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Five Point Geometry


Five point geometry is a finite geometry subject to the following three axioms:

1. there exist exactly five points,

2. each two distinct points have exactly one line on both of them, and

3. each line has exactly two points.

Five point geometry is categorical.

Like many finite geometries, the number of provable theorems in five point geometry is small. One can show that in this scheme, there are exactly 10 lines and that each point has exactly four lines on it.


See also

Axiom, Categorical Axiomatic System, Fano's Geometry, Finite Geometry, Four Line Geometry, Four Point Geometry, Line, Point, Three Point Geometry, Young's Geometry

This entry contributed by Christopher Stover

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References

Smart, J. "Finite Geometries and Axiomatic Systems." 2002. http://www.beva.org/math323/asgn5/nov5.htm.

Cite this as:

Stover, Christopher. "Five Point Geometry." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/FivePointGeometry.html

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