Quadric Surfaces by JohnShea

Quadric Surfaces by JohnShea
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2019-01-25 01:19
This example demonstrates the geometric construction of quadric surfaces, which are surfaces in three-dimensional space defined by quadratic equations, including ellipsoids, hyperboloids, and paraboloids. By adjusting parameters, different types of quadric surfaces can be observed. The example uses GeoGebra commands such as a, b, c, etc., to show how the shape of the surface can be changed by adjusting parameters. Suitable for high school mathematics education and students learning three-dimensional geometry.

GeoGebra Commands & Parameters

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