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Point, Circle, Sphere with Animated Views

Point, Circle, Sphere with Animated Views
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2017-02-14 10:54
CircleSolid GeometryParametric EquationGeometric ConstructionSlider Animation
This example demonstrates dynamic views of points, circles, and spheres. It involves core math concepts like circles, spheres, area, set theory, median value, arithmetic, and standard deviation. Construction highlights include commands/objects such as Point, Circle, Vector, Angle, Line, Rotate, PathParameter, Segment, Sphere, PointIn. Suitable for high school and above students learning solid geometry and parametric equations applications.

GeoGebra Commands & Parameters

  1. Point(zAxis) → O
  2. Circle(O, B, xOyPlane) → c
  3. Vector((0, 0), (0, 1, 0)) → u
  4. Circle(O, B, u) → d
  5. Point(d) → Q
  6. Angle(B, O, Q) → α
  7. Line(C, O) → a
  8. Rotate(c, (-α), a) → c'
  9. Rotate(c, α, a) → c''
  10. PathParameter(Q) → b
  11. Vector(O, Q) → r_Q
  12. Vector(V, O) → w
  13. Segment((-4, 0, 0), (4, 0, 0)) → xaxisline
  14. Segment((0, -4, 0), (0, 4, 0)) → yaxisline
  15. Segment((0, 0, -4), (0, 0, 4)) → zaxisline
  16. Point(c) → P
  17. Vector(O, P) → r_P
  18. Sphere(O, Q) → h
  19. Sphere(O, C') → i
  20. PointIn(i) → E
  21. Vector(O, E) → k
  22. Vector(O, V_d) → u_d
  23. Circle(O, Distance[O, B], u_d) → p
  24. Point(p) → J
  25. Vector(O, J) → r_J