Individual #geometry  the pure mathematics of points and lines and curves and surfaces
  >part of:  #pure_mathematics  the branches of mathematics that study and develop the principles of mathematics for their own sake rather than for their immediate usefulness
  >part:  #elementary_geometry__parabolic_geometry__parabolicgeometry__Euclidean_geometry  geometry based on Euclid's axioms: e.g., only one line can be drawn through a point parallel to another line
  >part:  #non-Euclidean_geometry  geometry based on axioms different from Euclid's
     >part:  #hyperbolic_geometry  a non-Euclidean geometry in which it is assumed that through any point there are two or more parallel lines that do not intersect a given line in the plane
     >part:  #elliptic_geometry__Riemannian_geometry  a non-Euclidean geometry that regards space is like a sphere and a line is a great circle
  >part:  #spherical_geometry__sphericalgeometry  the geometry of figures on the surface of a sphere
  >part:  #analytic_geometry__analytical_geometry__coordinate_geometry  the use of algebra to study geometric properties; operates on symbols defined in a coordinate system
  >part:  #plane_geometry__planegeometry  the geometry of 2-dimensional figures
  >part:  #solid_geometry__solidgeometry  the geometry of 3-dimensional space
  >part:  #projective_geometry__descriptive_geometry__descriptivegeometry  the geometry of properties that remain invariant under projection

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