{\displaystyle a=(a_{0}:a_{1}:a_{2}:\cdots )} its polarhypersurface P a ( C ) {\displaystyle P_{a}(C)} is the hypersurface a 0 f 0 + a 1 f 1 + a 2 f 2 + ⋯ = 0 ,...
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...
locus of points whose polar conics are degenerate, of degree 3(n−2) called the Hessian curve of C. Polarhypersurface Pole and polar Follows Salmon pp. 49-50...
coordinate system we may speak of coordinate planes. Similarly, coordinate hypersurfaces are the (n − 1)-dimensional spaces resulting from fixing a single coordinate...
normals. In three dimensions, the curl of a polar vector field at a point and the cross product of two polar vectors are pseudovectors. A number of quantities...
(quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas). It is a hypersurface (of dimension...
circle, so the polar reciprocal is the inverse of the pedal of C. Similarly, generalizing to higher dimensions, given a hypersurface, the tangent space...
tropical hypersurface of f is supported on a subfan of the normal fan of the Newton polytope P of f. In particular, the tropical hypersurface is supported...
geometry, a Steinerian of a hypersurface, introduced by Steiner (1854), is the locus of the singular points of its polar quadrics. Coolidge, Julian Lowell...
set. The stereographic projection presents the quadric hypersurface as a rational hypersurface. This construction plays a role in algebraic geometry and...
Victor Batyrev using the polar duality for d {\displaystyle d} -dimensional convex polyhedra. The most famous examples of the polar duality provide Platonic...
zero. The gradient of F is then normal to the hypersurface. Similarly, an affine algebraic hypersurface may be defined by an equation F(x1, ..., xn) =...
{O}}_{X}(5))=(1+h)^{5}=1+5h+10h^{2}+10h^{3}} Since the Chow ring of a hypersurface is difficult to compute, we will consider this sequence as a sequence...
Strictly speaking, the Laplace sphere is not a sphere but a changing hypersurface defined at each point of the path of a gravitational mass. The criterion...
in a Euclidean space of dimension n {\displaystyle n} , is a quadric hypersurface defined by a polynomial of degree two that has a homogeneous part of...
^{n}.} The coordinates of a point x of E are the components of f(x). The polar coordinate system (dimension 2) and the spherical and cylindrical coordinate...
corresponding timelike congruence vanishes; thus, this Killing vector field is hypersurface orthogonal. The fact that the spacetime admits an irrotational timelike...
together with the subspace hyperplanes separating hemispheres are the hypersurfaces of the Poincaré disc model of hyperbolic geometry. Since inversion in...
{\displaystyle \mathbf {q} =(q^{1},q^{2},\dots ,q^{d})} in which the coordinate hypersurfaces all meet at right angles (note that superscripts are indices, not exponents)...
point from the other axis. Another widely used coordinate system is the polar coordinate system, which specifies a point in terms of its distance from...
3. (Noun) The first polar, second polar, and so on are varieties of degrees n–1, n–2, ... formed from a point and a hypersurface of degree n by polarizing...
of curvature Second fundamental form for the extrinsic curvature of hypersurfaces in general Sinuosity Torsion of a curve Clagett, Marshall (1968), Nicole...
"at rest" in spacetime, i.e. with 4-velocity perpendicular to spatial hypersurfaces. Relativistic Euler equations Euler top Newton–Euler equations d'Alembert–Euler...
are great circles, i.e., intersections of the hypersphere with flat hypersurfaces of dimension n passing through the origin. In the projective model of...
corresponding timelike congruence vanishes; thus, this Killing vector field is hypersurface orthogonal. The fact that our spacetime admits an irrotational timelike...
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