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Projective Line Geometry is the geometry of lines. The concepts precede Euclidian Geometry. Learning Projective Line Geometry gives the student command of the fundamentals of Geometry and can be used to introduce the concepts of Constructions and Theorems – discoverable patterns in space-time.
This is because patterns of points and lines can be expressed in number patterns, as well.
Learn Projective Geometry with A/Professor NJ Wildberger here.
Subject matter of this video by author and mathematician NJ Wildberger:
Theorem: A Key Result that is not evident without the mathematical construct. The Key Result or phenomenon becomes evident as the mathematical construct is revealed. By “phenomenon” we mean the same result is evident every time. A Theorem must hold true using the same construct, every time.
Projective Line Geometry: Geometry of Lines, including points and patterns Projective Geometry is expressed in two dimensions.
Points:
Two points in space for a line
Three points in space can form a triangle
Four points in space form a quadrangle
Two lines connect is a vertex
Three lines connect is a trilateral
Four liens connect is a quadrilateral *
Please note the use of “lateral” root indicates it is maybe a plane. Remember at this level of study we are only talking about 2 dimensions – points and lines.