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  2. 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 ),

  3. Six-dimensional space - Wikipedia

    en.wikipedia.org/wiki/Six-dimensional_space

    The 6-sphere, or hypersphere in seven dimensions, is the six-dimensional surface equidistant from a point. It has symbol S 6, and the equation for the 6-sphere, radius r, centre the origin is = {: ‖ ‖ =}. The volume of the space bounded by this 6-sphere is

  4. 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]

  5. 6-cube - Wikipedia

    en.wikipedia.org/wiki/6-cube

    In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces. It has Schläfli symbol {4,3 4 }, being composed of 3 5-cubes around each 4-face.

  6. Gauss–Codazzi equations - Wikipedia

    en.wikipedia.org/wiki/Gauss–Codazzi_equations

    The equations were originally discovered in the context of surfaces in three-dimensional Euclidean space. In this context, the first equation, often called the Gauss equation (after its discoverer Carl Friedrich Gauss ), says that the Gauss curvature of the surface, at any given point, is dictated by the derivatives of the Gauss map at that ...

  7. Volume form - Wikipedia

    en.wikipedia.org/wiki/Volume_form

    In mathematics, a volume form or top-dimensional form is a differential form of degree equal to the differentiable manifold dimension. Thus on a manifold M {\displaystyle M} of dimension n {\displaystyle n} , a volume form is an n {\displaystyle n} -form.

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