incidence geometry

Incidence geometry is an axiomatic system in geometry.

With primitive notions of point, line, and incident, the incidence axioms are

1. For every pair of distinct points $P$ and $Q$, there is exactly one line $l$ such that $P$ and $Q$ are incident to $l$.
2. For every line $l$, there exist at least two distinct points $P$ and Q such that $P$ and $Q$ are incident to $l$.
3. There exist three noncollinear points.

Models for incidence geometry include

• three-point geometry
• Euclidean geometry
• Poincare disk
• Fano's geometry