# Projective geometry

**Projective geometry **can be thought of informally as the geometry which
arises from placing one's eye at a point. That is, every line which intersects
the "eye" appears only as a point in the projective plane because the eye cannot
"see" the points behind it. Projective geometry has also been a useful tool in
proving a number of theorems from Euclidean
geometry.

Whatever the precise foundational status, projective geometry did include basic incidence properties. That means that any two distinct lines L and M in the projective plane intersect in exactly one point P. The special case in analytic geometry of parallel lines has been subsumed in the smoother form of a line at infinity on which P will lie in that case. The point is then that the line at infinity is a line like any other in the theory: it is in no way special or distinguished.

**See also**

2D | Two-dimensional coordinate system |

3D | Three-dimensional coordinate system |

Angle | Definition of an angle |

Axis | Definition of Cartesian axis |

Cartesian geometry | What is Cartesian geometry? |

Coordinate system | Definition of coordinates |

Curve | Definition of a curve |

Distance | Definition of distance |

Euclidean geometry | What is Euclidean geometry? |

Geometry | Definition of geometry |

Length | Definition of length |

Line | Definition of a line |

Origin | Definition of origin in a Cartesian coordinate system |

Perspective projection | Definition of perspective projection |

Planar homography | Definition of planar homography |

Plane | Definition of a plane |

Point | Definition of a point |

Point (kinematics) | Definition of a point (kinematics) |

Projective geometry | What is projective geometry? |

Segment (kinematics) | Definition of a segment (kinematics) |

Vanishing points | Definition of vanishing points and vanishing lines in perspective projection |

Vector | Definition of a vector |