Comparison of Euclidean, spherical, and hyperbolic geometries

Comparison of Euclidean, spherical, and hyperbolic geometries

Table
Comparison of Euclidean, spherical, and hyperbolic geometries
Given a line and a point not on the line, there exist(s) ____________ through the given point
and parallel to the given line.
a) exactly one line (Euclidean)
b) no lines (spherical)
c) infinitely many lines (hyperbolic)
Euclid s fifth postulate is ____________.
a) true (Euclidean)
b) false (spherical)
c) false (hyperbolic)
The sum of the interior angles of a triangle ______ 180 degrees.
a) = (Euclidean)
b) > (spherical)
c) < (hyperbolic)
See as table:

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Universalium. 2010.

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