In geometry, a hypercone (or spherical cone) is the figure in the 4-dimensional Euclidean space represented by the equation 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.
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- Гиперконус (ru)
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| - In geometry, a hypercone (or spherical cone) is the figure in the 4-dimensional Euclidean space represented by the equation 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. (en)
- Гиперконус (англ. Hypercone) — четырёхмерная фигура, образованная следующим образом. В четырёхмерной системе координат ставим точку А. Затем рисуем шар с центром в точке В, так чтобы прямая АВ была перпендикулярна шару. Из каждой точки шара проводим отрезок в точку A. Из полученных отрезков вырождается фигура — гиперконус. А — его вершина, В — его основание. Его гиперобъем: (ru)
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| - In geometry, a hypercone (or spherical cone) is the figure in the 4-dimensional Euclidean space represented by the equation 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. (en)
- Гиперконус (англ. Hypercone) — четырёхмерная фигура, образованная следующим образом. В четырёхмерной системе координат ставим точку А. Затем рисуем шар с центром в точке В, так чтобы прямая АВ была перпендикулярна шару. Из каждой точки шара проводим отрезок в точку A. Из полученных отрезков вырождается фигура — гиперконус. А — его вершина, В — его основание. Его гиперобъем: (ru)
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