http://geometrie.idea-sketch.com/index.php?action=history&feed=atom&title=Zu_den_L%C3%B6sungen_Serie_04_WiSe_2011%2F12 Zu den Lösungen Serie 04 WiSe 2011/12 - Versionsgeschichte 2026-08-11T04:13:48Z Versionsgeschichte dieser Seite in Geometrie-Wiki MediaWiki 1.43.9 http://geometrie.idea-sketch.com/index.php?title=Zu_den_L%C3%B6sungen_Serie_04_WiSe_2011/12&diff=11796&oldid=prev HecklF: /* Aufgabe 4.2 */ 2012-04-20T18:52:23Z <p><span class="autocomment">Aufgabe 4.2</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 20. April 2012, 18:52 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l71">Zeile 71:</td> <td colspan="2" class="diff-lineno">Zeile 71:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Und noch kurz ikonisch nachgeschickt:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Und noch kurz ikonisch nachgeschickt:</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;br /&gt;&lt;br /&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; 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color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;br /&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;br /&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>--[[Benutzer:HecklF|Flo60]] 20:45, 20. Apr. 2012 (CEST)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>--[[Benutzer:HecklF|Flo60]] 20:45, 20. Apr. 2012 (CEST)</div></td></tr> <!-- diff cache key geometrie:diff:1.41:old-11795:rev-11796:php=table --> </table> HecklF http://geometrie.idea-sketch.com/index.php?title=Zu_den_L%C3%B6sungen_Serie_04_WiSe_2011/12&diff=11795&oldid=prev HecklF: /* Aufgabe 4.2 */ 2012-04-20T18:48:36Z <p><span class="autocomment">Aufgabe 4.2</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 20. April 2012, 18:48 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l71">Zeile 71:</td> <td colspan="2" class="diff-lineno">Zeile 71:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Und noch kurz ikonisch nachgeschickt:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Und noch kurz ikonisch nachgeschickt:</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;br /&gt;&lt;br /&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; 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color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;br /&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;br /&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>--[[Benutzer:HecklF|Flo60]] 20:45, 20. Apr. 2012 (CEST)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>--[[Benutzer:HecklF|Flo60]] 20:45, 20. Apr. 2012 (CEST)</div></td></tr> <!-- diff cache key geometrie:diff:1.41:old-11794:rev-11795:php=table --> </table> HecklF http://geometrie.idea-sketch.com/index.php?title=Zu_den_L%C3%B6sungen_Serie_04_WiSe_2011/12&diff=11794&oldid=prev HecklF: /* Aufgabe 4.2 */ 2012-04-20T18:45:59Z <p><span class="autocomment">Aufgabe 4.2</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 20. April 2012, 18:45 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l68">Zeile 68:</td> <td colspan="2" class="diff-lineno">Zeile 68:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>7. Der Winkel (LZJ&#039;) ist genau so groß wie der der Dreiecke (LZP&#039;) addiert mit dem Winkel (P&#039;ZJ).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>7. Der Winkel (LZJ&#039;) ist genau so groß wie der der Dreiecke (LZP&#039;) addiert mit dem Winkel (P&#039;ZJ).</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>8. Da bereits bewiesen wurde, dass die Dreiecke (LZP&#039;) und (P&#039;ZJ je Kongruent zu den &quot;Nachbardreiecken&quot; (LZP) und (JZP&#039;&#039;) sind, ergibt sich daraus, dass der Drehwinkel alpa genau doppelt so groß sein muss, wie der Winkel zwischen den beiden Geraden a b. (Puh fertig aufgeschrieben!! Alles klar? :-D) [[Benutzer:Pipi Langsocke|Pipi Langsocke]] 17:43, 16. Nov. 2011 (CET)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>8. Da bereits bewiesen wurde, dass die Dreiecke (LZP&#039;) und (P&#039;ZJ je Kongruent zu den &quot;Nachbardreiecken&quot; (LZP) und (JZP&#039;&#039;) sind, ergibt sich daraus, dass der Drehwinkel alpa genau doppelt so groß sein muss, wie der Winkel zwischen den beiden Geraden a b. (Puh fertig aufgeschrieben!! Alles klar? :-D) [[Benutzer:Pipi Langsocke|Pipi Langsocke]] 17:43, 16. Nov. 2011 (CET)</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;br /&gt;&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Und noch kurz ikonisch nachgeschickt:</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;br /&gt;&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;ggb_applet width="1000" height="628"  version="4.0" ggbBase64="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" showResetIcon = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "false" /&gt; </ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">--[[Benutzer:HecklF|Flo60]] 20:45, 20. Apr. 2012 (CEST)</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Aufgabe 4.3=</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Aufgabe 4.3=</div></td></tr> </table> HecklF http://geometrie.idea-sketch.com/index.php?title=Zu_den_L%C3%B6sungen_Serie_04_WiSe_2011/12&diff=10026&oldid=prev HecklF: /* Des ist ja Humbug - des geht ja viel einfacher :-) */ 2011-12-11T13:41:24Z <p><span class="autocomment">Des ist ja Humbug - des geht ja viel einfacher :-)</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 11. Dezember 2011, 13:41 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l25">Zeile 25:</td> <td colspan="2" class="diff-lineno">Zeile 25:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{| class=&quot;wikitable sortable&quot;  </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{| class=&quot;wikitable sortable&quot;  </div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>!<del style="font-weight: bold; text-decoration: none;">Überschrift 1</del>!!<del style="font-weight: bold; text-decoration: none;">Überschrift 2</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>!<ins style="font-weight: bold; text-decoration: none;">Nummer</ins>!!<ins style="font-weight: bold; text-decoration: none;">Beweisschritt!!Begründung</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-  </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-  </div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| 1 || |AP| = |A&#039;P&#039;| = |A&#039;P&#039;&#039;| || Definition Bewegung, Voraussetzung und Annahme, dass &lt;math&gt;\ P&#039;&#039; \ = \ \varphi (P)&lt;/math&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| 1 || |AP| = |A&#039;P&#039;| = |A&#039;P&#039;&#039;| || Definition Bewegung, Voraussetzung und Annahme, dass &lt;math&gt;\ P&#039;&#039; \ = \ \varphi (P)&lt;/math&gt;</div></td></tr> </table> HecklF http://geometrie.idea-sketch.com/index.php?title=Zu_den_L%C3%B6sungen_Serie_04_WiSe_2011/12&diff=10025&oldid=prev HecklF: /* Des ist ja Hubug - des geht ja viel einfacher :-) */ 2011-12-11T13:40:15Z <p><span class="autocomment">Des ist ja Hubug - des geht ja viel einfacher :-)</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 11. Dezember 2011, 13:40 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l16">Zeile 16:</td> <td colspan="2" class="diff-lineno">Zeile 16:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Ich werde das ganze evtl. nochmal schöner schreiben, da es vielleicht verwirrend ist. Wenn mein Geogebra wieder funktioniert, schicke ich eine Applikation nach. --[[Benutzer:HecklF|Flo60]] 20:21, 15. Nov. 2011 (CET)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Ich werde das ganze evtl. nochmal schöner schreiben, da es vielleicht verwirrend ist. Wenn mein Geogebra wieder funktioniert, schicke ich eine Applikation nach. --[[Benutzer:HecklF|Flo60]] 20:21, 15. Nov. 2011 (CET)</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>==Des ist ja <del style="font-weight: bold; text-decoration: none;">Hubug </del>- des geht ja viel einfacher :-)==</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>==Des ist ja <ins style="font-weight: bold; text-decoration: none;">Humbug </ins>- des geht ja viel einfacher :-)==</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Voraussetzung: &lt;math&gt;\operatorname{nkoll}(A, B, C)&lt;/math&gt;, die Bilder der Punkte bzgl. &lt;math&gt;\varphi&lt;/math&gt; seine A&#039;, B&#039; und C&#039;&lt;br /&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Voraussetzung: &lt;math&gt;\operatorname{nkoll}(A, B, C)&lt;/math&gt;, die Bilder der Punkte bzgl. &lt;math&gt;\varphi&lt;/math&gt; seine A&#039;, B&#039; und C&#039;&lt;br /&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Behauptung: &lt;math&gt;\varphi (P) = P&#039;&lt;/math&gt; ist eindeutig bestimmt.&lt;br /&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Behauptung: &lt;math&gt;\varphi (P) = P&#039;&lt;/math&gt; ist eindeutig bestimmt.&lt;br /&gt;</div></td></tr> </table> HecklF http://geometrie.idea-sketch.com/index.php?title=Zu_den_L%C3%B6sungen_Serie_04_WiSe_2011/12&diff=10024&oldid=prev HecklF: /* Aufgabe 4.1 */ 2011-12-11T13:39:53Z <p><span class="autocomment">Aufgabe 4.1</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 11. Dezember 2011, 13:39 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l15">Zeile 15:</td> <td colspan="2" class="diff-lineno">Zeile 15:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Wenn P und C bzgl. AB in verschiedenen Halbebenen liegen, liegen auch P&#039; und C&#039; in verschiedenen Halbebenen bzgl. AB. Wenn P und C bzgl. AB in ein und derselben Halbebene liegen, liegen auch P&#039; und C&#039; in ein und derselben Halbebene bzgl. AB. Demnach ist P&#039; eindeutig.&lt;br /&gt;&lt;br /&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Wenn P und C bzgl. AB in verschiedenen Halbebenen liegen, liegen auch P&#039; und C&#039; in verschiedenen Halbebenen bzgl. AB. Wenn P und C bzgl. AB in ein und derselben Halbebene liegen, liegen auch P&#039; und C&#039; in ein und derselben Halbebene bzgl. AB. Demnach ist P&#039; eindeutig.&lt;br /&gt;&lt;br /&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Ich werde das ganze evtl. nochmal schöner schreiben, da es vielleicht verwirrend ist. Wenn mein Geogebra wieder funktioniert, schicke ich eine Applikation nach. --[[Benutzer:HecklF|Flo60]] 20:21, 15. Nov. 2011 (CET)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Ich werde das ganze evtl. nochmal schöner schreiben, da es vielleicht verwirrend ist. Wenn mein Geogebra wieder funktioniert, schicke ich eine Applikation nach. --[[Benutzer:HecklF|Flo60]] 20:21, 15. Nov. 2011 (CET)</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==Des ist ja Hubug - des geht ja viel einfacher :-)==</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Voraussetzung: &lt;math&gt;\operatorname{nkoll}(A, B, C)&lt;/math&gt;, die Bilder der Punkte bzgl. &lt;math&gt;\varphi&lt;/math&gt; seine A', B' und C'&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Behauptung: &lt;math&gt;\varphi (P) = P'&lt;/math&gt; ist eindeutig bestimmt.&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Beweis durch Widerspruch&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">'''Annahme:''' &lt;math&gt;\exists P'' \in \epsilon : P'' \neq \ P' \ und P'' \ = \ \varphi (P)&lt;/math&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">{| class="wikitable sortable" </ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">!Überschrift 1!!Überschrift 2</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|- </ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">| 1 || |AP| = |A'P'| = |A'P''| || Definition Bewegung, Voraussetzung und Annahme, dass &lt;math&gt;\ P'' \ = \ \varphi (P)&lt;/math&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|- </ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">| 2 || |BP| = |B'P'| = |B'P''| || Definition Bewegung, Voraussetzung und Annahme, dass &lt;math&gt;\ P'' \ = \ \varphi (P)&lt;/math&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|-</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">| 3 || |CP| = |C'P'| = |C'P''| || Definition Bewegung, Voraussetzung und Annahme, dass &lt;math&gt;\ P'' \ = \ \varphi (P)&lt;/math&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|-</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">| 4 || Weil sowohl A' als auch B' und C' zu den Endpunkten der Strecke &lt;math&gt;\overline{P'P''}&lt;/math&gt; jeweils ein und denselben Abstand haben liegen sie allesamt auf der Mittelsenkrechten dieser Strecke. || (1), (2), (3), Mittelsenkrechtenkriterium</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|-</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">| 5 || Es gilt: &lt;math&gt;\operatorname{koll}(A', B', C')&lt;/math&gt; || (4)</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|-</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">| 6 || &lt;math&gt;\angle ABC = \angle A'B'C' &lt;/math&gt; und &lt;math&gt;\angle BCA = \angle B'C'A' &lt;/math&gt; und &lt;math&gt;\angle CAB = \angle C'A'B' &lt;/math&gt; || Satz der Winkeltreue bei Bewegungen</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|-</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">| 7 || A, B und C sind ebenfalls kollinear || (5), (6)</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|-</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">| 8 || Widerspruch zur Voraussetzung, dass &lt;math&gt;\operatorname{nkoll}(A, B, C)&lt;/math&gt; - Annahme ist zu verwerfen || (7)</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|}</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">--[[Benutzer:HecklF|Flo60]] 14:39, 11. Dez. 2011 (CET)</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Aufgabe 4.2=</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Aufgabe 4.2=</div></td></tr> </table> HecklF http://geometrie.idea-sketch.com/index.php?title=Zu_den_L%C3%B6sungen_Serie_04_WiSe_2011/12&diff=9614&oldid=prev HecklF: /* Aufgabe 4.4 */ 2011-11-22T21:54:30Z <p><span class="autocomment">Aufgabe 4.4</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 22. November 2011, 21:54 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l64">Zeile 64:</td> <td colspan="2" class="diff-lineno">Zeile 64:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Meine Ausdrucksweise hier ist irgendwie kompliziert. Wenn jemand ein paar gute Bezeichnungen für den ganzen Sums hier hat, der schreibe hier bitte vergnüglich ein paar (brauchbare) Aspekte an.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Meine Ausdrucksweise hier ist irgendwie kompliziert. Wenn jemand ein paar gute Bezeichnungen für den ganzen Sums hier hat, der schreibe hier bitte vergnüglich ein paar (brauchbare) Aspekte an.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Zur Findung des dritten Drehzentrums geht man analog vor.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Zur Findung des dritten Drehzentrums geht man analog vor <ins style="font-weight: bold; text-decoration: none;">ODER berechnet direkt von M aus die Veränderung der X-Koordinaten, da MN immer parallel zur X-Achse scheint</ins>.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>--[[Benutzer:HecklF|Flo60]] 22:53, 22. Nov. 2011 (CET)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>--[[Benutzer:HecklF|Flo60]] 22:53, 22. Nov. 2011 (CET)</div></td></tr> </table> HecklF http://geometrie.idea-sketch.com/index.php?title=Zu_den_L%C3%B6sungen_Serie_04_WiSe_2011/12&diff=9613&oldid=prev HecklF: /* Aufgabe 4.4 */ 2011-11-22T21:53:00Z <p><span class="autocomment">Aufgabe 4.4</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 22. November 2011, 21:53 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l58">Zeile 58:</td> <td colspan="2" class="diff-lineno">Zeile 58:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Weil wir es ja mit einer Verschiebung zu tun haben, und das Drehzentrum von (o. B. d. A.) A in gleicher Positionierung zu M steht, wie A zu M1, können wir damit rechnen.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Weil wir es ja mit einer Verschiebung zu tun haben, und das Drehzentrum von (o. B. d. A.) A in gleicher Positionierung zu M steht, wie A zu M1, können wir damit rechnen.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt;{M1x - Ax \choose M1y - Ay} = {1,5 - 2,5 \choose 3,33 - 4,33}  = \vec{m} {-1 \choose -1}&lt;/math&gt; Diesen &lt;math&gt;\vec{m}&lt;math<del style="font-weight: bold; text-decoration: none;">/</del>&gt; Vektor müssen wir nun an Z ansetzen und Punkt Z daran verschieben. Das Bild von m(Z) ist dann folgen M.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt;{M1x - Ax \choose M1y - Ay} = {1,5 - 2,5 \choose 3,33 - 4,33}  = \vec{m} {-1 \choose -1}&lt;/math&gt; Diesen &lt;math&gt;\vec{m}&lt;<ins style="font-weight: bold; text-decoration: none;">/</ins>math&gt; Vektor müssen wir nun an Z ansetzen und Punkt Z daran verschieben. Das Bild von m(Z) ist dann folgen M.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Warum weiß ich, dass ich die A - Koordinaten von den M1 - Koordinaten abziehen muss und nicht andersherum? Das ist unmittelbar ersichtlich, da ich einen negativen Richtungssinn sowohl auf der x-Achse, als auch auf der y-Achse.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Warum weiß ich, dass ich die A - Koordinaten von den M1 - Koordinaten abziehen muss und nicht andersherum? Das ist unmittelbar ersichtlich, da ich einen negativen Richtungssinn sowohl auf der x-Achse, als auch auf der y-Achse.</div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l66">Zeile 66:</td> <td colspan="2" class="diff-lineno">Zeile 66:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Zur Findung des dritten Drehzentrums geht man analog vor.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Zur Findung des dritten Drehzentrums geht man analog vor.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>--<del style="font-weight: bold; text-decoration: none;">~~~~</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>--<ins style="font-weight: bold; text-decoration: none;">[[Benutzer:HecklF|Flo60]] 22:53, 22. Nov. 2011 (CET)</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Elementargeometrie]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Elementargeometrie]]</div></td></tr> </table> HecklF http://geometrie.idea-sketch.com/index.php?title=Zu_den_L%C3%B6sungen_Serie_04_WiSe_2011/12&diff=9612&oldid=prev HecklF: /* Aufgabe 4.4 */ 2011-11-22T21:52:29Z <p><span class="autocomment">Aufgabe 4.4</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 22. November 2011, 21:52 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l51">Zeile 51:</td> <td colspan="2" class="diff-lineno">Zeile 51:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Aufgabe 4.4=</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Aufgabe 4.4=</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Sowohl die Punkte &lt;math&gt;M_i, 0&lt;i&lt;13, i \in \mathbb{N}&lt;/math&gt; als auch die Punkte &lt;math&gt;N_i, 0&lt;i&lt;13, i \in \mathbb{N}&lt;/math&gt; sind zueinander Bilder bei Drehungen um das Zentrum &lt;math&gt;Z_M&lt;/math&gt; bzw. &lt;math&gt;Z_N&lt;/math&gt;. Berechnen Sie die Koordinaten dieser Drehzentren.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Sowohl die Punkte &lt;math&gt;M_i, 0&lt;i&lt;13, i \in \mathbb{N}&lt;/math&gt; als auch die Punkte &lt;math&gt;N_i, 0&lt;i&lt;13, i \in \mathbb{N}&lt;/math&gt; sind zueinander Bilder bei Drehungen um das Zentrum &lt;math&gt;Z_M&lt;/math&gt; bzw. &lt;math&gt;Z_N&lt;/math&gt;. Berechnen Sie die Koordinaten dieser Drehzentren.</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Wir benötigen hierzu den Vektor. Da wir schlussendlich vom Drehzentrum Z ausgehen, ist es sehr günstig, dass dieser Punkt den Ursprung markiert, das erleichtert uns die Sache ein bischen, aber nicht der Rede wert.</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Wie berechnen wir den Vektor?</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Weil wir es ja mit einer Verschiebung zu tun haben, und das Drehzentrum von (o. B. d. A.) A in gleicher Positionierung zu M steht, wie A zu M1, können wir damit rechnen.</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;{M1x - Ax \choose M1y - Ay} = {1,5 - 2,5 \choose 3,33 - 4,33}  = \vec{m} {-1 \choose -1}&lt;/math&gt; Diesen &lt;math&gt;\vec{m}&lt;math/&gt; Vektor müssen wir nun an Z ansetzen und Punkt Z daran verschieben. Das Bild von m(Z) ist dann folgen M.</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Warum weiß ich, dass ich die A - Koordinaten von den M1 - Koordinaten abziehen muss und nicht andersherum? Das ist unmittelbar ersichtlich, da ich einen negativen Richtungssinn sowohl auf der x-Achse, als auch auf der y-Achse.</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Meine Ausdrucksweise hier ist irgendwie kompliziert. Wenn jemand ein paar gute Bezeichnungen für den ganzen Sums hier hat, der schreibe hier bitte vergnüglich ein paar (brauchbare) Aspekte an.</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Zur Findung des dritten Drehzentrums geht man analog vor.</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">--~~~~</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Elementargeometrie]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Kategorie:Elementargeometrie]]</div></td></tr> </table> HecklF http://geometrie.idea-sketch.com/index.php?title=Zu_den_L%C3%B6sungen_Serie_04_WiSe_2011/12&diff=9412&oldid=prev Pipi Langsocke: /* Aufgabe 4.2 */ 2011-11-16T16:43:35Z <p><span class="autocomment">Aufgabe 4.2</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 16. November 2011, 16:43 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l19">Zeile 19:</td> <td colspan="2" class="diff-lineno">Zeile 19:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Es seien &lt;math&gt;a&lt;/math&gt; und &lt;math&gt;b&lt;/math&gt; zwei Geraden, die sich in genau dem Punkt &lt;math&gt;Z&lt;/math&gt; schneiden. Man beweise:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Es seien &lt;math&gt;a&lt;/math&gt; und &lt;math&gt;b&lt;/math&gt; zwei Geraden, die sich in genau dem Punkt &lt;math&gt;Z&lt;/math&gt; schneiden. Man beweise:</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die Nacheinanderausführung &lt;math&gt;S_b \circ S_a&lt;/math&gt; ist eine Drehung um Z, wobei der Drehwinkel dieser Drehung doppelt so groß ist wie der Winkel zwischen den beiden Geraden &lt;math&gt;a&lt;/math&gt; und &lt;math&gt;b&lt;/math&gt;.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die Nacheinanderausführung &lt;math&gt;S_b \circ S_a&lt;/math&gt; ist eine Drehung um Z, wobei der Drehwinkel dieser Drehung doppelt so groß ist wie der Winkel zwischen den beiden Geraden &lt;math&gt;a&lt;/math&gt; und &lt;math&gt;b&lt;/math&gt;.</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;ggb_applet width="1035" height="556"  version="4.0" ggbBase64="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" framePossible = "false" showResetIcon = "false" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" /&gt; [[Benutzer:Pipi Langsocke|Pipi Langsocke]] 17:43, 16. Nov. 2011 (CET)&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">VSS: Die Geraden &lt;math&gt;a&lt;/math&gt; und &lt;math&gt;b&lt;/math&gt; schneiden sich in dem Punkt &lt;math&gt;Z&lt;/math&gt;.</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Behauptung: 1. &lt;math&gt;S_b \circ S_a&lt;/math&gt; ist eine Drehung um &lt;math&gt;Z&lt;/math&gt;. --&gt; Trivial nach Satz der VL vom 8.11.: Die NAF zweier Spiegelungen mit sich schneidender Spiegelachsen ist eine Drehung.</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">2. Drehwinkel alpha ist doppelt so groß, wie der Winkel zwischen den Geraden &lt;math&gt;a&lt;/math&gt; und &lt;math&gt;b&lt;/math&gt;.&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">zu 2.:&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">1. a ist Mittelsenkrechte von &lt;math&gt;PP'&lt;/math&gt; --&gt; |&lt;math&gt;|PP'| = |PL|+|PL'|&lt;/math&gt;, weil L (Lotfußpunkt) Element a --&gt; L ist Fixpunkt bei Spiegelung an a und es gilt das Mittelsenkrechtenkriterium&lt;br /&gt;&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">2.Z istz Fixpunkt &lt;math&gt;S_a&lt;/math&gt; --&gt;|&lt;math&gt;|ZP'| = |ZP'|&lt;/math&gt;, weil L (Lotfußpunkt) Element a --&gt; L ist Fixpunkt bei Spiegelung an a und es gilt das Mittelsenkrechtenkriterium&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">3. |&lt;math&gt;|ZL| = |ZL|&lt;/math&gt;, weil L Element a und deshalb Fixpunkt (Definition 3.3 Fixpunktgerade)&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">4. Die Dreiecke LPZ und LP'Z sind kongruent zueinander (SSS)&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">5. b ist Mittelsenkrechte vin P'P'' mit Lotfußpunkt J --&gt; (gleiche Begründungen wie bei 1.)&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">6. Die Dreiecke P'ZJ und JZP'' sind kongruent zueinander (habe die Schritte von oben übersprungen, weil sie analog sind.)&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">7. Der Winkel (LZJ') ist genau so groß wie der der Dreiecke (LZP') addiert mit dem Winkel (P'ZJ).</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">8. Da bereits bewiesen wurde, dass die Dreiecke (LZP') und (P'ZJ je Kongruent zu den "Nachbardreiecken" (LZP) und (JZP'') sind, ergibt sich daraus, dass der Drehwinkel alpa genau doppelt so groß sein muss, wie der Winkel zwischen den beiden Geraden a b. (Puh fertig aufgeschrieben!! Alles klar? :-D) [[Benutzer:Pipi Langsocke|Pipi Langsocke]] 17:43, 16. Nov. 2011 (CET)</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Aufgabe 4.3=</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Aufgabe 4.3=</div></td></tr> </table> Pipi Langsocke