翻訳と辞書 Words near each other ・ Hypercompe simplex ・ Hypercompe suffusa ・ Hypercompe tenebra ・ Hypercompe tessellata ・ Hypercompe testacea ・ Hypercompe theophila ・ Hypercompe trinitatis ・ Hypercompe turruptianoides ・ Hypercompetition ・ Hypercomplex analysis ・ Hypercomplex cell ・ Hypercomplex manifold ・ Hypercomplex number ・ Hypercomputation ・ Hyperconcentrated flow ・ Hypercone ・ Hypercone (spacecraft) ・ Hyperconjugation ・ Hyperconnected space ・ Hyperconnectivity ・ Hyperconsumerism ・ Hypercorrection ・ Hypercoryphodon ・ HyperCourseware ・ Hypercube ・ Hypercube graph ・ Hypercubic honeycomb ・ Hypercycle ・ Hypercycle (chemistry) ・ Hypercycle (hyperbolic geometry) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Hypercone ： ウィキペディア英語版 Hypercone In geometry, a hypercone (or spherical cone) is the figure in the 4-dimensional Euclidean space represented by the equation :$x^2\; +\; y^2\; +\; z^2\; -\; w^2\; =\; 0.$ 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 spherical 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 spherical 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. ==Parametric form== A right spherical hypercone can be described by the function :$\backslash vec\; \backslash sigma\; (\backslash phi,\; \backslash theta,\; t)\; =\; (t\; s\; \backslash cos\; \backslash theta\; \backslash cos\; \backslash phi,\; t\; s\; \backslash cos\; \backslash theta\; \backslash sin\; \backslash phi,\; t\; s\; \backslash sin\; \backslash theta,\; t)$ with vertex at the origin and expansion speed ''s''. An oblique spherical hypercone could then be described by the function :$\backslash vec\; \backslash sigma\; (\backslash phi,\; \backslash theta,\; t)\; =\; (v\_x\; t\; +\; t\; s\; \backslash cos\; \backslash theta\; \backslash cos\; \backslash phi,\; v\_y\; t\; +\; t\; s\; \backslash cos\; \backslash theta\; \backslash sin\; \backslash phi,\; v\_z\; t\; +\; t\; s\; \backslash sin\; \backslash theta,\; t)$ where $(v\_x,\; v\_y,\; v\_z)$ is the 3-velocity of the center of the expanding sphere. An example of such a cone would be an expanding sound wave as seen from the point of view of a moving reference frame: e.g. the sound wave of a jet aircraft as seen from the jet's own reference frame. Note that the 3D-surfaces above enclose 4D-hypervolumes, which are the 4-cones proper. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hypercone」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.