Level Curves of Plane and Sphere

Level Curves of Plane and Sphere
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2016-07-14 22:35
This example demonstrates the level curves on a plane and a sphere. It involves core mathematical concepts such as level curves, 3D vectors, function graphs, and analytical geometry. The construction uses GeoGebra commands like IntersectPath with objects f, a, b, c, d, g, i, e, h, eq1, eq2, eq3. It is suitable for high school and above students studying solid geometry, calculus, and 3D graph visualization.

GeoGebra Commands & Parameters

  1. IntersectPath(z = -6, f) → a
  2. IntersectPath(z = 0, f) → b
  3. IntersectPath(z = 6, f) → c
  4. IntersectPath(z = 12, f) → d
  5. IntersectPath(z = 0, g) → i
  6. IntersectPath(z = 0.5, g) → e
  7. IntersectPath(z = 1, g) → h
  8. IntersectPath(z = 1.5, g) → eq1
  9. IntersectPath(z = 2, g) → eq2
  10. IntersectPath(z = 2.5, g) → eq3