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Section 1.3 Consistency
Definition 1.3.1 . Five Point Geometry.
Use the following axioms and definitions of intersection and parallel as a definition of the five point geometry.
There exist exactly five points.
There exist exactly five lines.
Any two distinct points have exactly one line on both of them.
Each line is on exactly two points.
Checkpoint 1.3.2 .
Explore the five point geometry as follows.
Draw five points using Geogebra.
Use Axiom 3 to draw all required lines.
How many lines did you construct?
Compare this answer to Axiom 2.
Solution .
I did as instructed and below is my construction. In this construction there are 10 lines, with is does not correspond with Axion 2, there will have to be some modification to the Axioms of the 1.3.1 Five Point Geometry definition.
