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Answers for “在双曲几何中,平行公理有何不同?”

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Non-Euclidean geometry is needed because Euclidean geometry is limited to flat planes. When dealing with curved surfaces, such as a football, or the curved space and time of the universe, Euclidean geometry faces significant problems and cannot accurately model these situations.

Conditions: Applying geometry to curved surfaces.; Modeling the universe's spacetime.