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A real world example of what? Math in general? Geometry nets? Name the math concept and it'll be easier for readers to give you a real world example.
Non-Euclidean geometry is most practical when used for calculations in three dimensions, as opposed to only two. For example, planning the fastest route for an airplane or a ship to travel across the world requires non-Euclidean geometry, because the Earth is a sphere.
-- The shoreline of any coastal land is a fractal. -- The distant view of any mountain range is a fractal. -- Your eyes perceive changes in light brightness on a logarithmic scale. -- Your ears perceive changes in sound loudness on a logarithmic scale.