Pythagoras und der Abstand von Punkten

Bewegen Sie auf der linken Seite die Eckpunkte des rechtwinkligen Dreiecks.[br]Die Flächeninhalte der beiden kleinen Quadrate sind zusammen stets genauso groß, wie der Flächeninhalt des großen Quadrats.
Sie können im Folgenden Applet die beiden Punkte bewegen.[br]Der Abstand der beiden Punkte ergibt sich als die Länge der Hypotenuse eines Dreiecks mit den Seitenlängen [math]x_2-x_1[/math] und [math]y_2-y_1[/math].[br]
Abstand zweier Punkte in 2 Dimensionen
Den Abstand zweier Punkte im 2.dimensionalen Koordinatensystem kann man mit der Formel[br][math]|AB|^2=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/math][br]berechnen.
Abstand zweier Punkte in 3 Dimensionen
Der Abstand der Punkte[br][math]A(x_A|y_A|z_A)[/math] und [math]B(x_B|y_B|z_B)[/math] soll berechnet werden.[br]Dazu kann man sich zunächst vorstellen, dass man nur den Abstand in einer Ebene die parallel zur xy-Ebene liegt berechnet. Das geht mit der Formel für 2 Dimensionen[br][math]|AB|_{2D}=\sqrt{(x_B-x_A)^2+(y_b-y_A)^2}[/math][br]Mit der Verbindungslinie der Punkte in der Ebene lässt sich anschließend erneut ein rechtwinkliges Dreieck zeichnen. [br][math]|AB|^2=|AB|_{2D}^2+(z_B-z_A)^2[/math][br]Damit ergibt sich die folgende Formel[br][img]data:image/png;base64,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[/img][br]

Information: Pythagoras und der Abstand von Punkten