Associated Topics || Dr. Math Home || Search Dr. Math

Curvature of Non-Euclidean Space

```
Date: 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

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/
```
Associated Topics:
College Non-Euclidean Geometry
High School Non-Euclidean Geometry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search