Kreise 2012 13: Unterschied zwischen den Versionen
*m.g.* (Diskussion | Beiträge) (→Aufgabe 1) |
*m.g.* (Diskussion | Beiträge) (→DerAlgorithmus von Bresenham) |
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(28 dazwischenliegende Versionen von einem Benutzer werden nicht angezeigt) | |||
Zeile 7: | Zeile 7: | ||
Lassen Sie die folgenden Punktmengen in der obigen Geogebraapplikation grafisch darstellen. Um was für geometrische Objekte handelt es ich in jedem Fall? Begründen Sie Ihre Antwort. | Lassen Sie die folgenden Punktmengen in der obigen Geogebraapplikation grafisch darstellen. Um was für geometrische Objekte handelt es ich in jedem Fall? Begründen Sie Ihre Antwort. | ||
# <math>\left\{P\left(x_P|y_P\right)|x_P^2+y_P^2=1, x_P,x_P \in \mathbb{R} \right\}</math> | # <math>\left\{P\left(x_P|y_P\right)|x_P^2+y_P^2=1, x_P,x_P \in \mathbb{R} \right\}</math> | ||
+ | # <math>\left\{P\left(x_P|y_P\right)|\left(x_P-3\right)^2+\left(y_P-2\right)^2=5^2, x_P,y_P \in \mathbb{R}\right\}</math> | ||
+ | ==Aufgabe 2== | ||
+ | Lassen Sie die folgenden Kreise mittels Geoegebra grafisch darstellen, indem Sie jeweils eine entsprechende Gleichung in die Eingabezeile eintragen. | ||
+ | # Mittelpunkt: <math>M(0|0)</math> Radius: <math>r=5</math> | ||
+ | # Mittelpunkt: <math>A(2|2)</math> Radius: <math>r=4</math> | ||
+ | =Kreise in der synthetischen Geometrie= | ||
+ | ==Vereinbarung== | ||
+ | Alle unsere folgenden Betrachtungen beziehen sich auf die Geometrie in der Ebene. | ||
+ | ==Kreisdefinition== | ||
+ | {{Definition|1=Es seien <math>M</math> ein Punkt und <math>r</math> eine positive reelle Zahl. Unter dem Kreis mit dem Mittelpunkt <math>M</math> und dem radius <math>r</math> versteht man ...}} | ||
+ | =Abstände von Punkten= | ||
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+ | <br /><br /> | ||
+ | Wir beziehen uns auf die obigen Punkte <math>A\left(x_A,y_A\right)</math> und <math>B\left(x_B,y_B\right)</math>.<br /> | ||
+ | Der Punkt <math>C </math> ist der Schnittpunkt der Senkrechten durch <math>A</math> auf die x-Achse mit der Senkrechten von <math>B</math> auf die y-Achse.<br /> Der Punkt <math>C</math> hat damit die Koordinaten <math>\left(x_A-x_B|y_A-y_B\right)</math>. | ||
+ | <br /> | ||
+ | Das Dreieck <math>\overline{ABC}</math> ist rechtwinklig. Nach dem Satz des Pythagoras gilt:<br /> | ||
+ | (I) <math>|AB|^2=|AC|^2+|BC|^2</math><br /> | ||
+ | Unter Berücksichtigung der Koordinaten von <math>A, B, C</math> schreibt sich (I) wie folgt:<br /> | ||
+ | (II) <math>|AB|^2=\left(x_A-x_B\right)^2+\left(y_A-y_B\right)^2</math><br /><br /> | ||
+ | Abstand zweier Punkte: | ||
+ | {| class="wikitable" | ||
+ | | <math>|AB|=\sqrt{\left(x_A-x_B\right)^2+\left(y_A-y_B\right)^2}</math> | ||
+ | |- | ||
+ | |||
+ | |} | ||
+ | |||
+ | |||
+ | =Analytische Beschreibung von Kreisen mittels des Satzes von Pythagoras= | ||
+ | ==Kreis in Mittelpunktslage== | ||
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+ | |||
+ | <br /><br /> | ||
+ | Kreis <math>k</math> in Mittelpunktslage, Radius:r<br /><br /> | ||
+ | |||
+ | {| class="wikitable" | ||
+ | |||
+ | |||
+ | | <math>k=\left{A\left(x_A|y_A\right)|x_A^2+y_A^2=r^2\right}</math> | ||
+ | |- | ||
+ | |||
+ | |} | ||
+ | |||
+ | ==allgemeine Lage== | ||
+ | =DerAlgorithmus von Bresenham= | ||
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" 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+ | [[Kategorie:Linalg]] | ||
|} | |} | ||
</div> | </div> |
Aktuelle Version vom 1. November 2012, 09:19 Uhr
Aufgaben zum Einstieg
Aufgabe 1Lassen Sie die folgenden Punktmengen in der obigen Geogebraapplikation grafisch darstellen. Um was für geometrische Objekte handelt es ich in jedem Fall? Begründen Sie Ihre Antwort. Aufgabe 2Lassen Sie die folgenden Kreise mittels Geoegebra grafisch darstellen, indem Sie jeweils eine entsprechende Gleichung in die Eingabezeile eintragen.
Kreise in der synthetischen GeometrieVereinbarungAlle unsere folgenden Betrachtungen beziehen sich auf die Geometrie in der Ebene. KreisdefinitionDefinition Es seien Abstände von Punkten
Analytische Beschreibung von Kreisen mittels des Satzes von PythagorasKreis in Mittelpunktslage
allgemeine LageDerAlgorithmus von Bresenham
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