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High Quality Content by WIKIPEDIA articles! In mathematics, an n-dimensional space is a topological space whose dimension is n (where n is a fixed natural number). The archetypical example is n-dimensional Euclidean space, which describes Euclidean geometry in n dimensions. Many familiar geometric objects can be generalized to any number of dimensions. For example, the two-dimensional triangle and the three-dimensional tetrahedron can be seen as specific instances of the n-dimensional simplex. Also, the circle and the sphere can be seen as specific instances of the n-dimensional hypersphere. More generally, an n-dimensional manifold is a space that locally looks like n-dimensional Euclidean space, but whose global structure may be non-Euclidean.