Difference between revisions of "Summary of Geometries"
(New page: =Summary of the Euclidean, Hyperbolic, and Elliptic Geometries= <table border="1" cellpadding="12"> <tr> <th></th> <th>Euclidean</th> <th>Hyperbolic</th> <th>Elliptic</th> </tr> <tr> <t...) 

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−  =  +  =Euclidean, Hyperbolic, and Elliptic Geometries= 
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<tr>  <tr>  
<td>Triangles</td>  <td>Triangles</td>  
−  <td>  +  <td>Angles must sum to exactly 180 degrees 
−  <td>  +  
−  <td>  +  
+  [[Image:Euclid_Triangle.pngcenter]]</td>  
+  <td>Angles must sum to less that 180 degrees  
+  
+  
+  [[Image:Hyperbolic_Triangle.pngcenter]]</td>  
+  <td>Angles must sum to greater 180 degrees  
+  
+  
+  [[Image:Elliptic_Triangle.pngcenter]]</td>  
</tr>  </tr>  
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[[Image:Euclid_parallel.pngcenter200px]]</td>  [[Image:Euclid_parallel.pngcenter200px]]</td>  
<td>There are infinitely many lines that are parallel to line ''l'' and pass through a point ''P'' [[Image:Poincare_Disk_Model.pngcenter201px]]</td>  <td>There are infinitely many lines that are parallel to line ''l'' and pass through a point ''P'' [[Image:Poincare_Disk_Model.pngcenter201px]]</td>  
−  <td>There is no line that is parallel to line ''l'' and passes through a point ''P''</td>  +  <td>There is no line that is parallel to line ''l'' and passes through a point ''P'' [[Image:Elliptic Lines Fixed.jpegcenter]]</td> 
</tr>  </tr>  
</table>  </table> 
Latest revision as of 13:54, 24 May 2011
Euclidean, Hyperbolic, and Elliptic Geometries
Euclidean  Hyperbolic  Elliptic  

Triangles  Angles must sum to exactly 180 degrees

Angles must sum to less that 180 degrees

Angles must sum to greater 180 degrees

Parallel Lines  There is only one line that is parallel to line l and passes through a point P

There are infinitely many lines that are parallel to line l and pass through a point P  There is no line that is parallel to line l and passes through a point P 