File:Hyperboloid sections.gif

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Hyperboloid_sections.gif(400 × 400 pixels, file size: 1.89 MB, MIME type: image/gif, looped, 44 frames, 44 s)

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English: Here we take a hyperboloid x2+y2-z2=1 and produce its sections by planes that contain the point (x0,0,0) are parallel to Oy axis and are inclined to Ox axis on angles t in such a way, that we have:
  • Ellipses (0<=e<1)
  • Parabola (e=1)
  • Hyperbolas (1<e)
The eccentricity is actually not bounded here: the closer we take the angle t in the last frame to 45 degrees, the higher eccentricity we get.
Русский: Здесь мы рассматриваем однополостный гиперболоид x2+y2-z2=1 и производим его сечения плоскостями, содержащими точку (x0,0,0), параллельными оси Oy и составляющими с осью Ox угол t таким образом, что мы имеем:
  • Эллипсы (0<=e<1)
  • Параболу (e=1)
  • Гиперболы (1<e)
Значения эксцентриситета здесь не ограничены сверху: чем ближе мы возьмём угол t к 45 градусам в последнем кадре, тем больший эксцентриситет получим.
Date
Source Own work
Author Cmapm

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Date/TimeThumbnailDimensionsUserComment
current20:32, 12 December 2012Thumbnail for version as of 20:32, 12 December 2012400 × 400 (1.89 MB)Cmapm (talk | contribs)User created page with UploadWizard

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