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Parabola Motion Demo

Parabola Motion Demo
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2016-06-19 14:56
VectorCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the motion trajectory and geometric properties of a parabola. It involves core mathematical concepts such as parabola, symmetry, exponent functions, logic reasoning, cuboid in solid geometry, and median value theorem. The construction highlights the use of GeoGebra commands/objects like Intersect (intersection), OrthogonalLine (perpendicular line), Cone (cone), Mirror (reflection), Line (line), Vector (vector), Circle (circle), Midpoint (midpoint), Rotate (rotation), Plane (plane), Point (point), IntersectPath (path intersection), AngularBisector (angle bisector), Sphere (sphere), OrthogonalPlane (orthogonal plane), Angle (angle), and Segment (segment). Suitable for high school and above learners to understand dynamic changes and geometric constructions of parabolas.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, zAxis) → O
  2. OrthogonalLine(O, xOyPlane) → f
  3. Cone(C, O, rc) → a, c, b
  4. Mirror(C, O) → C'
  5. Cone(C', O, rc) → d, e, g
  6. Line(A, O) → i
  7. Mirror(A, B) → A'
  8. Vector(O, C) → u
  9. Circle(A, ra, u) → k
  10. Circle(B, rb, f) → h
  11. Line(A', O) → j
  12. Intersect(h, k) → D, E_1, ,
  13. Midpoint(D, E_1) → G'
  14. Line(G', i) → n
  15. Intersect(n, zAxis) → G
  16. Rotate(B, β, G, xOyPlane) → B'
  17. Plane(G, G', A) → l
  18. Plane(E_1, D, G) → m
  19. OrthogonalLine(G, m) → q
  20. Point(q) → H
  21. Vector(G, H) → v
  22. Plane(E_1, D, I) → o
  23. IntersectPath(o, a) → r
  24. IntersectPath(o, d) → s
  25. Intersect(j, r) → J,
  26. Intersect(f, o) → K
  27. Line(J, I) → t
  28. AngularBisector(t, j) → f_1, g_1
  29. Intersect(f, f_1) → L_1
  30. OrthogonalLine(L_1, j, space) → h_1
  31. Intersect(j, h_1) → M_1
  32. Sphere(L_1, M_1) → w
  33. OrthogonalLine(L_1, o) → i_1
  34. Intersect(i_1, o) → F
  35. OrthogonalPlane(M_1, f) → a_1
  36. IntersectPath(a_1, w) → c_1
  37. Intersect(i, s) → N,
  38. Midpoint(J, N) → M
  39. Mirror(F, M) → F'
  40. Mirror(T, B) → T'
  41. Line(T', O) → p
  42. Line(T, O) → j_1
  43. Line(T, O) → k_1
  44. IntersectPath(o, a_1) → L
  45. Line(R, O) → m_1
  46. Intersect(m_1, r) → P,
  47. Intersect(m_1, c_1) → E,
  48. OrthogonalLine(P, a_1) → n_1
  49. Intersect(n_1, a_1) → S
  50. OrthogonalLine(P, L, space) → p_1
  51. Intersect(L, p_1) → U
  52. Angle(L, p_1) → γ
  53. Segment(U, S) → q_1
  54. Segment(S, E) → r_1
  55. Segment(P, U) → s_1
  56. Segment(P, E) → t_1
  57. Segment(F, P) → b_1
  58. Angle(r_1, n_1) → δ
  59. Segment(P, S) → d_1

AI Drawing Prompt Reference

Draw a parabola motion demonstration, showing trajectory and symmetry, highlighting core mathematical concepts. Start with coordinate axes intersection and perpendicular lines, construct cones and reflections, then create vectors, circles, and rotations. Use path intersections, midpoints, and angle bisectors to build geometric bodies, and finally complete the dynamic changes with spheres, planes, and angle bisectors.
The prompt above was compiled from the original drawing commands and is for reference only.