Individual #non-Euclidean_geometry  geometry based on axioms different from Euclid's
  >part:  #hyperbolic_geometry  #elliptic_geometry
  >part of:  #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 of:  #mathematics__math__maths__math  a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement

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