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Lösung von Aufgabe 13.1P (SoSe 23) - Versionsgeschichte
2026-08-16T12:47:44Z
Versionsgeschichte dieser Seite in Geometrie-Wiki
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http://geometrie.idea-sketch.com/index.php?title=L%C3%B6sung_von_Aufgabe_13.1P_(SoSe_23)&diff=39404&oldid=prev
Matze2000 am 16. Juli 2023 um 10:54 Uhr
2023-07-16T10:54:15Z
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<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. Juli 2023, 10:54 Uhr</td>
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<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;">Zeigen Sie</del>, <del style="font-weight: bold; text-decoration: none;">dass bei der Verkettung einer Schubspiegelung </del><math><del style="font-weight: bold; text-decoration: none;">G_</del>{<del style="font-weight: bold; text-decoration: none;">a</del>,<del style="font-weight: bold; text-decoration: none;">b,c</del>}</math> <del style="font-weight: bold; text-decoration: none;">(</del><math><del style="font-weight: bold; text-decoration: none;">a </del>\<del style="font-weight: bold; text-decoration: none;">parallel b </del>\<del style="font-weight: bold; text-decoration: none;">wedge a </del>\<del style="font-weight: bold; text-decoration: none;">perp c</del></math><del style="font-weight: bold; text-decoration: none;">) mit einer Spiegelung </del><math><del style="font-weight: bold; text-decoration: none;">S_d</del></math> <del style="font-weight: bold; text-decoration: none;">(</del><math><del style="font-weight: bold; text-decoration: none;">d </del>\<del style="font-weight: bold; text-decoration: none;">perp c</del></math>) <del style="font-weight: bold; text-decoration: none;">eine Punktspiegelung entsteht</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;">Dargestellt ist hier die Nacheinanderausführung zweier Abbildungen <math>\varphi_1</math> und <math>\varphi_2</math></ins>, <ins style="font-weight: bold; text-decoration: none;">mit <math>\varphi_1\left( \overline{ABC} \right) = \overline{A'B'C'}</math> und </ins><math><ins style="font-weight: bold; text-decoration: none;">\varphi_2\left( \overline{A'B'C'} \right) = \overline</ins>{<ins style="font-weight: bold; text-decoration: none;">A''B''C''}</math>. <br /></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;">'''Hinweis:''' Der Punkt E hat eine besondere Bedeutung für <math>\varphi_2</math>. </ins></div></td></tr>
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<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;"><br /></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;">#Um welche Arten von Abbildungen handelt es sich bei <math>\varphi_1</ins></math> <ins style="font-weight: bold; text-decoration: none;">und </ins><math>\<ins style="font-weight: bold; text-decoration: none;">varphi_2</math>?</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;">#Zeichnen Sie jeweils für <math></ins>\<ins style="font-weight: bold; text-decoration: none;">varphi_1</math> und <math></ins>\<ins style="font-weight: bold; text-decoration: none;">varphi_2</ins></math> <ins style="font-weight: bold; text-decoration: none;">die passende Anzahl von Spiegelachsen in die Skizze ein.</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 betrachten nun die Verkettung </ins><math><ins style="font-weight: bold; text-decoration: none;">\varphi_1\circ \varphi_2 </ins></math><ins style="font-weight: bold; text-decoration: none;">. Durch welche Ersatzabbildung kann diese Verkettung </ins><math>\<ins style="font-weight: bold; text-decoration: none;">varphi_1\circ \varphi_2 </ins></math> <ins style="font-weight: bold; text-decoration: none;">ersetzt werden? (Begründen Sie Ihre Entscheidung</ins>)<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;">#Zeichnen Sie die Achsen der Ersatzabbildung in die Skizze oben ein. Hinweis: Sie dürfen das Gitter im Hintergrund als Orientierung nutzen</ins>. </div></td></tr>
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http://geometrie.idea-sketch.com/index.php?title=L%C3%B6sung_von_Aufgabe_13.1P_(SoSe_23)&diff=39294&oldid=prev
Matze2000: Die Seite wurde neu angelegt: „Zeigen Sie, dass bei der Verkettung einer Schubspiegelung <math>G_{a,b,c}</math> (<math>a \parallel b \wedge a \perp c</math>) mit einer Spiegelung <math>S_d</…“
2023-05-18T09:59:16Z
<p>Die Seite wurde neu angelegt: „Zeigen Sie, dass bei der Verkettung einer Schubspiegelung <math>G_{a,b,c}</math> (<math>a \parallel b \wedge a \perp c</math>) mit einer Spiegelung <math>S_d</…“</p>
<p><b>Neue Seite</b></p><div>Zeigen Sie, dass bei der Verkettung einer Schubspiegelung <math>G_{a,b,c}</math> (<math>a \parallel b \wedge a \perp c</math>) mit einer Spiegelung <math>S_d</math> (<math>d \perp c</math>) eine Punktspiegelung entsteht.<br />
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[[Kategorie:Geo_P]]</div>
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