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...) 

Line 12:  Line 12:  
<tr>  <tr>  
<td>Triangles</td>  <td>Triangles</td>  
−  <td>Angle summation must equal 180 degrees [[Image:Euclid_Triangle.pngcenter]]</td>  +  <td>Angle summation must equal 180 degrees 
−  <td>Angle summation must be less that 180 degrees [[Image:Hyperbolic_Triangle.pngcenter]]</td>  +  
−  <td>Angle summation must be greater 180 degrees [[Image:Elliptic_Triangle.pngcenter]]</td>  +  
+  [[Image:Euclid_Triangle.pngcenter]]</td>  
+  <td>Angle summation must be less that 180 degrees  
+  
+  
+  [[Image:Hyperbolic_Triangle.pngcenter]]</td>  
+  <td>Angle summation must be greater 180 degrees  
+  
+  
+  [[Image:Elliptic_Triangle.pngcenter]]</td>  
</tr>  </tr>  
Line 24:  Line 33:  
[[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.gifcenter]]</td> 
</tr>  </tr>  
</table>  </table> 
Revision as of 11:14, 3 July 2009
Summary of the Euclidean, Hyperbolic, and Elliptic Geometries
Euclidean  Hyperbolic  Elliptic  

Triangles  Angle summation must equal 180 degrees

Angle summation must be less that 180 degrees

Angle summation must be 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 