Difference between revisions of "Summary of Geometries"

From Math Images
Jump to: navigation, search
(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.png|center]]</td>
+
<td>Angle summation must equal 180 degrees  
<td>Angle summation must be less that 180 degrees [[Image:Hyperbolic_Triangle.png|center]]</td>
+
 
<td>Angle summation must be greater 180 degrees [[Image:Elliptic_Triangle.png|center]]</td>
+
 
 +
[[Image:Euclid_Triangle.png|center]]</td>
 +
<td>Angle summation must be less that 180 degrees  
 +
 
 +
 
 +
[[Image:Hyperbolic_Triangle.png|center]]</td>
 +
<td>Angle summation must be greater 180 degrees  
 +
 
 +
 
 +
[[Image:Elliptic_Triangle.png|center]]</td>
 
</tr>
 
</tr>
  
Line 24: Line 33:
 
[[Image:Euclid_parallel.png|center|200px]]</td>
 
[[Image:Euclid_parallel.png|center|200px]]</td>
 
<td>There are infinitely many lines that are parallel to line ''l'' and pass through a point ''P'' [[Image:Poincare_Disk_Model.png|center|201px]]</td>
 
<td>There are infinitely many lines that are parallel to line ''l'' and pass through a point ''P'' [[Image:Poincare_Disk_Model.png|center|201px]]</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.gif|center]]</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


Euclid Triangle.png
Angle summation must be less that 180 degrees


Hyperbolic Triangle.png
Angle summation must be greater 180 degrees


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


Euclid parallel.png
There are infinitely many lines that are parallel to line l and pass through a point P
Poincare Disk Model.png
There is no line that is parallel to line l and passes through a point P
Elliptic Lines.gif