Summary of Geometries

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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