Tons of Quadric Surfaces and Cylinders in 3D

Tons of Quadric Surfaces and Cylinders in 3D
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2017-06-15 11:14
① This GeoGebra example displays a rich collection of quadric surfaces (ellipsoids, hyperboloids, paraboloids, etc.) and cylinders in a 3D view, allowing users to visually grasp their shapes and key features. ② Core mathematical concepts include standard equations of quadric surfaces, definition of cylinders, rotation and symmetry in space, and the use of parametric equations for 3D plotting. ③ Construction highlights: based on the summary, multiple named objects (a through k) are used, likely as sliders or parameters to adjust dimensions and positions; surfaces are generated via GeoGebra's surface commands or implicit equations, with rotation tools for viewpoint adjustment. ④ Suitable for high school to university-level analytic geometry or solid geometry instruction, as well as introductory computer graphics or mathematical modeling, serving as classroom demonstrations or self-guided exploration.

GeoGebra Commands & Parameters

  1. y = x^(2)
  2. z = y^(2)
  3. x^(2) + z^(2) = 1
  4. d: z = 2^(y)
  5. x^(2) / 4 + y^(2) / 16 + z^(2) / 9 = 1
  6. z = (3 * x^(2)) + (2 * y^(2))
  7. z = y^(2) - x^(2)
  8. x^(2) / 9 + y^(2) / 4 - z^(2) / 9 = 1
  9. (6 * x^(2)) - y^(2) + (3 * z^(2)) + 12 = 0
  10. x^(2) + (2 * z^(2)) - (8 * x) - y + 10 = 0
  11. z^(2) - (4 * z) - (4 * x^(2)) - (8 * x) - y^(2) + (6 * y) - 9 = 0