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Quadric Surfaces (3D Graphing)

Quadric Surfaces (3D Graphing)
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2014-12-09 01:20
Coordinate GeometrySolid GeometryCalculus
In collections Calc 2
This example demonstrates various quadric surfaces such as ellipsoid, elliptic cone, hyperbolic paraboloid, one-sheet hyperboloid, and two-sheet hyperboloid. Key mathematical concepts include the geometric properties and equations of quadric surfaces. By adjusting parameters a, b, c, etc., the shapes and transformations of these surfaces can be dynamically displayed. Suitable for high school and above students and educators.

GeoGebra Commands & Parameters

  1. Surface(((a * cos(u)) * sin(v)), ((b * sin(u)) * sin(v)), (c * cos(v)), u, 0, 6.28319, v, 0, 3.141592653589793) → Ellipsoid
  2. Surface((((a * (c - w))) / c * cos(v)), (((b * (c - w))) / c * sin(v)), w, v, 0, 6.28319, w, 0, (2 * c)) → EllipticCone
  3. Surface(u, v, (u * v), u, (-a), a, v, (-b), b) → HyperbolicParaboloid
  4. Surface(((a * cosh(w)) * cos(v)), ((b * cosh(w)) * sin(v)), (c * sinh(w)), v, 0, 6.283185307179586, w, -10, 10) → HyperboloidOneSheet
  5. Surface(((a * sinh(w)) * cos(v)), ((b * sinh(w)) * sin(v)), (c * cosh(w)), v, 0, 6.283185307179586, w, 0, 100) → HyperboloidTwoSheetTop
  6. Surface(((a * sinh(w)) * cos(v)), ((b * sinh(w)) * sin(v)), ((-c) * cosh(w)), v, 0, 6.28319, w, 0, 100) → HyperboloidTwoSheetBottom
  7. Plane((-1, 0, 0), (1, 0, 0), (0, 0, 1)) → f
  8. Surface(((a * sqrt(w)) * cos(v)), ((b * sqrt(w)) * sin(v)), w, v, 0, 6.28319, w, 0, 6) → EllipticParaboloid

AI Drawing Prompt Reference

Draw an ellipsoid, then an elliptic cone, followed by a hyperbolic paraboloid, a one-sheet hyperboloid, and finally a two-sheet hyperboloid with both top and bottom. Adjust parameters a, b, and c to change the shape and size.
The prompt above was compiled from the original drawing commands and is for reference only.