Young's geometry is a finite geometry which satisfies
the following five axioms:
1. There exists at least one line.
2. Every line of the geometry
has exactly three points on it.
3. Not all points of the geometry
are on the same line.
4. For two distinct points, there exists exactly one line on both of them.
5. If a point does not lie on a given line, then there exists exactly one line on that point
that does not intersect the given line.
Cherowitzo (2006) notes that the last axiom bears a strong resemblance to the parallel postulate of Euclidean geometry.
See also
Axiom,
Categorical Axiomatic System,
Fano's Geometry,
Finite
Geometry,
Five Point Geometry,
Four
Line Geometry,
Four Point Geometry,
Line,
Point,
Three
Point Geometry
This entry contributed by Christopher
Stover
Explore with Wolfram|Alpha
References
Cherowitzo, W. "Higher Geometry." 2006. http://www-math.ucdenver.edu/~wcherowi/courses/m3210/lecture1.pdf.
Cite this as:
Stover, Christopher. "Young's Geometry." From MathWorld--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/YoungsGeometry.html
Subject classifications
