Hypercone

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In geometry, a hypercone (or spherical cone) is the figure in the 4-dimensional Euclidean space represented by the equation

${\displaystyle x^{2}+y^{2}+z^{2}-w^{2}=0.}$

It is a quadric surface, and is one of the possible 3-manifolds which are 4-dimensional equivalents of the conical surface in 3 dimensions. It is also named "spherical cone" because its intersections with hyperplanes perpendicular to the w-axis are spheres. A four-dimensional right hypercone can be thought of as a sphere which expands with time, starting its expansion from a single point source, such that the center of the expanding sphere remains fixed. An oblique hypercone would be a sphere which expands with time, again starting its expansion from a point source, but such that the center of the expanding sphere moves with a uniform velocity.