Euclidean geometry/Euclid's axioms
Lesson One: Euclid's Axioms
Euclid was known as the “Father of Geometry.” In his book, The Elements, Euclid begins by stating his assumptions to help determine the method of solving a problem. These assumptions were known as the five axioms. An axiom is a statement that is accepted without proof. In order they are:
- 1. A line can be drawn from a point to any other point.
- 2. A finite line can be extended indefinitely.
- 3. A circle can be drawn, given a center and a radius.
- 4. All right angles are ninety degrees.
- 5. If a line intersects two other lines such that the sum of the interior angles on one side of the intersecting line is less than the sum of two right angles, then the lines meet on that side and not on the other side. (also known as the Parallel Postulate)
To explain, axioms 1-3 establish lines and circles as the basic constructs of Euclidean geometry. The fourth axiom establishes a measure for angles and invariability of figures. The fifth axiom basically means that given a point and a line, there is only one line through that point parallel to the given line.