Mathematics
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Non-Euclidean geometry
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Non-Euclidean geometry
Non-Euclidean geometry means, in the literal sense — all geometric systems distinct from Euclidean geometry; usually, however, the term “non-Euclidean geometries” is reserved for geometric systems (distinct from Euclidean geometry) in which the motion of figures is defined, and this with the same degree of freedom as in Euclidean geometry.
The degree of freedom of motion of figures in the Euclidean plane is characterized by the condition that every figure can be moved, without changing the distances between its points, in such a way that any selected point of the figure can be made to occupy a previously-designated position; moreover, every figure can be rotated about any of its points.
In the Euclidean three-dimensional space, every figure can be moved in such a way that any selected point of the figure will occupy any prescribed position; besides, every figure can be rotated about any axis through any of its points.
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