Three point geometry is a finite geometry subject to the following four axioms:
1. There exist exactly three points.
2. Two distinct points are on exactly one line.
3. Not all the three points are collinear.
4. Two distinct lines are on at least one point.
Three point geometry is categorical.
Like many finite geometries, the number of provable theorems in three point geometry is small. One can prove from this collection of axioms that two distinct lines are on exactly one point and that three point geometry contains exactly three lines. In this sense, three point geometry is extremely simple. On the other hand, note that the axioms say nothing about whether the lines are straight or curved, whereby it is possible that a number of different (but equivalent) visualizations of three point geometry may exist.
