Two-dimensional geometric space defined by a system of axioms.

A system of axioms for a geometric plane may include the following:

  • A1 : A geometric plane is a set of points with at least two elements.
  • A2 : Every line is included in the plane.
  • A3 : Every pair of points in the plane determines a line.
  • A4 : Consider a line l in the plane and a point P that does not belong to the line; there is one and only one line l’ n the plane that contains P and does not have a point in common with l. Therefore, lines l and l’ are said to be parallel.
  • A plane is a flat surface that extends infinitely in all directions and contains every line that joins two of its points.
  • The term “plane” generally is a synonym for “geometric plane.”
  • The Greek capital letter ∏, which is read “pi,” is often used as a symbol to refer to a plane.
  • A projection plane is a plane that contains the images of three-dimensional objects transformed by a projection of three-dimensional space onto a two-dimensional space (plane).

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