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 Eric
W. Weisstein . https://mathworld.wolfram.com/FivePointGeometry.html
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