The study of geometrical systems which differ from that of Eculid, specifically with respect to the 5th or an equivalent to the Parallel Postulate, which states: If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough. This means that in the Euclidean world that lines that are not parallel must inevitably meet. This is not always true in non-Euclidean geometry. This category may also contain webpages with discussion of the validity or otherwise of these different geometries.
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