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Young's Geometry


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, Line, Point, Three Point Geometry

This entry contributed by Christopher Stover

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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

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