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Euclidean Geometry

Asked by a student at Lincolin High School on September 24, 1997:
What is Euclidean Geometry? Can you also give me an example of it. Thank you very much.
Euclidean geometry is just another name for the familiar geometry which is typically taught in grade school: the theory of points, lines, angles, etc. on a flat plane. It is given the name "Euclidean" because it was Euclid who first axiomatized it (rigorously described it).

Another reason it is given the special name "Euclidean geometry" is to distinguish it from non-Euclidean geometries (described in the answer to another question).

The difference is that Euclidean geometry satisfies the Parallel Postulate (sometimes known as the Fifth Postulate). This postulate states that for every line l and every point p which does not lie on l, there is a unique line l' which passes through p and does not intersect l (i.e., which is parallel to l).

Geometry on a curved surface, for example, may not satisfy this postulate, and hence is non-Euclidean geometry.

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