Analytic geometry
![Cartesian coordinates](/Images/godic/202501/11/Punktkoordinaten.svg4126.png")
![](/Images/godic/202501/11/Stereographic_projection_in_3D4126.png")
![Illustration of a Cartesian coordinate plane. Four points are marked and labeled with their coordinates: (2,3) in green, (−3,1) in red, (−1.5,−2.5) in blue, and the origin (0,0) in purple.](/Images/godic/202501/11/Cartesian-coordinate-system.svg4127.png")
![The distance formula on the plane follows from the Pythagorean theorem.](/Images/godic/202501/11/Distance_Formula.svg4127.png")
In classical mathematics, analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.
Analytic geometry is widely used in physics and engineering, and is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry.