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Six Non-Cylinder and Non-degenerate Quadric Surfaces

Six Non-Cylinder and Non-degenerate Quadric Surfaces
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2017-08-28 22:23
FunctionCoordinate GeometrySolid Geometry
This example demonstrates six non-cylinder and non-degenerate quadric surfaces, including ellipsoids, hyperboloids, and paraboloids. It involves basic concepts of quadric surfaces. By adjusting parameters, you can observe the shape changes of different surfaces. The example uses GeoGebra objects a, b, c, d, e, f to construct these surfaces. Suitable for high school mathematics education and learning about quadric surfaces.

GeoGebra Commands & Parameters

  1. x^(2) / 4 + y^(2) / 16 + z^(2) / 9 = 1
  2. x^(2) / 4 + y^(2) / 16 - z^(2) / 25 = 1
  3. ((-x^(2))) / 1 - y^(2) / 9 + z^(2) / 4 = 1
  4. x^(2) / 4 + y^(2) / 9 = z
  5. y^(2) / 9 - x^(2) / 4 = z
  6. x^(2) + y^(2) - z^(2) = 0

AI Drawing Prompt Reference

Draw an ellipsoid with semi-axes 2, 4, and 3 along the x, y, and z axes respectively; then draw a hyperbolic paraboloid with semi-axes 2 and 4 along the x and y axes and an opening of -25 along the z axis; next, draw a saddle-shaped hyperboloid with an opening of -1 along the x axis, a semi-axis of 3 along the y axis, and a semi-axis of 2 along the z axis; then draw a paraboloid with semi-axes 2 and 3 along the x and y axes and an opening upwards along the z axis; next, draw a hyperbolic paraboloid with semi-axes 3 and -2 along the y and x axes and an opening upwards along the z axis; finally, draw a hyperboloid with semi-axes 1 and 1 along the x and y axes and an opening upwards along the z axis.
The prompt above was compiled from the original drawing commands and is for reference only.