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|}
 
|}
 
{|class="wikitable center"
 
{|class="wikitable center"
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| <math>\ G</math> ist eine ...
 
| <math>\ G</math> ist eine ...
  
−
|}
+
|-
−
 
+
−
{|class="wikitable center"
+
 
| colspan="2"  style="background: #DDFFDD;"| <center>Dimension von <math>\ G</math></center>
 
| colspan="2"  style="background: #DDFFDD;"| <center>Dimension von <math>\ G</math></center>
  
Zeile 28: Zeile 27:
 
|  Dimension von  
 
|  Dimension von  
  
−
|}
+
|-
−
{| class="wikitable center"
+
 
| colspan="2"  style="background: #DDFFDD;"| <center> Objekt <math>\ T</math>, das <math>\ G</math> in Klassen einteilt</center>
 
| colspan="2"  style="background: #DDFFDD;"| <center> Objekt <math>\ T</math>, das <math>\ G</math> in Klassen einteilt</center>
  
Zeile 36: Zeile 34:
 
|  <math>\ T</math> ist ...
 
|  <math>\ T</math> ist ...
  
−
|}
+
|-
−
 
+
−
{| class="wikitable center"
+
 
| colspan="2"  style="background: #DDFFDD;"| <center>Dimension von <math>\ T</math></center>
 
| colspan="2"  style="background: #DDFFDD;"| <center>Dimension von <math>\ T</math></center>
  
Zeile 45: Zeile 41:
 
|  <math>\ T</math> hat die Dimension ...
 
|  <math>\ T</math> hat die Dimension ...
  
−
|}
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|-
−
 
+
−
{| class="wikitable center"
+
 
| colspan="2"  style="background: #DDFFDD; "| <center>Referenzpunkt <math>\ Q</math> teilt <math>\ G \setminus_{\{ Q \}}</math> in genau zwei Klassen</center>
 
| colspan="2"  style="background: #DDFFDD; "| <center>Referenzpunkt <math>\ Q</math> teilt <math>\ G \setminus_{\{ Q \}}</math> in genau zwei Klassen</center>
  
 
|-
 
|-
−
| colspan="2"  | <center>Klasse 1: </center>
+
| colspan="2"  |  
−
 
+
<center>Klasse 1: </center>
 
<center>Menge aller Punkte <math>\ P\mathrm{\in }G</math> , die mit <math>\ Q</math> bezüglich <math>\ T</math> „auf derselben Seite liegen“</center>
 
<center>Menge aller Punkte <math>\ P\mathrm{\in }G</math> , die mit <math>\ Q</math> bezüglich <math>\ T</math> „auf derselben Seite liegen“</center>
  
Zeile 69: Zeile 63:
  
 
|}
 
|}
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=== Definition des Begriffs der Halbebene ===

Version vom 3. Juni 2010, 08:26 Uhr

Inhaltsverzeichnis

Halbebenen und das Axiom von Pasch

Halbebenen

Analogiebetrachtungen

Halbgeraden
Halbebenen
Objekt \ G, das in Klassen eingeteilt wird
\ G ist eine ... \ G ist eine ...
Dimension von \ G
Dimension von Dimension von
Objekt \ T, das \ G in Klassen einteilt
\ T ist ... \ T ist ...
Dimension von \ T
\ T hat die Dimension ... \ T hat die Dimension ...
Referenzpunkt \ Q teilt \ G \setminus_{\{ Q \}} in genau zwei Klassen
Klasse 1:
Menge aller Punkte \ P\mathrm{\in }G , die mit \ Q bezüglich \ T „auf derselben Seite liegen“
\ AQ^{+} = \{P| ... \} \ gQ^{+} = \{P| ... \}
Klasse 2:
Menge aller Punkte P\mathrm{\in }G, die bezüglich \ T nicht auf der Seite von \ Qliegen.
\ AQ^{-} = \{P| ... \} \ gQ^{-} = \{P| ... \}

Definition des Begriffs der Halbebene

Von „http://geometrie.zum.de/index.php?title=Benutzer:*m.g.*&oldid=1464“