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  2. Hypersurface - Wikipedia

    en.wikipedia.org/wiki/Hypersurface

    In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface.A hypersurface is a manifold or an algebraic variety of dimension n − 1, which is embedded in an ambient space of dimension n, generally a Euclidean space, an affine space or a projective space. [1]

  3. Hyperplane - Wikipedia

    en.wikipedia.org/wiki/Hyperplane

    In geometry, a hyperplane of an n-dimensional space V is a subspace of dimension n − 1, or equivalently, of codimension 1 in V.The space V may be a Euclidean space or more generally an affine space, or a vector space or a projective space, and the notion of hyperplane varies correspondingly since the definition of subspace differs in these settings; in all cases however, any hyperplane can ...

  4. Decision boundary - Wikipedia

    en.wikipedia.org/wiki/Decision_boundary

    In a statistical-classification problem with two classes, a decision boundary or decision surface is a hypersurface that partitions the underlying vector space into two sets, one for each class. The classifier will classify all the points on one side of the decision boundary as belonging to one class and all those on the other side as belonging ...

  5. n-sphere - Wikipedia

    en.wikipedia.org/wiki/N-sphere

    Considered extrinsically, as a hypersurface embedded in ⁠ (+) ⁠-dimensional Euclidean space, an ⁠ ⁠-sphere is the locus of points at equal distance (the radius) from a given center point. Its interior , consisting of all points closer to the center than the radius, is an ⁠ ( n + 1 ) {\displaystyle (n+1)} ⁠ -dimensional ball .

  6. 3-sphere - Wikipedia

    en.wikipedia.org/wiki/3-sphere

    The four Euclidean coordinates for S 3 are redundant since they are subject to the condition that x 0 2 + x 1 2 + x 2 2 + x 3 2 = 1. As a 3-dimensional manifold one should be able to parameterize S 3 by three coordinates, just as one can parameterize the 2-sphere using two coordinates (such as latitude and longitude ).

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    Discover the best free online games at AOL.com - Play board, card, casino, puzzle and many more online games while chatting with others in real-time.

  8. Second fundamental form - Wikipedia

    en.wikipedia.org/wiki/Second_fundamental_form

    The second fundamental form of a parametric surface S in R 3 was introduced and studied by Gauss. First suppose that the surface is the graph of a twice continuously differentiable function, z = f(x,y), and that the plane z = 0 is tangent to the surface at the origin. Then f and its partial derivatives with respect to x and y vanish at (0,0).

  9. Trump's trade plan could mean higher prices, and avoiding the ...

    www.aol.com/news/trumps-trade-plan-could-mean...

    It's beginning to look a lot like tariffs. With less than two months until the presidential inauguration, the potential impact of one of President-elect Donald Trump's key proposed policies is ...

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