Proporción raíz de 2

[code][/code]Raíz de 2 representa la relación entre la diagonal de un cuadrado y su lado.[br][img]data:image/png;base64,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[/img][center][/center]En la siguiente actividad vamos a ver cómo se puede dividir un segmento dado AB en dos partes que guarden entre sí esta proporción. En los tres pasos se detalla el proceso. Fíjate bien cómo se va desarrollando para que puedas contestas, con dos decimales, a las preguntas que se formulan.[br][br][br]
Contesta a las siguientes preguntas, utilizando el applet anterior
¿Cuánto mide AC? [br][br]Por tanto, AF mide .....[br][br]¿Cuál es el resultado de dividir FB entre AF?
Papiroflexia
Partiendo de una hoja de papel cuadrada, puedes conseguir un rectángulo que tenga esta proporción entre sus lados siguiendo estos pasos. Inténtalo.[br][img]data:image/png;base64,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[/img]
¿Cómo saber si un rectángulo está en proporción raíz de 2?
Fíjate en los pasos que se indican en el applet de debajo. [br]Utiliza ese procedimiento para comprobar si el rectángulo de la actividad que va a continuación tiene o no esta proporción.
PROPIEDADES
[br]El rectángulo con proporciones raíz de dos es importante a nivel práctico porque resuelve el problema de la duplicación manteniendo las proporciones. Si dividimos un rectángulo en dos rectángulos iguales, las dos partes en que se divide ya no mantienen, en general, la misma proporción. Puedes comprobarlo en el siguiente applet, en el cual tienes un rectángulo azul que puedes cambiar de tamaño de los puntos B y C. y un rectángulo amarillo que es la mitad del azul.[br]En la aplicación van apareciendo la relación entre los lados (lado mayor/lado menor) de los dos rectángulos. Como puedes ver son distintos números. ¿Habrá algún rectángulo para el que se obtenga la misma proporción de los lados?[br][br][br]
Una aplicación de esta propiedad la encontramos en los formatos DIN. Un DIN A0 es una hoja de [b]1m[/b][sup][b]2[/b] [/sup]con proporción de raíz de dos entre sus lados.[br]Al cortarla por la mitad se obtiene el DIN A1, volviendo a cortar por la mitad, el DIN A2, etc.[br][br][img]https://www.bilder-plus.de/bilder/bilder/din-a-formate.jpg[/img][br]¿Cuánto medirán los lados del A0?
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Information: Proporción raíz de 2