Tetraeder: Unterschied zwischen den Versionen

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<br><br>[[Datei:Hexaeder Erde Hintergrund -F0E9CA.png|rechts|Hexaeder Erde]][[Datei:Tetrahedron-white.gif|links|Tetraeder]]
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<br><br>[[Datei:Hexaeder Erde Hintergrund -F0E9CA.png|rechts|120px|Hexaeder Erde]][[Datei:Tetrahedron-white.gif|links|Tetraeder]]
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<center><u><font size="6">Tetraeder</font></u></center>
 
<center><u><font size="6">Tetraeder</font></u></center>
<br><br><br><br><br><br>
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<br><br><br>
<font size="4">Eigenschaften des Tetraeders/Vierflächners:<br>
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<center><ggb_applet width="1131" height="629"  version="3.2" 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" framePossible = "false" showResetIcon = "false" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" allowRescaling = "true" /></center>
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[[Datei:Hexaeder Erde Hintergrund -F0E9CA.png|rechts|120px|Hexaeder Erde]][[Datei:Tetrahedron-white.gif|links|Tetraeder]]
  
4 Flächen<br>
 
4 Ecken<br>
 
6 Kanten<br>
 
2 verschiedene Netze<br>
 
3 Kanten zu jeder Ecke<br>
 
3 Ecke zu jeder Fläche<br>
 
<u>Volumen:</u><br><br>
 
.          <math>V = a^3/12 * sqrt{2}</math> ≈ <math> 0,12a^3</math><br>
 
<u>Oberflächeninhalt:</u><br><br>
 
.          <math>O =  a^2  *  sqrt{3}</math> ≈ <math> 1,73a^2</math><br>
 
<u>Inkugelradius:</u><br><br>
 
.          <math>p =  a/12  *  sqrt{6}= p </math> ≈ <math> 0,2a</math><br>
 
<u>Umkugelradius:</u><br><br>
 
.          <math>R =  a/4  *  sqrt{6}= 3p </math> ≈ <math> 0,61a</math><br>
 
<u>Kantenkugelradius:</u><br><br>
 
.          <math>O =  a/4  *  sqrt{2}</math> ≈ <math> 0,35a</math><br>
 
<u>Pyramidenhöhe:</u><br><br>
 
.          <math>k = a^3  *  sqrt{6}= R + p </math> ≈ <math> 0,82a</math><br>
 
<u>Verhältnis von Volumen:</u><br><br>
 
.          <math>V / (V</math><sub>UK</sub><math>) = 2/9  * </math> π <math> *  sqrt{3}</math><br>
 
<u>Flächenwinkel:</u><br><br>
 
.          <math>cos </math> α <math> = 1/3</math><br>
 
 
</font>
 
 
<center>{{#slideshare:eigenschaftendestetraeders-131005035717-phpapp01}}</center>
 
<center>Umsetzen mit Geo Gebra</center>
 
{{#widget:SlideShare
 
|doc=eigenschaftendestetraeders-131005035717-phpapp01
 
|width=600
 
|height=450
 
}}
 
  
 +
<!--<center>{{#slideshare:eigenschaftendestetraeders-131005035717-phpapp01}}</center>
 
|}<noinclude>
 
|}<noinclude>
 
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