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  2. Five-dimensional space - Wikipedia

    en.wikipedia.org/wiki/Five-dimensional_space

    Therefore, the geometry of the 5th dimension studies the invariant properties of such space-time, as we move within it, expressed in formal equations. [11] Fifth dimensional geometry is generally represented using 5 coordinate values (x,y,z,w,v), where moving along the v axis involves moving between different hyper-volumes. [12]

  3. List of formulas in elementary geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables r {\displaystyle r} is the radius, C = 2 π r {\displaystyle C=2\pi r} is the circumference (the length of any one of its great circles ),

  4. List of mathematical shapes - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_shapes

    Tessellations of euclidean and hyperbolic space may also be considered regular polytopes. Note that an 'n'-dimensional polytope actually tessellates a space of one dimension less. For example, the (three-dimensional) platonic solids tessellate the 'two'-dimensional 'surface' of the sphere.

  5. Geometry - Wikipedia

    en.wikipedia.org/wiki/Geometry

    A surface is a two-dimensional object, such as a sphere or paraboloid. [55] In differential geometry [53] and topology, [49] surfaces are described by two-dimensional 'patches' (or neighborhoods) that are assembled by diffeomorphisms or homeomorphisms, respectively. In algebraic geometry, surfaces are described by polynomial equations. [54]

  6. 5-simplex - Wikipedia

    en.wikipedia.org/wiki/5-simplex

    In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.It has six vertices, 15 edges, 20 triangle faces, 15 tetrahedral cells, and 6 5-cell facets.It has a dihedral angle of cos −1 (⁠ 1 / 5 ⁠), or approximately 78.46°.

  7. 5-cube - Wikipedia

    en.wikipedia.org/wiki/5-cube

    In five-dimensional geometry, a 5-cube is a name for a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract 4-faces. It is represented by Schläfli symbol {4,3,3,3} or {4,3 3 }, constructed as 3 tesseracts, {4,3,3}, around each cubic ridge .

  8. Numerical differentiation - Wikipedia

    en.wikipedia.org/wiki/Numerical_differentiation

    The classical finite-difference approximations for numerical differentiation are ill-conditioned. However, if is a holomorphic function, real-valued on the real line, which can be evaluated at points in the complex plane near , then there are stable methods.

  9. Space (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Space_(mathematics)

    Also, the distinction between a Euclidean plane and a Euclidean 3-dimensional space is not an upper-level distinction; the question "what is the dimension" makes sense in both cases. The second-level classification distinguishes, for example, between Euclidean and non-Euclidean spaces; between finite-dimensional and infinite-dimensional spaces ...

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