0.418452:0.574765:0.418452:0.000000:0.000000
A:@0.460793:0.462898:0.472063:0.462898:0.472063:0.446430:0.460793:0.446430:0.000000
A B:@0.515602:0.462898:0.543325:0.462898:0.543325:0.446430:0.515602:0.446430:0.000000:0.000000:0.000000
B:@0.569891:0.462898:0.579081:0.462898:0.579081:0.446430:0.569891:0.446430:0.000000
AB:@0.447346:0.492019:0.483121:0.492019:0.483121:0.475550:0.447346:0.475550:0.000000:0.000000
AB:@0.518434:0.492019:0.554209:0.492019:0.554209:0.475550:0.518434:0.475550:0.000000:0.000000
A:@0.607439:0.492019:0.618709:0.492019:0.618709:0.475550:0.607439:0.475550:0.000000
B:@0.652770:0.492019:0.661959:0.492019:0.661959:0.475550:0.652770:0.475550:0.000000
,:@0.453992:0.302058:0.456747:0.302058:0.456747:0.285561:0.453992:0.285561:0.000000
=2:@0.570353:0.327043:0.592296:0.327043:0.592296:0.310546:0.570353:0.310546:0.000000:0.000000
.:@0.683478:0.327043:0.686233:0.327043:0.686233:0.310546:0.683478:0.310546:0.000000
=(:@0.499265:0.358911:0.518665:0.358911:0.518665:0.342413:0.499265:0.342413:0.000000:0.000000
)(:@0.554749:0.358911:0.573995:0.358911:0.573995:0.342413:0.554749:0.342413:0.000000:0.000000
):@0.610097:0.358911:0.616050:0.358911:0.616050:0.342413:0.610097:0.342413:0.000000
=:@0.440526:0.382984:0.451334:0.382984:0.451334:0.366487:0.440526:0.366487:0.000000
2(:@0.501404:0.382984:0.515795:0.382984:0.515795:0.366487:0.501404:0.366487:0.000000:0.000000
):@0.543826:0.382984:0.549778:0.382984:0.549778:0.366487:0.543826:0.366487:0.000000
=:@0.440526:0.406841:0.451334:0.406841:0.451334:0.390344:0.440526:0.390344:0.000000
2(:@0.500460:0.406841:0.514831:0.406841:0.514831:0.390344:0.500460:0.390344:0.000000:0.000000
):@0.542862:0.406841:0.548815:0.406841:0.548815:0.390344:0.542862:0.390344:0.000000
,:@0.589619:0.406841:0.592373:0.406841:0.592373:0.390344:0.589619:0.390344:0.000000
=(:@0.499265:0.434805:0.518665:0.434805:0.518665:0.418307:0.499265:0.418307:0.000000:0.000000
)(:@0.554749:0.434805:0.573995:0.434805:0.573995:0.418307:0.554749:0.418307:0.000000:0.000000
):@0.610097:0.434805:0.616050:0.434805:0.616050:0.418307:0.610097:0.418307:0.000000
=:@0.440526:0.462783:0.451334:0.462783:0.451334:0.446285:0.440526:0.446285:0.000000
2(:@0.500460:0.462783:0.514831:0.462783:0.514831:0.446285:0.500460:0.446285:0.000000:0.000000
):@0.542862:0.462783:0.548815:0.462783:0.548815:0.446285:0.542862:0.446285:0.000000
,:@0.589619:0.462783:0.592373:0.462783:0.592373:0.446285:0.589619:0.446285:0.000000
=2:@0.570334:0.491903:0.592277:0.491903:0.592277:0.475405:0.570334:0.475405:0.000000:0.000000
.:@0.683459:0.491903:0.686214:0.491903:0.686214:0.475405:0.683459:0.475405:0.000000
2:@0.498882:0.294132:0.504054:0.294132:0.504054:0.284090:0.498882:0.284090:0.000000
2:@0.490932:0.479219:0.496103:0.479219:0.496103:0.469177:0.490932:0.469177:0.000000
2:@0.562195:0.479219:0.567366:0.479219:0.567366:0.469177:0.562195:0.469177:0.000000
2:@0.490756:0.314357:0.495927:0.314357:0.495927:0.304315:0.490756:0.304315:0.000000
2:@0.565525:0.314357:0.570696:0.314357:0.570696:0.304315:0.565525:0.304315:0.000000
2:@0.626252:0.314246:0.631170:0.314246:0.631170:0.304698:0.626252:0.304698:0.000000
2:@0.669595:0.314246:0.674513:0.314246:0.674513:0.304698:0.669595:0.304698:0.000000
2:@0.490756:0.346222:0.495927:0.346222:0.495927:0.336180:0.490756:0.336180:0.000000
2:@0.479615:0.394153:0.484787:0.394153:0.484787:0.384110:0.479615:0.384110:0.000000
2:@0.592262:0.394153:0.597433:0.394153:0.597433:0.384110:0.592262:0.384110:0.000000
2:@0.490756:0.422131:0.495927:0.422131:0.495927:0.412089:0.490756:0.412089:0.000000
2:@0.479615:0.452363:0.484787:0.452363:0.484787:0.442321:0.479615:0.442321:0.000000
2:@0.587278:0.452363:0.592449:0.452363:0.592449:0.442321:0.587278:0.442321:0.000000
2:@0.626246:0.479215:0.631417:0.479215:0.631417:0.469173:0.626246:0.469173:0.000000
2:@0.671827:0.479215:0.676999:0.479215:0.676999:0.469173:0.671827:0.469173:0.000000
R:@0.484172:0.305138:0.498081:0.305138:0.498081:0.283797:0.484172:0.283797:0.000000
+:@0.460815:0.327679:0.471392:0.327679:0.471392:0.311399:0.460815:0.311399:0.000000
+:@0.498517:0.327679:0.509093:0.327679:0.509093:0.311399:0.498517:0.311399:0.000000
−:@0.531903:0.327679:0.542480:0.327679:0.542480:0.311399:0.531903:0.311399:0.000000
+:@0.633989:0.327679:0.644565:0.327679:0.644565:0.311399:0.633989:0.311399:0.000000
+:@0.460815:0.359547:0.471392:0.359547:0.471392:0.343266:0.460815:0.343266:0.000000
+ ⋅:@0.532905:0.359547:0.567004:0.359547:0.567004:0.343266:0.532905:0.343266:0.000000:0.000000:0.000000
+:@0.588254:0.359547:0.598830:0.359547:0.598830:0.343266:0.588254:0.343266:0.000000
⋅+:@0.467789:0.383621:0.498883:0.383621:0.498883:0.367340:0.467789:0.367340:0.000000:0.000000
⋅+ ⋅:@0.529206:0.383621:0.580682:0.383621:0.580682:0.367340:0.529206:0.367340:0.000000:0.000000:0.000000:0.000000
+:@0.487362:0.407478:0.497939:0.407478:0.497939:0.391197:0.487362:0.391197:0.000000
⋅ +:@0.528243:0.407478:0.561706:0.407478:0.561706:0.391197:0.528243:0.391197:0.000000:0.000000:0.000000
−:@0.460834:0.435441:0.471411:0.435441:0.471411:0.419161:0.460834:0.419161:0.000000
− ⋅:@0.532924:0.435441:0.567023:0.435441:0.567023:0.419161:0.532924:0.419161:0.000000:0.000000:0.000000
−:@0.588273:0.435441:0.598849:0.435441:0.598849:0.419161:0.588273:0.419161:0.000000
−:@0.487362:0.463419:0.497939:0.463419:0.497939:0.447138:0.487362:0.447138:0.000000
⋅ +:@0.528243:0.463419:0.561706:0.463419:0.561706:0.447138:0.528243:0.447138:0.000000:0.000000:0.000000
+:@0.460834:0.492539:0.471411:0.492539:0.471411:0.476258:0.460834:0.476258:0.000000
+:@0.498536:0.492539:0.509113:0.492539:0.509113:0.476258:0.498536:0.476258:0.000000
−:@0.531922:0.492539:0.542499:0.492539:0.542499:0.476258:0.531922:0.476258:0.000000
+:@0.634008:0.492539:0.644585:0.492539:0.644585:0.476258:0.634008:0.476258:0.000000
. Entonces, :@0.504749:0.302241:0.583794:0.302241:0.583794:0.285743:0.504749:0.285743:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.623411:0.309191:0.630592:0.309191:0.630592:0.298230:0.623411:0.298230:0.000000
.:@0.685014:0.309191:0.686844:0.309191:0.686844:0.298230:0.685014:0.298230:0.000000
2:@0.616176:0.300724:0.619934:0.300724:0.619934:0.293427:0.616176:0.293427:0.000000
2:@0.649358:0.300724:0.653115:0.300724:0.653115:0.293427:0.649358:0.293427:0.000000
2:@0.681168:0.300724:0.684925:0.300724:0.684925:0.293427:0.681168:0.293427:0.000000
AB:@0.584665:0.293240:0.611044:0.293240:0.611044:0.282298:0.584665:0.282298:0.000000:0.000000
AB:@0.588415:0.309262:0.611108:0.309262:0.611108:0.298321:0.588415:0.298321:0.000000:0.000000
A:@0.636859:0.309262:0.644347:0.309262:0.644347:0.298321:0.636859:0.298321:0.000000
B:@0.669933:0.309262:0.676038:0.309262:0.676038:0.298321:0.669933:0.298321:0.000000
⊥:@0.594403:0.293585:0.602825:0.293585:0.602825:0.282769:0.594403:0.282769:0.000000
+:@0.596838:0.309613:0.603865:0.309613:0.603865:0.298797:0.596838:0.298797:0.000000
+:@0.655548:0.309613:0.662575:0.309613:0.662575:0.298797:0.655548:0.298797:0.000000
si y solo si :@0.634103:0.302241:0.708175:0.302241:0.708175:0.285743:0.634103:0.285743:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.621181:0.328115:0.631989:0.328115:0.631989:0.311617:0.621181:0.311617:0.000000
.:@0.713905:0.328115:0.716660:0.328115:0.716660:0.311617:0.713905:0.311617:0.000000
2:@0.610292:0.315370:0.615949:0.315370:0.615949:0.304387:0.610292:0.304387:0.000000
2:@0.660237:0.315370:0.665893:0.315370:0.665893:0.304387:0.660237:0.304387:0.000000
2:@0.708116:0.315370:0.713772:0.315370:0.713772:0.304387:0.708116:0.304387:0.000000
AB:@0.562861:0.304105:0.602567:0.304105:0.602567:0.287637:0.562861:0.287637:0.000000:0.000000
AB:@0.568515:0.328230:0.602673:0.328230:0.602673:0.311762:0.568515:0.311762:0.000000:0.000000
A:@0.641442:0.328230:0.652712:0.328230:0.652712:0.311762:0.641442:0.311762:0.000000
B:@0.691223:0.328230:0.700413:0.328230:0.700413:0.311762:0.691223:0.311762:0.000000
⊥:@0.577520:0.304626:0.590196:0.304626:0.590196:0.288345:0.577520:0.288345:0.000000
+:@0.581180:0.328743:0.591757:0.328743:0.591757:0.312463:0.581180:0.312463:0.000000
+:@0.669550:0.328743:0.680126:0.328743:0.680126:0.312463:0.669550:0.312463:0.000000
Demostración. :@0.404235:0.372282:0.524411:0.372282:0.524411:0.355337:0.404235:0.355337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Debemos probar una equivalencia.:@0.517630:0.371820:0.771311:0.371820:0.771311:0.355322:0.517630:0.355322:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
)  Supongamos que :@0.421975:0.390502:0.569218:0.390502:0.569218:0.374004:0.421975:0.374004:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.631459:0.414962:0.642267:0.414962:0.642267:0.398464:0.631459:0.398464:0.000000
.:@0.724183:0.414962:0.726938:0.414962:0.726938:0.398464:0.724183:0.398464:0.000000
2:@0.620570:0.402217:0.626226:0.402217:0.626226:0.391234:0.620570:0.391234:0.000000
2:@0.670514:0.402217:0.676170:0.402217:0.676170:0.391234:0.670514:0.391234:0.000000
2:@0.718394:0.402217:0.724050:0.402217:0.724050:0.391234:0.718394:0.391234:0.000000
AB:@0.573139:0.390953:0.612845:0.390953:0.612845:0.374485:0.573139:0.374485:0.000000:0.000000
AB:@0.578784:0.415071:0.612941:0.415071:0.612941:0.398602:0.578784:0.398602:0.000000:0.000000
A:@0.651703:0.415071:0.662973:0.415071:0.662973:0.398602:0.651703:0.398602:0.000000
B:@0.701484:0.415071:0.710674:0.415071:0.710674:0.398602:0.701484:0.398602:0.000000
⊥:@0.587797:0.391474:0.600474:0.391474:0.600474:0.375193:0.587797:0.375193:0.000000
+:@0.591458:0.415591:0.602034:0.415591:0.602034:0.399311:0.591458:0.399311:0.000000
+:@0.679827:0.415591:0.690404:0.415591:0.690404:0.399311:0.679827:0.399311:0.000000
. Por la definición de vectores perpen-:@0.614857:0.390502:0.891772:0.390502:0.891772:0.374004:0.614857:0.374004:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
diculares, se tiene :@0.404230:0.409949:0.532417:0.409949:0.532417:0.393452:0.404230:0.393452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.532916:0.283011:0.542505:0.283011:0.542505:0.265826:0.532916:0.265826:0.000000
AB:@0.534163:0.308388:0.566991:0.308388:0.566991:0.291203:0.534163:0.291203:0.000000:0.000000
A:@0.534163:0.333766:0.545923:0.333766:0.545923:0.316581:0.534163:0.316581:0.000000
B:@0.532916:0.359143:0.542505:0.359143:0.542505:0.341958:0.532916:0.341958:0.000000
A:@0.534163:0.384520:0.545923:0.384520:0.545923:0.367336:0.534163:0.367336:0.000000
AB:@0.534163:0.409898:0.566991:0.409898:0.566991:0.392713:0.534163:0.392713:0.000000:0.000000
AB:@0.534163:0.435275:0.572238:0.435275:0.572238:0.418090:0.534163:0.418090:0.000000:0.000000
BB:@0.532916:0.460652:0.560618:0.460652:0.560618:0.443468:0.532916:0.443468:0.000000:0.000000
B:@0.532916:0.486030:0.542505:0.486030:0.542505:0.468845:0.532916:0.468845:0.000000
.:@0.582751:0.282860:0.585626:0.282860:0.585626:0.265645:0.582751:0.265645:0.000000
.=0:@0.550406:0.308237:0.593084:0.308237:0.593084:0.291022:0.550406:0.291022:0.000000:0.000000:0.000000
,:@0.586933:0.333615:0.589808:0.333615:0.589808:0.316400:0.586933:0.316400:0.000000
=0.:@0.545461:0.358992:0.572097:0.358992:0.572097:0.341777:0.545461:0.341777:0.000000:0.000000:0.000000
.=0,:@0.550386:0.409762:0.597447:0.409762:0.597447:0.392547:0.550386:0.392547:0.000000:0.000000:0.000000:0.000000
=:@0.548818:0.435139:0.560095:0.435139:0.560095:0.417924:0.548818:0.417924:0.000000
=0:@0.563573:0.460517:0.586671:0.460517:0.586671:0.443302:0.563573:0.443302:0.000000:0.000000
=0:@0.545461:0.485894:0.568559:0.485894:0.568559:0.468679:0.545461:0.468679:0.000000:0.000000
2:@0.575060:0.274509:0.580186:0.274509:0.580186:0.264557:0.575060:0.264557:0.000000
2:@0.578408:0.325274:0.583533:0.325274:0.583533:0.315322:0.578408:0.315322:0.000000
2:@0.578408:0.376039:0.583533:0.376039:0.583533:0.366087:0.578408:0.366087:0.000000
∈:@0.545481:0.283554:0.559814:0.283554:0.559814:0.266565:0.545481:0.266565:0.000000
∈:@0.548838:0.334324:0.563171:0.334324:0.563171:0.317335:0.548838:0.317335:0.000000
∈:@0.548838:0.385094:0.563171:0.385094:0.563171:0.368105:0.548838:0.368105:0.000000
⋅:@0.544496:0.461241:0.549521:0.461241:0.549521:0.444252:0.544496:0.444252:0.000000
. Luego, de la definición de norma y de las :@0.593769:0.409957:0.895845:0.409957:0.895845:0.393460:0.593769:0.393460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propiedades del producto escalar, se deduce :@0.404238:0.427308:0.723860:0.427308:0.723860:0.410811:0.404238:0.410811:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=(:@0.588600:0.451153:0.608000:0.451153:0.608000:0.434655:0.588600:0.434655:0.000000:0.000000
)(:@0.642465:0.451153:0.662135:0.451153:0.662135:0.434655:0.642465:0.434655:0.000000:0.000000
):@0.696601:0.451153:0.702554:0.451153:0.702554:0.434655:0.696601:0.434655:0.000000
=:@0.529128:0.480273:0.539936:0.480273:0.539936:0.463776:0.529128:0.463776:0.000000
2:@0.588812:0.480273:0.597308:0.480273:0.597308:0.463776:0.588812:0.463776:0.000000
=:@0.669849:0.480267:0.680657:0.480267:0.680657:0.463769:0.669849:0.463769:0.000000
. )(:@0.764460:0.480267:0.779047:0.481645:0.779047:0.465147:0.764460:0.463769:0.000000:0.000000:0.000000:0.000000
2:@0.577711:0.438409:0.583367:0.438409:0.583367:0.427425:0.577711:0.427425:0.000000
2:@0.708902:0.467513:0.714558:0.467513:0.714558:0.456529:0.708902:0.456529:0.000000
2:@0.758423:0.467513:0.764079:0.467513:0.764079:0.456529:0.758423:0.456529:0.000000
AB:@0.535935:0.451269:0.570092:0.451269:0.570092:0.434800:0.535935:0.434800:0.000000:0.000000
AB:@0.608758:0.451269:0.642915:0.451269:0.642915:0.434800:0.608758:0.434800:0.000000:0.000000
AB:@0.662893:0.451269:0.697050:0.451269:0.697050:0.434800:0.662893:0.434800:0.000000:0.000000
AA:@0.543738:0.480389:0.575121:0.480389:0.575121:0.463920:0.543738:0.463920:0.000000:0.000000
AB BB AB:@0.598701:0.480389:0.687004:0.481761:0.687004:0.465292:0.598701:0.463920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.690109:0.480383:0.701379:0.480383:0.701379:0.463914:0.690109:0.463914:0.000000
B:@0.742029:0.480383:0.751219:0.480383:0.751219:0.463914:0.742029:0.463914:0.000000
+:@0.548603:0.451789:0.559180:0.451789:0.559180:0.435508:0.548603:0.435508:0.000000
+ ⋅:@0.621426:0.451789:0.654716:0.451789:0.654716:0.435508:0.621426:0.435508:0.000000:0.000000:0.000000
+:@0.675561:0.451789:0.686138:0.451789:0.686138:0.435508:0.675561:0.435508:0.000000
⋅+:@0.556406:0.480909:0.587095:0.480909:0.587095:0.464629:0.556406:0.464629:0.000000:0.000000
⋅+ ⋅ +:@0.611370:0.480909:0.676092:0.482281:0.676092:0.466000:0.611370:0.464629:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+ + ⋅:@0.718226:0.480903:0.771628:0.482281:0.771628:0.466000:0.718226:0.464622:0.000000:0.000000:0.000000:0.000000:0.000000
)  Recíprocamente, sean  :@0.421975:0.511539:0.600140:0.511539:0.600140:0.495041:0.421975:0.495041:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.599770:0.511472:0.625354:0.511472:0.625354:0.495003:0.599770:0.495003:0.000000:0.000000
AB:@0.605434:0.536457:0.641209:0.536457:0.641209:0.519988:0.605434:0.519988:0.000000:0.000000
AB:@0.676522:0.536457:0.712298:0.536457:0.712298:0.519988:0.676522:0.519988:0.000000:0.000000
A:@0.765527:0.536457:0.776797:0.536457:0.776797:0.519988:0.765527:0.519988:0.000000
B:@0.810858:0.536457:0.820047:0.536457:0.820047:0.519988:0.810858:0.519988:0.000000
AB:@0.605453:0.568324:0.641229:0.568324:0.641229:0.551855:0.605453:0.551855:0.000000:0.000000
AB:@0.677524:0.568324:0.713299:0.568324:0.713299:0.551855:0.677524:0.551855:0.000000:0.000000
AB:@0.732873:0.568324:0.768648:0.568324:0.768648:0.551855:0.732873:0.551855:0.000000:0.000000
AA:@0.613236:0.592398:0.644196:0.592398:0.644196:0.575929:0.613236:0.575929:0.000000:0.000000
AB:@0.674654:0.592398:0.702376:0.592398:0.702376:0.575929:0.674654:0.575929:0.000000:0.000000
BB:@0.723279:0.592398:0.749017:0.592398:0.749017:0.575929:0.723279:0.575929:0.000000:0.000000
A:@0.618900:0.616255:0.630170:0.616255:0.630170:0.599787:0.618900:0.599787:0.000000
A B:@0.673710:0.616255:0.701432:0.616255:0.701432:0.599787:0.673710:0.599787:0.000000:0.000000:0.000000
B:@0.727999:0.616255:0.737188:0.616255:0.737188:0.599787:0.727999:0.599787:0.000000
AB:@0.605453:0.644219:0.641229:0.644219:0.641229:0.627750:0.605453:0.627750:0.000000:0.000000
AB:@0.677524:0.644219:0.713299:0.644219:0.713299:0.627750:0.677524:0.627750:0.000000:0.000000
AB:@0.732873:0.644219:0.768648:0.644219:0.768648:0.627750:0.732873:0.627750:0.000000:0.000000
A:@0.618900:0.672196:0.630170:0.672196:0.630170:0.655728:0.618900:0.655728:0.000000
A B:@0.673710:0.672196:0.701432:0.672196:0.701432:0.655728:0.673710:0.655728:0.000000:0.000000:0.000000
B:@0.727999:0.672196:0.737188:0.672196:0.737188:0.655728:0.727999:0.655728:0.000000
AB:@0.605453:0.701316:0.641229:0.701316:0.641229:0.684848:0.605453:0.684848:0.000000:0.000000
AB:@0.676542:0.701316:0.712317:0.701316:0.712317:0.684848:0.676542:0.684848:0.000000:0.000000
A:@0.765546:0.701316:0.776816:0.701316:0.776816:0.684848:0.765546:0.684848:0.000000
B:@0.810877:0.701316:0.820067:0.701316:0.820067:0.684848:0.810877:0.684848:0.000000
,:@0.612100:0.511356:0.614855:0.511356:0.614855:0.494859:0.612100:0.494859:0.000000
=2:@0.728461:0.536341:0.750404:0.536341:0.750404:0.519844:0.728461:0.519844:0.000000:0.000000
.:@0.841585:0.536341:0.844340:0.536341:0.844340:0.519844:0.841585:0.519844:0.000000
=(:@0.657373:0.568208:0.676773:0.568208:0.676773:0.551711:0.657373:0.551711:0.000000:0.000000
)(:@0.712856:0.568208:0.732102:0.568208:0.732102:0.551711:0.712856:0.551711:0.000000:0.000000
):@0.768205:0.568208:0.774158:0.568208:0.774158:0.551711:0.768205:0.551711:0.000000
=:@0.598634:0.592282:0.609441:0.592282:0.609441:0.575785:0.598634:0.575785:0.000000
2(:@0.659511:0.592282:0.673902:0.592282:0.673902:0.575785:0.659511:0.575785:0.000000:0.000000
):@0.701933:0.592282:0.707886:0.592282:0.707886:0.575785:0.701933:0.575785:0.000000
=:@0.598634:0.616139:0.609441:0.616139:0.609441:0.599642:0.598634:0.599642:0.000000
2(:@0.658567:0.616139:0.672939:0.616139:0.672939:0.599642:0.658567:0.599642:0.000000:0.000000
):@0.700970:0.616139:0.706923:0.616139:0.706923:0.599642:0.700970:0.599642:0.000000
,:@0.747726:0.616139:0.750481:0.616139:0.750481:0.599642:0.747726:0.599642:0.000000
=(:@0.657373:0.644103:0.676773:0.644103:0.676773:0.627605:0.657373:0.627605:0.000000:0.000000
)(:@0.712856:0.644103:0.732102:0.644103:0.732102:0.627605:0.712856:0.627605:0.000000:0.000000
):@0.768205:0.644103:0.774158:0.644103:0.774158:0.627605:0.768205:0.627605:0.000000
=:@0.598634:0.672081:0.609441:0.672081:0.609441:0.655583:0.598634:0.655583:0.000000
2(:@0.658567:0.672081:0.672939:0.672081:0.672939:0.655583:0.658567:0.655583:0.000000:0.000000
):@0.700970:0.672081:0.706923:0.672081:0.706923:0.655583:0.700970:0.655583:0.000000
,:@0.747726:0.672081:0.750481:0.672081:0.750481:0.655583:0.747726:0.655583:0.000000
=2 .:@0.728442:0.701201:0.739686:0.703577:0.739686:0.687080:0.728442:0.684703:0.000000:0.000000:0.000000:0.000000
.:@0.841566:0.701201:0.844321:0.701201:0.844321:0.684703:0.841566:0.684703:0.000000
2:@0.656990:0.503431:0.662161:0.503431:0.662161:0.493389:0.656990:0.493389:0.000000
2:@0.649039:0.688518:0.654210:0.688518:0.654210:0.678476:0.649039:0.678476:0.000000
2:@0.720302:0.688518:0.725473:0.688518:0.725473:0.678476:0.720302:0.678476:0.000000
2:@0.648863:0.523656:0.654035:0.523656:0.654035:0.513614:0.648863:0.513614:0.000000
2:@0.723632:0.523656:0.728804:0.523656:0.728804:0.513614:0.723632:0.513614:0.000000
2:@0.784358:0.523544:0.789276:0.523544:0.789276:0.513995:0.784358:0.513995:0.000000
2:@0.827701:0.523544:0.832618:0.523544:0.832618:0.513995:0.827701:0.513995:0.000000
2:@0.648861:0.555520:0.654033:0.555520:0.654033:0.545478:0.648861:0.545478:0.000000
2:@0.637721:0.603450:0.642893:0.603450:0.642893:0.593408:0.637721:0.593408:0.000000
2:@0.750368:0.603450:0.755539:0.603450:0.755539:0.593408:0.750368:0.593408:0.000000
2:@0.648861:0.631429:0.654033:0.631429:0.654033:0.621387:0.648861:0.621387:0.000000
2:@0.637721:0.661661:0.642893:0.661661:0.642893:0.651619:0.637721:0.651619:0.000000
2:@0.745384:0.661661:0.750555:0.661661:0.750555:0.651619:0.745384:0.651619:0.000000
2:@0.784351:0.688513:0.789523:0.688513:0.789523:0.678471:0.784351:0.678471:0.000000
2:@0.829933:0.688513:0.835104:0.688513:0.835104:0.678471:0.829933:0.678471:0.000000
R:@0.642278:0.514436:0.656187:0.514436:0.656187:0.493095:0.642278:0.493095:0.000000
∈:@0.628418:0.511992:0.642154:0.511992:0.642154:0.495712:0.628418:0.495712:0.000000
+:@0.618921:0.536977:0.629497:0.536977:0.629497:0.520697:0.618921:0.520697:0.000000
+:@0.656623:0.536977:0.667199:0.536977:0.667199:0.520697:0.656623:0.520697:0.000000
−:@0.690009:0.536977:0.700585:0.536977:0.700585:0.520697:0.690009:0.520697:0.000000
+:@0.792095:0.536977:0.802671:0.536977:0.802671:0.520697:0.792095:0.520697:0.000000
+:@0.618921:0.568845:0.629497:0.568845:0.629497:0.552564:0.618921:0.552564:0.000000
+ ⋅:@0.691011:0.568845:0.725110:0.568845:0.725110:0.552564:0.691011:0.552564:0.000000:0.000000:0.000000
+:@0.746359:0.568845:0.756936:0.568845:0.756936:0.552564:0.746359:0.552564:0.000000
⋅+:@0.625895:0.592919:0.656989:0.592919:0.656989:0.576638:0.625895:0.576638:0.000000:0.000000
⋅+ ⋅:@0.687312:0.592919:0.738788:0.592919:0.738788:0.576638:0.687312:0.576638:0.000000:0.000000:0.000000:0.000000
+:@0.645468:0.616776:0.656045:0.616776:0.656045:0.600495:0.645468:0.600495:0.000000
⋅ +:@0.686349:0.616776:0.719812:0.616776:0.719812:0.600495:0.686349:0.600495:0.000000:0.000000:0.000000
−:@0.618940:0.644739:0.629517:0.644739:0.629517:0.628458:0.618940:0.628458:0.000000
− ⋅:@0.691030:0.644739:0.725129:0.644739:0.725129:0.628458:0.691030:0.628458:0.000000:0.000000:0.000000
−:@0.746379:0.644739:0.756955:0.644739:0.756955:0.628458:0.746379:0.628458:0.000000
−:@0.645468:0.672717:0.656045:0.672717:0.656045:0.656436:0.645468:0.656436:0.000000
⋅ +:@0.686349:0.672717:0.719812:0.672717:0.719812:0.656436:0.686349:0.656436:0.000000:0.000000:0.000000
+:@0.618940:0.701837:0.629517:0.701837:0.629517:0.685556:0.618940:0.685556:0.000000
+:@0.656642:0.701837:0.667218:0.701837:0.667218:0.685556:0.656642:0.685556:0.000000
−:@0.690028:0.701837:0.700605:0.701837:0.700605:0.685556:0.690028:0.685556:0.000000
+:@0.792114:0.701837:0.802690:0.701837:0.802690:0.685556:0.792114:0.685556:0.000000
, tal que :@0.661483:0.511539:0.721667:0.511539:0.721667:0.495041:0.661483:0.495041:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=( =:@0.783197:0.511102:0.797561:0.510765:0.797561:0.494268:0.783197:0.494605:0.000000:0.000000:0.000000:0.000000
)(:@0.837063:0.511102:0.856733:0.511102:0.856733:0.494605:0.837063:0.494605:0.000000:0.000000
) .:@0.891198:0.511102:0.884119:0.510765:0.884119:0.494268:0.891198:0.494605:0.000000:0.000000:0.000000
=:@0.723725:0.540223:0.734533:0.540223:0.734533:0.523725:0.723725:0.523725:0.000000
2:@0.783409:0.540223:0.791905:0.540223:0.791905:0.523725:0.783409:0.523725:0.000000
=:@0.864439:0.540223:0.875247:0.540223:0.875247:0.523725:0.864439:0.523725:0.000000
.:@0.959050:0.540223:0.961805:0.540223:0.961805:0.523725:0.959050:0.523725:0.000000
2:@0.772308:0.498358:0.777964:0.498358:0.777964:0.487375:0.772308:0.487375:0.000000
2:@0.903505:0.527458:0.909161:0.527458:0.909161:0.516474:0.903505:0.516474:0.000000
2:@0.953026:0.527458:0.958682:0.527458:0.958682:0.516474:0.953026:0.516474:0.000000
AB BB:@0.730533:0.511218:0.783696:0.510881:0.783696:0.494412:0.730533:0.494749:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.803354:0.511218:0.837511:0.511218:0.837511:0.494749:0.803354:0.494749:0.000000:0.000000
AB:@0.857489:0.511218:0.891646:0.511218:0.891646:0.494749:0.857489:0.494749:0.000000:0.000000
AA:@0.738333:0.540338:0.769717:0.540338:0.769717:0.523870:0.738333:0.523870:0.000000:0.000000
AB BB:@0.793297:0.540338:0.861381:0.540338:0.861381:0.523870:0.793297:0.523870:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.884711:0.540338:0.895981:0.540338:0.895981:0.523870:0.884711:0.523870:0.000000
B:@0.936631:0.540338:0.945820:0.540338:0.945820:0.523870:0.936631:0.523870:0.000000
+ ⋅:@0.743201:0.511738:0.773034:0.511402:0.773034:0.495121:0.743201:0.495458:0.000000:0.000000:0.000000
+ ⋅ +:@0.816024:0.511738:0.845703:0.511402:0.845703:0.495121:0.816024:0.495458:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.870159:0.511738:0.880735:0.511738:0.880735:0.495458:0.870159:0.495458:0.000000
⋅+:@0.751003:0.540859:0.781693:0.540859:0.781693:0.524578:0.751003:0.524578:0.000000:0.000000
⋅+ ⋅:@0.805967:0.540859:0.850720:0.540859:0.850720:0.524578:0.805967:0.524578:0.000000:0.000000:0.000000:0.000000
+:@0.912812:0.540859:0.923389:0.540859:0.923389:0.524578:0.912812:0.524578:0.000000
 :@0.795271:0.511539:0.799413:0.511539:0.799413:0.495041:0.795271:0.495041:0.000000
=(:@0.705511:0.481645:0.724911:0.481645:0.724911:0.465147:0.705511:0.465147:0.000000:0.000000
):@0.813512:0.481645:0.819465:0.481645:0.819465:0.465147:0.813512:0.465147:0.000000
=:@0.646039:0.510765:0.656847:0.510765:0.656847:0.494268:0.646039:0.494268:0.000000
2:@0.705723:0.510765:0.714219:0.510765:0.714219:0.494268:0.705723:0.494268:0.000000
2:@0.694622:0.468901:0.700279:0.468901:0.700279:0.457917:0.694622:0.457917:0.000000
2:@0.825819:0.498001:0.831475:0.498001:0.831475:0.487017:0.825819:0.487017:0.000000
2:@0.875340:0.498001:0.880996:0.498001:0.880996:0.487017:0.875340:0.487017:0.000000
AB:@0.725669:0.481761:0.759827:0.481761:0.759827:0.465292:0.725669:0.465292:0.000000:0.000000
AB:@0.779805:0.481761:0.813962:0.481761:0.813962:0.465292:0.779805:0.465292:0.000000:0.000000
AA:@0.660649:0.510881:0.692032:0.510881:0.692032:0.494412:0.660649:0.494412:0.000000:0.000000
AB:@0.715613:0.510881:0.743760:0.510881:0.743760:0.494412:0.715613:0.494412:0.000000:0.000000
A:@0.807027:0.510881:0.818297:0.510881:0.818297:0.494412:0.807027:0.494412:0.000000
B:@0.858946:0.510881:0.868136:0.510881:0.868136:0.494412:0.858946:0.494412:0.000000
+:@0.792473:0.482281:0.803050:0.482281:0.803050:0.466000:0.792473:0.466000:0.000000
⋅+:@0.673317:0.511402:0.704007:0.511402:0.704007:0.495121:0.673317:0.495121:0.000000:0.000000
⋅+:@0.728281:0.511402:0.755811:0.511402:0.755811:0.495121:0.728281:0.495121:0.000000:0.000000
. :@0.881321:0.511539:0.888218:0.511539:0.888218:0.495041:0.881321:0.495041:0.000000:0.000000
Nuevamente, de la definición de norma y de las propiedades del  :@0.404236:0.528889:0.895905:0.528889:0.895905:0.512392:0.404236:0.512392:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
producto escalar, se obtiene :@0.404236:0.546240:0.607192:0.546240:0.607192:0.529742:0.404236:0.529742:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.605009:0.568409:0.615700:0.568409:0.615700:0.552090:0.605009:0.552090:0.000000
2:@0.665038:0.568409:0.673442:0.568409:0.673442:0.552090:0.665038:0.552090:0.000000
.:@0.749956:0.568409:0.752682:0.568409:0.752682:0.552090:0.749956:0.552090:0.000000
=:@0.605009:0.594955:0.615700:0.594955:0.615700:0.578635:0.605009:0.578635:0.000000
2:@0.665038:0.594955:0.673442:0.594955:0.673442:0.578635:0.665038:0.578635:0.000000
=:@0.751252:0.594955:0.761943:0.594955:0.761943:0.578635:0.751252:0.578635:0.000000
.:@0.843946:0.594955:0.846671:0.594955:0.846671:0.578635:0.843946:0.578635:0.000000
2:@0.594237:0.556929:0.599832:0.556929:0.599832:0.546065:0.594237:0.546065:0.000000
2:@0.643642:0.556929:0.649237:0.556929:0.649237:0.546065:0.643642:0.546065:0.000000
2:@0.740485:0.556929:0.746080:0.556929:0.746080:0.546065:0.740485:0.546065:0.000000
2:@0.594237:0.583477:0.599832:0.583477:0.599832:0.572612:0.594237:0.572612:0.000000
2:@0.643642:0.583477:0.649237:0.583477:0.649237:0.572612:0.643642:0.572612:0.000000
2:@0.740485:0.583477:0.746080:0.583477:0.746080:0.572612:0.740485:0.572612:0.000000
2:@0.789890:0.583477:0.795485:0.583477:0.795485:0.572612:0.789890:0.572612:0.000000
2:@0.834473:0.583477:0.840068:0.583477:0.840068:0.572612:0.834473:0.572612:0.000000
+:@0.564461:0.569038:0.574924:0.569038:0.574924:0.552934:0.564461:0.552934:0.000000
+:@0.652867:0.569038:0.663329:0.569038:0.663329:0.552934:0.652867:0.552934:0.000000
⋅+:@0.687341:0.569038:0.715564:0.569038:0.715564:0.552934:0.687341:0.552934:0.000000:0.000000
+:@0.564461:0.595584:0.574924:0.595584:0.574924:0.579479:0.564461:0.579479:0.000000
+:@0.652867:0.595584:0.663329:0.595584:0.663329:0.579479:0.652867:0.579479:0.000000
⋅+:@0.687341:0.595584:0.715564:0.595584:0.715564:0.579479:0.687341:0.579479:0.000000:0.000000
+:@0.799091:0.595584:0.809554:0.595584:0.809554:0.579479:0.799091:0.579479:0.000000
AB:@0.551929:0.568524:0.585717:0.568524:0.585717:0.552233:0.551929:0.552233:0.000000:0.000000
A:@0.625051:0.568524:0.636199:0.568524:0.636199:0.552233:0.625051:0.552233:0.000000
A B:@0.674808:0.568524:0.702651:0.568524:0.702651:0.552233:0.674808:0.552233:0.000000:0.000000:0.000000
B:@0.722870:0.568524:0.731960:0.568524:0.731960:0.552233:0.722870:0.552233:0.000000
AB:@0.551929:0.595069:0.585717:0.595069:0.585717:0.578778:0.551929:0.578778:0.000000:0.000000
A:@0.625051:0.595069:0.636199:0.595069:0.636199:0.578778:0.625051:0.578778:0.000000
A B:@0.674808:0.595069:0.702651:0.595069:0.702651:0.578778:0.674808:0.578778:0.000000:0.000000:0.000000
B:@0.722870:0.595069:0.731960:0.595069:0.731960:0.578778:0.722870:0.578778:0.000000
A:@0.771294:0.595069:0.782442:0.595069:0.782442:0.578778:0.771294:0.578778:0.000000
B:@0.816859:0.595069:0.825950:0.595069:0.825950:0.578778:0.816859:0.578778:0.000000
De esta igualdad y por la hipótesis, resulta que :@0.404235:0.595945:0.736111:0.595945:0.736111:0.579447:0.404235:0.579447:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.560819:0.598770:0.571510:0.598770:0.571510:0.582451:0.560819:0.582451:0.000000
2:@0.620849:0.598770:0.629253:0.598770:0.629253:0.582451:0.620849:0.582451:0.000000
.:@0.705767:0.598770:0.708492:0.598770:0.708492:0.582451:0.705767:0.582451:0.000000
=:@0.560819:0.625317:0.571510:0.625317:0.571510:0.608998:0.560819:0.608998:0.000000
2:@0.620849:0.625317:0.629253:0.625317:0.629253:0.608998:0.620849:0.608998:0.000000
=:@0.707061:0.625317:0.717752:0.625317:0.717752:0.608998:0.707061:0.608998:0.000000
.:@0.799754:0.625317:0.802479:0.625317:0.802479:0.608998:0.799754:0.608998:0.000000
2:@0.550047:0.587292:0.555643:0.587292:0.555643:0.576427:0.550047:0.576427:0.000000
2:@0.599452:0.587292:0.605047:0.587292:0.605047:0.576427:0.599452:0.576427:0.000000
2:@0.696295:0.587292:0.701890:0.587292:0.701890:0.576427:0.696295:0.576427:0.000000
2:@0.550047:0.613840:0.555643:0.613840:0.555643:0.602975:0.550047:0.602975:0.000000
2:@0.599452:0.613840:0.605047:0.613840:0.605047:0.602975:0.599452:0.602975:0.000000
2:@0.696295:0.613840:0.701890:0.613840:0.701890:0.602975:0.696295:0.602975:0.000000
2:@0.745700:0.613840:0.751295:0.613840:0.751295:0.602975:0.745700:0.602975:0.000000
2:@0.790284:0.613840:0.795879:0.613840:0.795879:0.602975:0.790284:0.602975:0.000000
+:@0.520272:0.599400:0.530734:0.599400:0.530734:0.583295:0.520272:0.583295:0.000000
+:@0.608677:0.599400:0.619139:0.599400:0.619139:0.583295:0.608677:0.583295:0.000000
⋅+:@0.643151:0.599400:0.671375:0.599400:0.671375:0.583295:0.643151:0.583295:0.000000:0.000000
+:@0.520272:0.625946:0.530734:0.625946:0.530734:0.609842:0.520272:0.609842:0.000000
+:@0.608677:0.625946:0.619139:0.625946:0.619139:0.609842:0.608677:0.609842:0.000000
⋅+:@0.643151:0.625946:0.671375:0.625946:0.671375:0.609842:0.643151:0.609842:0.000000:0.000000
+:@0.754902:0.625946:0.765364:0.625946:0.765364:0.609842:0.754902:0.609842:0.000000
AB:@0.507739:0.598885:0.541527:0.598885:0.541527:0.582594:0.507739:0.582594:0.000000:0.000000
A:@0.580861:0.598885:0.592009:0.598885:0.592009:0.582594:0.580861:0.582594:0.000000
A B:@0.630619:0.598885:0.658461:0.598885:0.658461:0.582594:0.630619:0.582594:0.000000:0.000000:0.000000
B:@0.678681:0.598885:0.687771:0.598885:0.687771:0.582594:0.678681:0.582594:0.000000
AB:@0.507739:0.625432:0.541527:0.625432:0.541527:0.609141:0.507739:0.609141:0.000000:0.000000
A:@0.580861:0.625432:0.592009:0.625432:0.592009:0.609141:0.580861:0.609141:0.000000
A B:@0.630619:0.625432:0.658461:0.625432:0.658461:0.609141:0.630619:0.609141:0.000000:0.000000:0.000000
B:@0.678681:0.625432:0.687771:0.625432:0.687771:0.609141:0.678681:0.609141:0.000000
A:@0.727102:0.625432:0.738250:0.625432:0.738250:0.609141:0.727102:0.609141:0.000000
B:@0.772667:0.625432:0.781757:0.625432:0.781757:0.609141:0.772667:0.609141:0.000000
Por la ley cancelativa de la adición (cancelando :@0.404235:0.659662:0.740429:0.659662:0.740429:0.643165:0.404235:0.643165:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=(:@0.649173:0.628973:0.668439:0.628973:0.668439:0.612589:0.649173:0.612589:0.000000:0.000000
)(:@0.702667:0.628973:0.722201:0.628973:0.722201:0.612589:0.702667:0.612589:0.000000:0.000000
):@0.756429:0.628973:0.762341:0.628973:0.762341:0.612589:0.756429:0.612589:0.000000
=:@0.590111:0.657892:0.600844:0.657892:0.600844:0.641508:0.590111:0.641508:0.000000
2:@0.649383:0.657892:0.657821:0.657892:0.657821:0.641508:0.649383:0.641508:0.000000
=:@0.729854:0.657892:0.740588:0.657892:0.740588:0.641508:0.729854:0.641508:0.000000
.:@0.823814:0.657892:0.826550:0.657892:0.826550:0.641508:0.823814:0.641508:0.000000
2:@0.638359:0.616316:0.643977:0.616316:0.643977:0.605409:0.638359:0.605409:0.000000
2:@0.768651:0.645215:0.774269:0.645215:0.774269:0.634308:0.768651:0.634308:0.000000
2:@0.817831:0.645215:0.823448:0.645215:0.823448:0.634308:0.817831:0.634308:0.000000
AB:@0.596872:0.629088:0.630794:0.629088:0.630794:0.612732:0.596872:0.612732:0.000000:0.000000
AB:@0.669192:0.629088:0.703114:0.629088:0.703114:0.612732:0.669192:0.612732:0.000000:0.000000
AB:@0.722955:0.629088:0.756876:0.629088:0.756876:0.612732:0.722955:0.612732:0.000000:0.000000
AA:@0.604621:0.658007:0.635787:0.658007:0.635787:0.641652:0.604621:0.641652:0.000000:0.000000
AB BB:@0.659205:0.658007:0.726819:0.658007:0.726819:0.641652:0.659205:0.641652:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.749989:0.658007:0.761181:0.658007:0.761181:0.641652:0.749989:0.641652:0.000000
B:@0.801550:0.658007:0.810677:0.658007:0.810677:0.641652:0.801550:0.641652:0.000000
+:@0.609453:0.629605:0.619957:0.629605:0.619957:0.613436:0.609453:0.613436:0.000000
+ ⋅:@0.681773:0.629605:0.714834:0.629605:0.714834:0.613436:0.681773:0.613436:0.000000:0.000000:0.000000
+:@0.735536:0.629605:0.746039:0.629605:0.746039:0.613436:0.735536:0.613436:0.000000
⋅+:@0.617202:0.658524:0.647680:0.658524:0.647680:0.642356:0.617202:0.642356:0.000000:0.000000
⋅+ ⋅:@0.671786:0.658524:0.716231:0.658524:0.716231:0.642356:0.671786:0.642356:0.000000:0.000000:0.000000:0.000000
+:@0.777895:0.658524:0.788398:0.658524:0.788398:0.642356:0.777895:0.642356:0.000000
), se sigue :@0.824410:0.659662:0.895922:0.659662:0.895922:0.643165:0.824410:0.643165:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que :@0.404235:0.679110:0.435386:0.679110:0.435386:0.662612:0.404235:0.662612:0.000000:0.000000:0.000000:0.000000
B:@0.435647:0.552171:0.445236:0.552171:0.445236:0.534987:0.435647:0.534987:0.000000
AB:@0.436893:0.577549:0.469721:0.577549:0.469721:0.560364:0.436893:0.560364:0.000000:0.000000
A:@0.436893:0.602926:0.448653:0.602926:0.448653:0.585741:0.436893:0.585741:0.000000
B:@0.435647:0.628303:0.445236:0.628303:0.445236:0.611119:0.435647:0.611119:0.000000
A:@0.436893:0.653681:0.448653:0.653681:0.448653:0.636496:0.436893:0.636496:0.000000
AB:@0.436893:0.679058:0.469721:0.679058:0.469721:0.661873:0.436893:0.661873:0.000000:0.000000
AB:@0.436893:0.704436:0.474968:0.704436:0.474968:0.687251:0.436893:0.687251:0.000000:0.000000
BB:@0.435647:0.729813:0.463349:0.729813:0.463349:0.712628:0.435647:0.712628:0.000000:0.000000
B:@0.435647:0.755190:0.445236:0.755190:0.445236:0.738006:0.435647:0.738006:0.000000
.:@0.485482:0.552021:0.488357:0.552021:0.488357:0.534806:0.485482:0.534806:0.000000
.=0:@0.453136:0.577398:0.495815:0.577398:0.495815:0.560183:0.453136:0.560183:0.000000:0.000000:0.000000
,:@0.489663:0.602775:0.492538:0.602775:0.492538:0.585560:0.489663:0.585560:0.000000
=0.:@0.448191:0.628153:0.474827:0.628153:0.474827:0.610938:0.448191:0.610938:0.000000:0.000000:0.000000
.=0,:@0.453116:0.678922:0.500177:0.678922:0.500177:0.661707:0.453116:0.661707:0.000000:0.000000:0.000000:0.000000
=:@0.451548:0.704300:0.462826:0.704300:0.462826:0.687085:0.451548:0.687085:0.000000
=0:@0.466304:0.729677:0.489402:0.729677:0.489402:0.712462:0.466304:0.712462:0.000000:0.000000
=0:@0.448191:0.755055:0.471289:0.755055:0.471289:0.737840:0.448191:0.737840:0.000000:0.000000
2:@0.477789:0.543670:0.482914:0.543670:0.482914:0.533717:0.477789:0.533717:0.000000
2:@0.481136:0.594435:0.486262:0.594435:0.486262:0.584482:0.481136:0.584482:0.000000
2:@0.481136:0.645200:0.486262:0.645200:0.486262:0.635247:0.481136:0.635247:0.000000
∈:@0.448211:0.552715:0.462545:0.552715:0.462545:0.535726:0.448211:0.535726:0.000000
∈:@0.451568:0.603484:0.465902:0.603484:0.465902:0.586496:0.451568:0.586496:0.000000
∈:@0.451568:0.654254:0.465902:0.654254:0.465902:0.637266:0.451568:0.637266:0.000000
⋅:@0.447226:0.730401:0.452252:0.730401:0.452252:0.713413:0.447226:0.713413:0.000000
 con lo cual :@0.496500:0.679118:0.582383:0.679118:0.582383:0.662620:0.496500:0.662620:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.644208:0.703577:0.655015:0.703577:0.655015:0.687080:0.644208:0.687080:0.000000
2:@0.633319:0.690832:0.638975:0.690832:0.638975:0.679849:0.633319:0.679849:0.000000
2:@0.683263:0.690832:0.688919:0.690832:0.688919:0.679849:0.683263:0.679849:0.000000
2:@0.731142:0.690832:0.736798:0.690832:0.736798:0.679849:0.731142:0.679849:0.000000
AB:@0.585889:0.679568:0.625595:0.679568:0.625595:0.663099:0.585889:0.663099:0.000000:0.000000
AB:@0.591534:0.703686:0.625691:0.703686:0.625691:0.687217:0.591534:0.687217:0.000000:0.000000
A:@0.664453:0.703686:0.675723:0.703686:0.675723:0.687217:0.664453:0.687217:0.000000
B:@0.714234:0.703686:0.723424:0.703686:0.723424:0.687217:0.714234:0.687217:0.000000
⊥:@0.600547:0.680089:0.613224:0.680089:0.613224:0.663808:0.600547:0.663808:0.000000
+:@0.604208:0.704206:0.614784:0.704206:0.614784:0.687925:0.604208:0.687925:0.000000
+:@0.692578:0.704206:0.703154:0.704206:0.703154:0.687925:0.692578:0.687925:0.000000
. :@0.626658:0.679118:0.633555:0.679118:0.633555:0.662620:0.626658:0.662620:0.000000:0.000000
Ley de los cosenos:@0.404235:0.725909:0.549132:0.725909:0.549132:0.708226:0.404235:0.708226:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Teorema:@0.404235:0.743079:0.471179:0.743079:0.471179:0.726133:0.404235:0.726133:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  :@0.404235:0.760589:0.450105:0.760589:0.450105:0.744091:0.404235:0.744091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
AB:@0.453659:0.760528:0.479243:0.760528:0.479243:0.744060:0.453659:0.744060:0.000000:0.000000
AB:@0.459323:0.785513:0.495098:0.785513:0.495098:0.769044:0.459323:0.769044:0.000000:0.000000
AB:@0.530411:0.785513:0.566186:0.785513:0.566186:0.769044:0.530411:0.769044:0.000000:0.000000
A:@0.619416:0.785513:0.630686:0.785513:0.630686:0.769044:0.619416:0.769044:0.000000
B:@0.664747:0.785513:0.673936:0.785513:0.673936:0.769044:0.664747:0.769044:0.000000
AB:@0.459342:0.817380:0.495118:0.817380:0.495118:0.800912:0.459342:0.800912:0.000000:0.000000
AB:@0.531413:0.817380:0.567188:0.817380:0.567188:0.800912:0.531413:0.800912:0.000000:0.000000
AB:@0.586762:0.817380:0.622537:0.817380:0.622537:0.800912:0.586762:0.800912:0.000000:0.000000
AA:@0.467125:0.841454:0.498084:0.841454:0.498084:0.824986:0.467125:0.824986:0.000000:0.000000
AB:@0.528542:0.841454:0.556265:0.841454:0.556265:0.824986:0.528542:0.824986:0.000000:0.000000
BB:@0.577168:0.841454:0.602906:0.841454:0.602906:0.824986:0.577168:0.824986:0.000000:0.000000
A:@0.472789:0.865311:0.484059:0.865311:0.484059:0.848843:0.472789:0.848843:0.000000
A B:@0.527598:0.865311:0.555321:0.865311:0.555321:0.848843:0.527598:0.848843:0.000000:0.000000:0.000000
B:@0.581887:0.865311:0.591077:0.865311:0.591077:0.848843:0.581887:0.848843:0.000000
AB:@0.459342:0.893275:0.495118:0.893275:0.495118:0.876806:0.459342:0.876806:0.000000:0.000000
AB:@0.531413:0.893275:0.567188:0.893275:0.567188:0.876806:0.531413:0.876806:0.000000:0.000000
AB:@0.586762:0.893275:0.622537:0.893275:0.622537:0.876806:0.586762:0.876806:0.000000:0.000000
A:@0.472789:0.921253:0.484059:0.921253:0.484059:0.904784:0.472789:0.904784:0.000000
A B:@0.527598:0.921253:0.555321:0.921253:0.555321:0.904784:0.527598:0.904784:0.000000:0.000000:0.000000
B B:@0.581887:0.921253:0.593644:0.920545:0.593644:0.904076:0.581887:0.904784:0.000000:0.000000:0.000000
AB:@0.459342:0.950373:0.495118:0.950373:0.495118:0.933904:0.459342:0.933904:0.000000:0.000000
AB:@0.530430:0.950373:0.566206:0.950373:0.566206:0.933904:0.530430:0.933904:0.000000:0.000000
A:@0.619435:0.950373:0.630705:0.950373:0.630705:0.933904:0.619435:0.933904:0.000000
B:@0.664766:0.950373:0.673955:0.950373:0.673955:0.933904:0.664766:0.933904:0.000000
,:@0.465989:0.760412:0.468744:0.760412:0.468744:0.743915:0.465989:0.743915:0.000000
=2:@0.582350:0.785397:0.604293:0.785397:0.604293:0.768900:0.582350:0.768900:0.000000:0.000000
.:@0.695474:0.785397:0.698229:0.785397:0.698229:0.768900:0.695474:0.768900:0.000000
=(:@0.511262:0.817265:0.530662:0.817265:0.530662:0.800767:0.511262:0.800767:0.000000:0.000000
)(:@0.566745:0.817265:0.585991:0.817265:0.585991:0.800767:0.566745:0.800767:0.000000:0.000000
):@0.622094:0.817265:0.628047:0.817265:0.628047:0.800767:0.622094:0.800767:0.000000
=:@0.452522:0.841339:0.463330:0.841339:0.463330:0.824841:0.452522:0.824841:0.000000
2(:@0.513400:0.841339:0.527791:0.841339:0.527791:0.824841:0.513400:0.824841:0.000000:0.000000
):@0.555822:0.841339:0.561775:0.841339:0.561775:0.824841:0.555822:0.824841:0.000000
=:@0.452522:0.865196:0.463330:0.865196:0.463330:0.848698:0.452522:0.848698:0.000000
2(:@0.512456:0.865196:0.526828:0.865196:0.526828:0.848698:0.512456:0.848698:0.000000:0.000000
):@0.554859:0.865196:0.560811:0.865196:0.560811:0.848698:0.554859:0.848698:0.000000
,:@0.601615:0.865196:0.604370:0.865196:0.604370:0.848698:0.601615:0.848698:0.000000
=(:@0.511262:0.893159:0.530662:0.893159:0.530662:0.876662:0.511262:0.876662:0.000000:0.000000
)(:@0.566745:0.893159:0.585991:0.893159:0.585991:0.876662:0.566745:0.876662:0.000000:0.000000
):@0.622094:0.893159:0.628047:0.893159:0.628047:0.876662:0.622094:0.876662:0.000000
=:@0.452522:0.921137:0.463330:0.921137:0.463330:0.904639:0.452522:0.904639:0.000000
2(:@0.512456:0.921137:0.526828:0.921137:0.526828:0.904639:0.512456:0.904639:0.000000:0.000000
):@0.554859:0.921137:0.560811:0.921137:0.560811:0.904639:0.554859:0.904639:0.000000
,:@0.601615:0.921137:0.604370:0.921137:0.604370:0.904639:0.601615:0.904639:0.000000
=2:@0.582331:0.950257:0.604274:0.950257:0.604274:0.933759:0.582331:0.933759:0.000000:0.000000
.:@0.695455:0.950257:0.698210:0.950257:0.698210:0.933759:0.695455:0.933759:0.000000
2:@0.510879:0.752487:0.516050:0.752487:0.516050:0.742445:0.510879:0.742445:0.000000
2:@0.502928:0.937574:0.508099:0.937574:0.508099:0.927532:0.502928:0.927532:0.000000
2:@0.574191:0.937574:0.579362:0.937574:0.579362:0.927532:0.574191:0.927532:0.000000
2:@0.502752:0.772712:0.507923:0.772712:0.507923:0.762670:0.502752:0.762670:0.000000
2:@0.577521:0.772712:0.582693:0.772712:0.582693:0.762670:0.577521:0.762670:0.000000
2:@0.638249:0.772602:0.643166:0.772602:0.643166:0.763053:0.638249:0.763053:0.000000
2:@0.681592:0.772602:0.686509:0.772602:0.686509:0.763053:0.681592:0.763053:0.000000
2:@0.502752:0.804576:0.507923:0.804576:0.507923:0.794534:0.502752:0.794534:0.000000
2:@0.491612:0.852507:0.496783:0.852507:0.496783:0.842465:0.491612:0.842465:0.000000
2:@0.604258:0.852507:0.609430:0.852507:0.609430:0.842465:0.604258:0.842465:0.000000
2:@0.502752:0.880485:0.507923:0.880485:0.507923:0.870443:0.502752:0.870443:0.000000
2:@0.491612:0.910717:0.496783:0.910717:0.496783:0.900675:0.491612:0.900675:0.000000
2:@0.599274:0.910717:0.604446:0.910717:0.604446:0.900675:0.599274:0.900675:0.000000
2:@0.638242:0.937569:0.643414:0.937569:0.643414:0.927527:0.638242:0.927527:0.000000
2:@0.683824:0.937569:0.688995:0.937569:0.688995:0.927527:0.683824:0.927527:0.000000
R:@0.496168:0.763492:0.510078:0.763492:0.510078:0.742151:0.496168:0.742151:0.000000
∈:@0.482309:0.761049:0.496045:0.761049:0.496045:0.744768:0.482309:0.744768:0.000000
+:@0.472811:0.786034:0.483388:0.786034:0.483388:0.769753:0.472811:0.769753:0.000000
+:@0.510513:0.786034:0.521090:0.786034:0.521090:0.769753:0.510513:0.769753:0.000000
−:@0.543900:0.786034:0.554476:0.786034:0.554476:0.769753:0.543900:0.769753:0.000000
+:@0.645985:0.786034:0.656562:0.786034:0.656562:0.769753:0.645985:0.769753:0.000000
+:@0.472811:0.817901:0.483388:0.817901:0.483388:0.801620:0.472811:0.801620:0.000000
+ ⋅:@0.544901:0.817901:0.579001:0.817901:0.579001:0.801620:0.544901:0.801620:0.000000:0.000000:0.000000
+:@0.600250:0.817901:0.610826:0.817901:0.610826:0.801620:0.600250:0.801620:0.000000
⋅+:@0.479785:0.841975:0.510879:0.841975:0.510879:0.825694:0.479785:0.825694:0.000000:0.000000
⋅+ ⋅:@0.541202:0.841975:0.592679:0.841975:0.592679:0.825694:0.541202:0.825694:0.000000:0.000000:0.000000:0.000000
+:@0.499359:0.865832:0.509935:0.865832:0.509935:0.849551:0.499359:0.849551:0.000000
⋅ +:@0.540239:0.865832:0.573703:0.865832:0.573703:0.849551:0.540239:0.849551:0.000000:0.000000:0.000000
−:@0.472831:0.893795:0.483407:0.893795:0.483407:0.877515:0.472831:0.877515:0.000000
− ⋅:@0.544921:0.893795:0.579020:0.893795:0.579020:0.877515:0.544921:0.877515:0.000000:0.000000:0.000000
−:@0.600269:0.893795:0.610846:0.893795:0.610846:0.877515:0.600269:0.877515:0.000000
−:@0.499359:0.921773:0.509935:0.921773:0.509935:0.905492:0.499359:0.905492:0.000000
⋅ +:@0.540239:0.921773:0.573703:0.921773:0.573703:0.905492:0.540239:0.905492:0.000000:0.000000:0.000000
+:@0.472831:0.950893:0.483407:0.950893:0.483407:0.934613:0.472831:0.934613:0.000000
+:@0.510532:0.950893:0.521109:0.950893:0.521109:0.934613:0.510532:0.934613:0.000000
−:@0.543919:0.950893:0.554495:0.950893:0.554495:0.934613:0.543919:0.934613:0.000000
+:@0.646005:0.950893:0.656581:0.950893:0.656581:0.934613:0.646005:0.934613:0.000000
 no nulos y :@0.523771:0.760596:0.618075:0.760596:0.618075:0.744098:0.523771:0.744098:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0,:@0.657800:0.760596:0.668974:0.760596:0.668974:0.744098:0.657800:0.744098:0.000000:0.000000
[ ]:@0.650262:0.764422:0.689024:0.764422:0.689024:0.741304:0.650262:0.741304:0.000000:0.000000:0.000000
θ∈:@0.624557:0.761232:0.651336:0.761232:0.651336:0.744951:0.624557:0.744951:0.000000:0.000000
π:@0.671102:0.761232:0.681678:0.761232:0.681678:0.744951:0.671102:0.744951:0.000000
 el ángulo que forman los :@0.692352:0.760596:0.895926:0.760596:0.895926:0.744098:0.692352:0.744098:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.891767:0.760596:0.895909:0.760596:0.895909:0.744098:0.891767:0.744098:0.000000
vectores   y  . Entonces, :@0.404240:0.781648:0.590824:0.781643:0.590824:0.765146:0.404240:0.765151:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
BB:@0.468319:0.756539:0.484368:0.756539:0.484368:0.739355:0.468319:0.739355:0.000000:0.000000
ABAB:@0.469566:0.781917:0.508853:0.781917:0.508853:0.764732:0.469566:0.764732:0.000000:0.000000:0.000000:0.000000
AA:@0.469566:0.807294:0.487785:0.807294:0.487785:0.790109:0.469566:0.790109:0.000000:0.000000
BB:@0.468319:0.832671:0.484368:0.832671:0.484368:0.815487:0.468319:0.815487:0.000000:0.000000
AA:@0.469566:0.858049:0.487785:0.858049:0.487785:0.840864:0.469566:0.840864:0.000000:0.000000
ABAB:@0.469566:0.883426:0.508853:0.883426:0.508853:0.866241:0.469566:0.866241:0.000000:0.000000:0.000000:0.000000
ABAB:@0.469566:0.908804:0.514100:0.908804:0.514100:0.891619:0.469566:0.891619:0.000000:0.000000:0.000000:0.000000
BBBB:@0.468319:0.934181:0.502481:0.934181:0.502481:0.916996:0.468319:0.916996:0.000000:0.000000:0.000000:0.000000
BB:@0.468319:0.959558:0.484368:0.959558:0.484368:0.942373:0.468319:0.942373:0.000000:0.000000
. .:@0.518154:0.756389:0.527489:0.756389:0.527489:0.739174:0.518154:0.739174:0.000000:0.000000:0.000000
.=00:@0.485809:0.781766:0.534947:0.781766:0.534947:0.764551:0.485809:0.764551:0.000000:0.000000:0.000000:0.000000
, ,:@0.522336:0.807143:0.531670:0.807143:0.531670:0.789928:0.522336:0.789928:0.000000:0.000000:0.000000
=0.=0.:@0.480863:0.832521:0.513959:0.832521:0.513959:0.815306:0.480863:0.815306:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.=0,0,:@0.485789:0.883290:0.539309:0.883290:0.539309:0.866075:0.485789:0.866075:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
==:@0.484220:0.908668:0.501958:0.908668:0.501958:0.891453:0.484220:0.891453:0.000000:0.000000
=0=0:@0.498976:0.934045:0.528534:0.934045:0.528534:0.916830:0.498976:0.916830:0.000000:0.000000:0.000000:0.000000
=0=0:@0.480863:0.959422:0.510421:0.959422:0.510421:0.942208:0.480863:0.942208:0.000000:0.000000:0.000000:0.000000
22:@0.510461:0.748038:0.522046:0.748038:0.522046:0.738085:0.510461:0.738085:0.000000:0.000000
22:@0.513809:0.798803:0.525394:0.798803:0.525394:0.788850:0.513809:0.788850:0.000000:0.000000
22:@0.513809:0.849568:0.525394:0.849568:0.525394:0.839615:0.513809:0.839615:0.000000:0.000000
∈∈:@0.480883:0.757083:0.501676:0.757083:0.501676:0.740094:0.480883:0.740094:0.000000:0.000000
∈∈:@0.484241:0.807852:0.505034:0.807852:0.505034:0.790864:0.484241:0.790864:0.000000:0.000000
∈∈:@0.484241:0.858622:0.505034:0.858622:0.505034:0.841634:0.484241:0.841634:0.000000:0.000000
⋅⋅:@0.479898:0.934769:0.491384:0.934769:0.491384:0.917781:0.479898:0.917781:0.000000:0.000000
.=:@0.492268:0.781766:0.523126:0.781766:0.523126:0.764551:0.492268:0.764551:0.000000:0.000000
.=:@0.492248:0.883290:0.523106:0.883290:0.523106:0.866075:0.492248:0.866075:0.000000:0.000000
=:@0.572295:0.803866:0.583102:0.803866:0.583102:0.787368:0.572295:0.787368:0.000000
2:@0.678465:0.803866:0.686961:0.803866:0.686961:0.787368:0.678465:0.787368:0.000000
cos( ).:@0.736357:0.803866:0.783345:0.803866:0.783345:0.787368:0.736357:0.787368:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=(:@0.572295:0.830702:0.591695:0.830702:0.591695:0.814204:0.572295:0.814204:0.000000:0.000000
)(:@0.627586:0.830702:0.647256:0.830702:0.647256:0.814204:0.627586:0.814204:0.000000:0.000000
):@0.683128:0.830702:0.689081:0.830702:0.689081:0.814204:0.683128:0.814204:0.000000
=:@0.522937:0.853374:0.533745:0.853374:0.533745:0.836876:0.522937:0.836876:0.000000
2(:@0.578748:0.853374:0.593120:0.853374:0.593120:0.836876:0.578748:0.836876:0.000000:0.000000
):@0.622558:0.853374:0.628511:0.853374:0.628511:0.836876:0.622558:0.836876:0.000000
=:@0.522937:0.876363:0.533745:0.876363:0.533745:0.859866:0.522937:0.859866:0.000000
2( =(:@0.581889:0.876363:0.634135:0.874768:0.634135:0.858270:0.581889:0.859866:0.000000:0.000000:0.000000:0.000000:0.000000
):@0.625698:0.876363:0.631651:0.876363:0.631651:0.859866:0.625698:0.859866:0.000000
. )(:@0.680604:0.876363:0.689696:0.874768:0.689696:0.858270:0.680604:0.859866:0.000000:0.000000:0.000000:0.000000
2:@0.561405:0.792261:0.567062:0.792261:0.567062:0.781278:0.561405:0.781278:0.000000
2:@0.609208:0.792261:0.614864:0.792261:0.614864:0.781278:0.609208:0.781278:0.000000
2:@0.656420:0.792261:0.662077:0.792261:0.662077:0.781278:0.656420:0.781278:0.000000
2:@0.561405:0.819099:0.567062:0.819099:0.567062:0.808115:0.561405:0.808115:0.000000
2:@0.559841:0.864756:0.565497:0.864756:0.565497:0.853772:0.559841:0.853772:0.000000
2:@0.671029:0.864756:0.676685:0.864756:0.676685:0.853772:0.671029:0.853772:0.000000
−:@0.529157:0.804502:0.539734:0.804502:0.539734:0.788221:0.529157:0.788221:0.000000
+:@0.618529:0.804502:0.629105:0.804502:0.629105:0.788221:0.618529:0.788221:0.000000
−:@0.666160:0.804502:0.676737:0.804502:0.676737:0.788221:0.666160:0.788221:0.000000
θ:@0.765472:0.804502:0.775510:0.804502:0.775510:0.788221:0.765472:0.788221:0.000000
−:@0.529165:0.831338:0.539741:0.831338:0.539741:0.815057:0.529165:0.815057:0.000000
−:@0.603394:0.831338:0.613970:0.831338:0.613970:0.815057:0.603394:0.815057:0.000000
⋅−:@0.635027:0.831338:0.669531:0.831338:0.669531:0.815057:0.635027:0.815057:0.000000:0.000000
⋅−:@0.548064:0.854010:0.577020:0.854010:0.577020:0.837729:0.548064:0.837729:0.000000:0.000000
⋅+ ⋅:@0.606534:0.854010:0.660920:0.854010:0.660920:0.837729:0.606534:0.837729:0.000000:0.000000:0.000000:0.000000
− −:@0.569564:0.877000:0.582174:0.875404:0.582174:0.859123:0.569564:0.860719:0.000000:0.000000:0.000000
⋅ + −:@0.609674:0.877000:0.656403:0.875404:0.656403:0.859123:0.609674:0.860719:0.000000:0.000000:0.000000:0.000000:0.000000
BA:@0.517064:0.803982:0.553879:0.803982:0.553879:0.787513:0.517064:0.787513:0.000000:0.000000
B:@0.591408:0.803982:0.600598:0.803982:0.600598:0.787513:0.591408:0.787513:0.000000
A:@0.637645:0.803982:0.648915:0.803982:0.648915:0.787513:0.637645:0.787513:0.000000
AB:@0.695383:0.803982:0.728384:0.803982:0.728384:0.787513:0.695383:0.787513:0.000000:0.000000
BA:@0.517064:0.830818:0.553879:0.830818:0.553879:0.814349:0.517064:0.814349:0.000000:0.000000
BA BA:@0.591293:0.830818:0.683650:0.830818:0.683650:0.814349:0.591293:0.814349:0.000000:0.000000:0.000000:0.000000:0.000000
BB:@0.536367:0.853489:0.563512:0.853489:0.563512:0.837020:0.536367:0.837020:0.000000:0.000000
AB:@0.593855:0.853489:0.622001:0.853489:0.622001:0.837020:0.593855:0.837020:0.000000:0.000000
AA:@0.643424:0.853489:0.674807:0.853489:0.674807:0.837020:0.643424:0.837020:0.000000:0.000000
B BA:@0.542012:0.876479:0.596322:0.874883:0.596322:0.858415:0.542012:0.860010:0.000000:0.000000:0.000000:0.000000
A B BA BA:@0.596976:0.876479:0.726092:0.874883:0.726092:0.858415:0.596976:0.860010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.652209:0.876479:0.663480:0.876479:0.663480:0.860010:0.652209:0.860010:0.000000
Demostración. :@0.404235:0.847110:0.524411:0.847110:0.524411:0.830164:0.404235:0.830164:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. De la definición del producto escalar, se tiene: :@0.517630:0.846647:0.852685:0.846647:0.852685:0.830149:0.517630:0.830149:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.614735:0.847932:0.625543:0.847932:0.625543:0.831434:0.614735:0.831434:0.000000
2:@0.720906:0.847932:0.729402:0.847932:0.729402:0.831434:0.720906:0.831434:0.000000
cos( ).:@0.778798:0.847932:0.825786:0.847932:0.825786:0.831434:0.778798:0.831434:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
):@0.725568:0.874768:0.731521:0.874768:0.731521:0.858270:0.725568:0.858270:0.000000
=:@0.565377:0.897439:0.576185:0.897439:0.576185:0.880942:0.565377:0.880942:0.000000
2(:@0.621189:0.897439:0.635561:0.897439:0.635561:0.880942:0.621189:0.880942:0.000000:0.000000
):@0.664998:0.897439:0.670951:0.897439:0.670951:0.880942:0.664998:0.880942:0.000000
=:@0.565377:0.920429:0.576185:0.920429:0.576185:0.903932:0.565377:0.903932:0.000000
2(:@0.624329:0.920429:0.638701:0.920429:0.638701:0.903932:0.624329:0.903932:0.000000:0.000000
):@0.668138:0.920429:0.674091:0.920429:0.674091:0.903932:0.668138:0.903932:0.000000
.:@0.723044:0.920429:0.725799:0.920429:0.725799:0.903932:0.723044:0.903932:0.000000
2:@0.603846:0.836327:0.609502:0.836327:0.609502:0.825343:0.603846:0.825343:0.000000
2:@0.651648:0.836327:0.657305:0.836327:0.657305:0.825343:0.651648:0.825343:0.000000
2:@0.698861:0.836327:0.704517:0.836327:0.704517:0.825343:0.698861:0.825343:0.000000
2:@0.603846:0.863165:0.609502:0.863165:0.609502:0.852181:0.603846:0.852181:0.000000
2:@0.602281:0.908821:0.607937:0.908821:0.607937:0.897838:0.602281:0.897838:0.000000
2:@0.713470:0.908821:0.719126:0.908821:0.719126:0.897838:0.713470:0.897838:0.000000
−:@0.571598:0.848568:0.582174:0.848568:0.582174:0.832287:0.571598:0.832287:0.000000
+:@0.660969:0.848568:0.671546:0.848568:0.671546:0.832287:0.660969:0.832287:0.000000
−:@0.708593:0.848568:0.719170:0.848568:0.719170:0.832287:0.708593:0.832287:0.000000
θ:@0.807905:0.848568:0.817942:0.848568:0.817942:0.832287:0.807905:0.832287:0.000000
⋅−:@0.677460:0.875404:0.711964:0.875404:0.711964:0.859123:0.677460:0.859123:0.000000:0.000000
⋅−:@0.590497:0.898076:0.619453:0.898076:0.619453:0.881795:0.590497:0.881795:0.000000:0.000000
⋅+ ⋅:@0.648967:0.898076:0.703353:0.898076:0.703353:0.881795:0.648967:0.881795:0.000000:0.000000:0.000000:0.000000
−:@0.611997:0.921065:0.622574:0.921065:0.622574:0.904785:0.611997:0.904785:0.000000
⋅ +:@0.652107:0.921065:0.686130:0.921065:0.686130:0.904785:0.652107:0.904785:0.000000:0.000000:0.000000
BA:@0.559506:0.848048:0.596322:0.848048:0.596322:0.831579:0.559506:0.831579:0.000000:0.000000
B:@0.633850:0.848048:0.643040:0.848048:0.643040:0.831579:0.633850:0.831579:0.000000
A:@0.680087:0.848048:0.691357:0.848048:0.691357:0.831579:0.680087:0.831579:0.000000
AB:@0.737825:0.848048:0.770826:0.848048:0.770826:0.831579:0.737825:0.831579:0.000000:0.000000
BB:@0.578810:0.897555:0.605954:0.897555:0.605954:0.881086:0.578810:0.881086:0.000000:0.000000
AB:@0.636297:0.897555:0.664444:0.897555:0.664444:0.881086:0.636297:0.881086:0.000000:0.000000
AA:@0.685867:0.897555:0.717250:0.897555:0.717250:0.881086:0.685867:0.881086:0.000000:0.000000
A B:@0.639418:0.920545:0.667565:0.920545:0.667565:0.904076:0.639418:0.904076:0.000000:0.000000:0.000000
A:@0.694652:0.920545:0.705922:0.920545:0.705922:0.904076:0.694652:0.904076:0.000000
Sismo Manabí. www.flirckagenciaandes_ec:@0.140887:0.793537:0.140887:0.674625:0.129418:0.674625:0.129418:0.793537:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad:@0.199644:0.506356:0.346429:0.506356:0.346429:0.490884:0.199644:0.490884:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática y Geología:@0.199880:0.535407:0.358578:0.535407:0.358578:0.519935:0.199880:0.519935:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los geólogos usan el teorema :@0.153337:0.550827:0.347950:0.550827:0.347950:0.535764:0.153337:0.535764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de Pitágoras cuando se rastrea :@0.153337:0.566669:0.353105:0.566669:0.353105:0.551606:0.153337:0.551606:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la actividad de un terremoto. :@0.153337:0.582511:0.344768:0.582511:0.344768:0.567448:0.153337:0.567448:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los terremotos tienen dos tipo :@0.153337:0.598353:0.357450:0.598353:0.357450:0.583290:0.153337:0.583290:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de ondas y una es más lenta :@0.153337:0.614195:0.339383:0.614195:0.339383:0.599132:0.153337:0.599132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que la otra.:@0.153337:0.630037:0.225701:0.630037:0.225701:0.614974:0.153337:0.614974:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.153344:0.811671:0.164824:0.811671:0.164824:0.801646:0.153344:0.801646:0.000000
 Sismo provincia de Manabí 2016.:@0.164824:0.812379:0.330310:0.812379:0.330310:0.800902:0.164824:0.800902:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Al triangular la distancia recorri-:@0.153344:0.844708:0.359728:0.844708:0.359728:0.829645:0.153344:0.829645:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
da por la onda más rápida con :@0.153344:0.860550:0.355256:0.860550:0.355256:0.845487:0.153344:0.845487:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la correspondiente a la onda :@0.153344:0.876392:0.341045:0.876392:0.341045:0.861329:0.153344:0.861329:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
más lenta, los geólogos pueden :@0.153344:0.892234:0.357228:0.892234:0.357228:0.877171:0.153344:0.877171:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
determinar el centro o la fuente :@0.153344:0.908076:0.360289:0.908076:0.360289:0.893013:0.153344:0.893013:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
del terremoto.:@0.153344:0.923918:0.245604:0.923918:0.245604:0.908855:0.153344:0.908855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000