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.
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.