Difference between revisions of "Summary of Geometries"

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<tr>
 
<tr>
 
<td>Triangles</td>
 
<td>Triangles</td>
<td>Angle summation must equal 180 degrees  
+
<td>Angles must sum to exactly 180 degrees  
  
  
 
[[Image:Euclid_Triangle.png|center]]</td>
 
[[Image:Euclid_Triangle.png|center]]</td>
<td>Angle summation must be less that 180 degrees  
+
<td>Angles must sum to less that 180 degrees  
  
  
 
[[Image:Hyperbolic_Triangle.png|center]]</td>
 
[[Image:Hyperbolic_Triangle.png|center]]</td>
<td>Angle summation must be greater 180 degrees  
+
<td>Angles must sum to greater 180 degrees  
  
  

Revision as of 11:15, 3 July 2009

Summary of the Euclidean, Hyperbolic, and Elliptic Geometries

Euclidean Hyperbolic Elliptic
Triangles Angles must sum to exactly 180 degrees


Euclid Triangle.png
Angles must sum to less that 180 degrees


Hyperbolic Triangle.png
Angles must sum to 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