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What is Non-Euclidean Geometry?

Non Euclidean geometry is geometry that refutes Euclid's fifth postulate: Given a point p and a line l, there is exactly one line through p that is parralel to l.

Other than this difference, non-Euclidean geometry holds to the rest of Euclid's postulates:

To see how this movement got started, please see the History section.

Now, there are two ways that you can refute this.

One way is to say: Given a line l and point p, there are no lines parralel to l through p. This leads to Spherical/Elliptical Geometry.

The other is to say: Given a line l and a point p, there are infinite lines through p parralel to l. This leads to Hyperbolic Geometry

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Bibliography

Here are some pages I found most useful in creating this webpage: