Curvature of Non-Euclidean SpaceDate: 05/22/2000 at 11:44:09 From: Michael Rosenof Subject: Positive/Negative Curvature What is the difference between positive and negative curvature in non-Euclidean geometry? I looked through your archives and I couldn't find the answer. Thank you. Date: 05/22/2000 at 15:58:27 From: Doctor Rob Subject: Re: Positive/Negative Curvature Thanks for writing to Ask Dr. Math, Michael. In a space of positive curvature, like the surface of a sphere, there are no lines parallel to a given line through an outside point. In a space of negative curvature, like the surface of an hyperbolic paraboloid, there are multiple lines parallel to a given line through an outside point. In a space of zero curvature, like a plane, there is a single line parallel to a given line through an outside point. - Doctor Rob, The Math Forum http://mathforum.org/dr.math/ |
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