1.3: Consistency

An IBL Introduction to Geometries · LibreTexts

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    Definition: Five Point Geometry

    Use the following axioms and definitions of intersection and parallel as a definition of the five point geometry.

    1. There exist exactly five points.
    2. There exist exactly five lines.
    3. Any two distinct points have exactly one line on both of them.
    4. Each line is on exactly two points.

    Explore the five point geometry as follows.

    1. Draw five points using Geogebra.
    2. Use Axiom 3 to draw all required lines.
    3. How many lines did you construct?
    4. Compare this answer to Axiom 2.

    This page titled 1.3: Consistency was last modified on Tue, 08 Mar 2022 01:58:47 GMT and is shared under a not declared license and was authored, remixed, and/or curated by Mark A. Fitch via source content that was edited to the style and standards of the LibreTexts platform.