33:@0.942772:0.974518:0.963274:0.974518:0.963274:0.956333:0.942772:0.956333:0.000000:0.000000
Pensamiento numérico:@0.721207:0.043661:0.926911:0.043661:0.926911:0.024916:0.721207:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DBA 2 (Ev. 3) Construye varias representaciones (geométrica, decimales o no decimales) de un mismo número racional o irracional.:@0.083241:0.964785:0.770216:0.964785:0.770216:0.952833:0.083241:0.952833:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DBA 7 (Ev. 5) Resuelve problemas utilizando teoremas básicos.:@0.083241:0.976888:0.409496:0.976888:0.409496:0.964936:0.083241:0.964936:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los números irracionales :@0.740193:0.783142:0.906978:0.783142:0.906978:0.768202:0.740193:0.768202:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
son muy importantes :@0.740193:0.798271:0.885915:0.798271:0.885915:0.783331:0.740193:0.783331:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuando se realizan cálculos :@0.740193:0.813400:0.922854:0.813400:0.922854:0.798460:0.740193:0.798460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
geométricos. Por ejemplo, :@0.740193:0.828529:0.916177:0.828529:0.916177:0.813589:0.740193:0.813589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el número   se utiliza para :@0.740193:0.843658:0.919179:0.843658:0.919179:0.828718:0.740193:0.828718:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.811781:0.843153:0.822942:0.843153:0.822942:0.830685:0.811781:0.830685:0.000000
calcular áreas y el volumen :@0.740193:0.858787:0.920708:0.858787:0.920708:0.843847:0.740193:0.843847:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de formas circulares o :@0.740193:0.873916:0.887495:0.873916:0.887495:0.858976:0.740193:0.858976:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
esféricas. :@0.740193:0.889045:0.802356:0.889045:0.802356:0.874105:0.740193:0.874105:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Responde:@0.802243:0.889045:0.871666:0.889045:0.871666:0.873890:0.802243:0.873890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: :@0.871571:0.889045:0.878147:0.889045:0.878147:0.874105:0.871571:0.874105:0.000000:0.000000
¿cuál es el valor de π?, :@0.740193:0.904174:0.888405:0.904174:0.888405:0.889234:0.740193:0.889234:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿es un número racional o :@0.740193:0.919302:0.910303:0.919302:0.910303:0.904363:0.740193:0.904363:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
irracional?:@0.740193:0.934431:0.806955:0.934431:0.806955:0.919492:0.740193:0.919492:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad :@0.740193:0.725435:0.906567:0.725435:0.906567:0.708488:0.740193:0.708488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática:@0.740193:0.742077:0.826380:0.742077:0.826380:0.725643:0.740193:0.725643:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y Geometría:@0.740193:0.758719:0.829327:0.758719:0.829327:0.742285:0.740193:0.742285:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.740294:0.144831:0.848854:0.144831:0.848854:0.127884:0.740294:0.127884:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.740294:0.161472:0.837769:0.161472:0.837769:0.144526:0.740294:0.144526:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Existen tres números :@0.740294:0.182996:0.880723:0.182996:0.880723:0.168056:0.740294:0.168056:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
irracionales muy famosos::@0.740294:0.198125:0.910270:0.198125:0.910270:0.183185:0.740294:0.183185:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.  El número  , que se :@0.740294:0.213254:0.895420:0.213254:0.895420:0.198314:0.740294:0.198314:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.830486:0.212749:0.841647:0.212749:0.841647:0.200281:0.830486:0.200281:0.000000
obtiene de dividir la :@0.759267:0.228383:0.894158:0.228383:0.894158:0.213443:0.759267:0.213443:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
longitud de cualquier :@0.759267:0.243512:0.905179:0.243512:0.905179:0.228572:0.759267:0.228572:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
circunferencia entre su :@0.759267:0.258641:0.912694:0.258641:0.912694:0.243701:0.759267:0.243701:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
diámetro.  :@0.759267:0.273770:0.829315:0.273770:0.829315:0.258830:0.759267:0.258830:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.758647:0.288394:0.769808:0.288394:0.772727:0.275925:0.761565:0.275925:0.000000
   3,141592... Como :@0.770344:0.288898:0.907473:0.288898:0.907473:0.273959:0.770344:0.273959:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.773942:0.288394:0.787882:0.288394:0.787882:0.275925:0.773942:0.275925:0.000000
es irracional, es decimal :@0.759267:0.304027:0.917842:0.304027:0.917842:0.289088:0.759267:0.289088:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
infinito no periódico. :@0.759267:0.319156:0.899878:0.319156:0.899878:0.304217:0.759267:0.304217:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.  El número de Euler, que :@0.740294:0.334285:0.919368:0.334285:0.919368:0.319345:0.740294:0.319345:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es la base de la función :@0.759267:0.349414:0.915845:0.349414:0.915845:0.334474:0.759267:0.334474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
exponencial que más :@0.759267:0.364543:0.904266:0.364543:0.904266:0.349603:0.759267:0.349603:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
adelante vamos a :@0.759267:0.379672:0.878974:0.379672:0.878974:0.364732:0.759267:0.364732:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
estudiar a detalle.  :@0.759267:0.394801:0.881541:0.394801:0.881541:0.379861:0.759267:0.379861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
e:@0.759267:0.411758:0.767053:0.411758:0.767053:0.395352:0.759267:0.395352:0.000000
   2,7182818284...:@0.766804:0.411443:0.888392:0.411443:0.888392:0.396503:0.766804:0.396503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.770401:0.410939:0.784341:0.410939:0.784341:0.398470:0.770401:0.398470:0.000000
3.  El número áureo o :@0.740294:0.426572:0.884618:0.426572:0.884618:0.411632:0.740294:0.411632:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
número de oro  , que :@0.759267:0.441701:0.908531:0.441701:0.908531:0.426761:0.759267:0.426761:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
w:@0.862347:0.441196:0.872572:0.441196:0.872572:0.428728:0.862347:0.428728:0.000000
se ha usado como :@0.759267:0.456830:0.883547:0.456830:0.883547:0.441890:0.759267:0.441890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
elemento de diseño :@0.759267:0.471959:0.895708:0.471959:0.895708:0.457019:0.759267:0.457019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en construcciones :@0.759267:0.487088:0.883833:0.487088:0.883833:0.472148:0.759267:0.472148:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
arquitectónicas tan :@0.759267:0.502217:0.889480:0.502217:0.889480:0.487277:0.759267:0.487277:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
antiguas como la :@0.759267:0.517345:0.876435:0.517345:0.876435:0.502406:0.759267:0.502406:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
pirámide de Keops, :@0.759267:0.532474:0.889761:0.532474:0.889761:0.517535:0.759267:0.517535:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
siempre con el :@0.759267:0.547603:0.860050:0.547603:0.860050:0.532664:0.759267:0.532664:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propósito de crear :@0.759267:0.562732:0.883931:0.562732:0.883931:0.547792:0.759267:0.547792:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
belleza, armonía y :@0.759267:0.577861:0.881618:0.577861:0.881618:0.562921:0.759267:0.562921:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
perfección.  :@0.759267:0.592990:0.839991:0.592990:0.839991:0.578050:0.759267:0.578050:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
w:@0.758647:0.607615:0.768871:0.607615:0.771790:0.595146:0.761565:0.595146:0.000000
   1,618...:@0.769407:0.608119:0.834301:0.608119:0.834301:0.593179:0.769407:0.593179:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.773005:0.607615:0.786944:0.607615:0.786944:0.595146:0.773005:0.595146:0.000000
3.1 Representación de números irracionales en la recta numérica:@0.073089:0.136363:0.579290:0.136363:0.579290:0.119417:0.073089:0.119417:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 2:@0.073089:0.167303:0.148872:0.167303:0.148872:0.150634:0.073089:0.150634:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Representa   2 y    2 en la recta numérica.:@0.073089:0.198237:0.380837:0.198237:0.380837:0.181803:0.073089:0.181803:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.192506:0.197682:0.207839:0.197682:0.207839:0.183967:0.192506:0.183967:0.000000
Solución:@0.073089:0.229174:0.139222:0.229174:0.139222:0.212505:0.073089:0.212505:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En la recta numérica, ubicamos la unidad. Sobre el final de esta, levantamos una :@0.073089:0.260114:0.710514:0.260114:0.710514:0.243681:0.073089:0.243681:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
perpendicular de medida igual a la unidad y unimos los dos segmentos, formando un :@0.073089:0.276756:0.709961:0.276756:0.709961:0.260322:0.073089:0.260322:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
triángulo rectángulo.:@0.073089:0.293398:0.225252:0.293398:0.225252:0.276964:0.073089:0.276964:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.539802:0.377717:0.545881:0.377717:0.545881:0.366782:0.539802:0.366782:0.000000
–1:@0.301744:0.389513:0.313388:0.389513:0.313388:0.379056:0.301744:0.379056:0.000000:0.000000
–2:@0.242918:0.389513:0.254561:0.389513:0.254561:0.379056:0.242918:0.379056:0.000000:0.000000
0:@0.371160:0.389513:0.376876:0.389513:0.376876:0.379056:0.371160:0.379056:0.000000
0:@0.349337:0.373602:0.355616:0.373602:0.355616:0.362817:0.349337:0.362817:0.000000
1:@0.352968:0.343066:0.359247:0.343066:0.359247:0.332282:0.352968:0.332282:0.000000
1:@0.444195:0.354292:0.450473:0.354292:0.450473:0.343508:0.444195:0.343508:0.000000
1:@0.394376:0.389513:0.400655:0.389513:0.400655:0.378729:0.394376:0.378729:0.000000
1:@0.423614:0.389513:0.429330:0.389513:0.429330:0.379056:0.423614:0.379056:0.000000
2:@0.481151:0.389513:0.486868:0.389513:0.486868:0.379056:0.481151:0.379056:0.000000
C:@0.380168:0.353948:0.386669:0.353948:0.386669:0.343331:0.380168:0.343331:0.000000
Aplicamos el teorema de Pitágoras para obtener la medida de la hipotenusa.:@0.073089:0.435277:0.626783:0.435277:0.626783:0.418843:0.073089:0.418843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c :@0.303429:0.466215:0.314326:0.466215:0.314326:0.449809:0.303429:0.449809:0.000000:0.000000
5 :@0.314268:0.465660:0.334111:0.465660:0.334111:0.451944:0.314268:0.451944:0.000000:0.000000
1  :@0.338621:0.466215:0.356745:0.466215:0.356745:0.449781:0.338621:0.449781:0.000000:0.000000:0.000000
2:@0.347523:0.460151:0.352760:0.460151:0.352760:0.450570:0.347523:0.450570:0.000000
1 :@0.356671:0.465660:0.376515:0.465660:0.376515:0.451944:0.356671:0.451944:0.000000:0.000000
1   :@0.376422:0.466215:0.412872:0.466215:0.412872:0.449781:0.376422:0.449781:0.000000:0.000000:0.000000:0.000000
2:@0.385317:0.460151:0.390553:0.460151:0.390553:0.450570:0.385317:0.450570:0.000000
c:@0.427160:0.466215:0.434817:0.466215:0.434817:0.449809:0.427160:0.449809:0.000000
     2:@0.434743:0.466215:0.475996:0.466215:0.475996:0.449781:0.434743:0.449781:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.438701:0.465660:0.454034:0.465660:0.454034:0.451944:0.438701:0.451944:0.000000
Tomamos un compás para trasladar la medida de la hipotenusa sobre la recta numérica. :@0.073089:0.497151:0.710766:0.497151:0.710766:0.480717:0.073089:0.480717:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Lo obtenido a la derecha de 0 es   2, y lo marcado a la izquierda es    2.:@0.073089:0.513793:0.590024:0.513793:0.590024:0.497359:0.073089:0.497359:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.553540:0.513238:0.568874:0.513238:0.568874:0.499522:0.553540:0.499522:0.000000
x:@0.563082:0.622030:0.572635:0.622030:0.572635:0.604847:0.563082:0.604847:0.000000
–1:@0.286284:0.633226:0.301254:0.633226:0.301254:0.619780:0.286284:0.619780:0.000000:0.000000
–2:@0.217879:0.633226:0.232849:0.633226:0.232849:0.619780:0.217879:0.619780:0.000000:0.000000
–  2:@0.244787:0.648919:0.267197:0.648919:0.267197:0.635473:0.244787:0.635473:0.000000:0.000000:0.000000:0.000000
0:@0.366973:0.633227:0.374322:0.633227:0.374322:0.619781:0.366973:0.619781:0.000000
0:@0.336581:0.615980:0.344653:0.615980:0.344653:0.602114:0.336581:0.602114:0.000000
1:@0.345828:0.579217:0.353900:0.579217:0.353900:0.565351:0.345828:0.565351:0.000000
1:@0.435950:0.601002:0.444022:0.601002:0.444022:0.587137:0.435950:0.587137:0.000000
1:@0.393976:0.633227:0.402049:0.633227:0.402049:0.619361:0.393976:0.619361:0.000000
1:@0.427968:0.633227:0.435317:0.633227:0.435317:0.619781:0.427968:0.619781:0.000000
2:@0.494882:0.633227:0.502231:0.633227:0.502231:0.619781:0.494882:0.619781:0.000000
C:@0.377470:0.591879:0.385829:0.591879:0.385829:0.578229:0.377470:0.578229:0.000000
2:@0.470472:0.648919:0.477821:0.648919:0.477821:0.635473:0.470472:0.635473:0.000000
Conjunto de números reales:@0.073089:0.681955:0.278981:0.681955:0.278981:0.665521:0.073089:0.665521:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El conjunto  formado  por  la unión del  conjunto de  los  números  racionales :@0.073089:0.712895:0.710366:0.712895:0.710366:0.696461:0.073089:0.696461:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y del conjunto de los números irracionales es el conjunto de los números reales.:@0.073089:0.729536:0.651064:0.729536:0.651064:0.713103:0.073089:0.713103:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3.2 Densidad de los números irracionales:@0.073089:0.760476:0.394752:0.760476:0.394752:0.743529:0.073089:0.743529:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Esta propiedad establece que siempre, entre dos números irracionales, hay otro número :@0.073089:0.791416:0.710830:0.791416:0.710830:0.774982:0.073089:0.774982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
irracional. En notación matemática, se escribe::@0.073089:0.808058:0.406028:0.808058:0.406028:0.791624:0.073089:0.791624:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si  ,   :@0.251768:0.838998:0.297418:0.838998:0.297418:0.822564:0.251768:0.822564:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.267948:0.838998:0.293460:0.838998:0.293460:0.822592:0.267948:0.822592:0.000000:0.000000:0.000000
[:@0.297344:0.838859:0.312678:0.838859:0.312678:0.824811:0.297344:0.824811:0.000000
Q:@0.312586:0.838998:0.324458:0.838998:0.324458:0.822592:0.312586:0.822592:0.000000
´ y      , :@0.324385:0.838998:0.394424:0.838998:0.394424:0.822564:0.324385:0.822564:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.345737:0.838998:0.354996:0.838998:0.354996:0.822592:0.345737:0.822592:0.000000
,:@0.358880:0.838443:0.374213:0.838443:0.374213:0.824728:0.358880:0.824728:0.000000
b:@0.378079:0.838998:0.387337:0.838998:0.387337:0.822592:0.378079:0.822592:0.000000
] [:@0.394332:0.838859:0.432490:0.838859:0.432490:0.824811:0.394332:0.824811:0.000000:0.000000:0.000000
c Q a   c:@0.409573:0.838998:0.495296:0.838998:0.495296:0.822592:0.409573:0.822592:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
´: :@0.444197:0.838998:0.456806:0.838998:0.456806:0.822564:0.444197:0.822564:0.000000:0.000000:0.000000
, ,:@0.469158:0.838443:0.514532:0.838443:0.514532:0.824728:0.469158:0.824728:0.000000:0.000000:0.000000
   :@0.495241:0.838998:0.518471:0.838998:0.518471:0.822564:0.495241:0.822564:0.000000:0.000000:0.000000
b:@0.518397:0.838998:0.527656:0.838998:0.527656:0.822592:0.518397:0.822592:0.000000
Esto significa que los números irracionales no poseen, ni sucesor, ni antecesor.:@0.073070:0.869938:0.637019:0.869938:0.637019:0.853504:0.073070:0.853504:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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