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Section 2.1 Euclidean Geometry

What is Euclidean geometry? The geometry described by Euclid? To this day, scholars argue over the exact interpretation of Euclid's postulates, which roughly assert that:

  1. Two distinct points determine a unique line;
  2. Measure distance as usual;
  3. Measure angles as usual ...
  4. ... including right angles;
  5. Euclidean Parallel Postulate: There is a unique line through each point parallel to a given line.

Euclid, and many after him, tried to prove that the Euclidean parallel postulate followed from the other four postulates. As we will see, it does not. Before exploring alternative geometries, we first study some of the properties of Euclidean geometry.

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