Summary of Geometries

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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 Fixed.jpeg