The best replacement for euclidean geometry is non euclidean geometry.

The best alternatives to euclidean geometry are rated as following:
★★★★★  non euclidean geometry
★★★  spherical geometry
★★  non euclidean
★★  non-euclidean geometry
★★  euclidean geometry
★  taxicab geometry
★  fractal geometry
  spherical
  fractal
  coordinate geometry

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euclidean geometry
non euclidean geometry
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