Euclid's Foundation

The word "geometry " comes from two Greek words geo and metria meaning "earth measuring." When Euclid wrote his books on geometry, he chose four undefined terms and five axioms or postulates to be the foundation of Euclidean geometry. Every other part of geometry is built upon this foundation.

Terms

point
line plane space

Five axioms

  • The shortest distance between any two points is a straight line
  • Any line segment can be extended infinitely in either direction
  • A circle can be made with any center and any radius
  • All right angles are equal to each other
  • Given a point and a line not on the point, only one line can be drawn parallel to the given line through the given point

A point has dimensions zero, a line is one-dimensional, a plane two-dimensional, and space is three-dimensional. What might be a four-dimensional concept?