1.4: Explain and Apply

An IBL Introduction to Geometries · LibreTexts

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    1. Explain what completeness is and why it is important. Note, an explanation is not a proof, just a clarification for someone else.
    2. Explain what consistency is and why it is important.
    3. Modify the axioms for the Fano geometry so they are complete and consistent. You might use the Four Point Geometry axioms as a model.
    4. Try to construct a Fano geometry with exactly seven points.
    5. Modify the axioms of the Five Point Geometry to be complete and consistent. You might use the Four Point Geometry axioms as a model.
    6. How many lines are there in this geometry?
    7. Modify the axioms of the Five Point Geometry to be complete and consistent and so that they result in five lines.

    This page titled 1.4: Explain and Apply was last modified on Fri, 18 Feb 2022 02:40:43 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.