运动对称 = 保持质心

运动对称 = 保持质心
几何画板及绘图内容加载中,请稍等……
2017-12-05 18:21
该 GeoGebra 范例直观演示了运动对称性下质心的不变性。通过点、线、圆弧、射线等几何构造,展示了在特定运动变换中,质心位置保持不变的数学原理。核心概念涉及对称性、质心、几何变换与三角函数关系。作图要点包括使用 Point、Segment、CircleArc、Intersect、Ray、OrthogonalLine、Angle、Line、Polygon 等命令,以及 E_k、E_ob、E_oa 等几何对象的组合应用。适合高中数学、物理及几何变换单元的教学与探究。

GeoGebra 命令及参数

  1. Point(yAxis) → R
  2. Point(yAxis) → A
  3. Segment(A, S) → i
  4. Point(xAxis) → C
  5. Point(yAxis) → B
  6. CircleArc(A, R, B) → c
  7. Intersect(c, i) → T,
  8. Ray(A, C) → b
  9. OrthogonalLine(C, b) → d
  10. CircleArc(A, C, T) → Arc
  11. Point(d) → K
  12. Angle(C, A, Rotate[C, alfa, A]) → α
  13. OrthogonalLine(T, yAxis) → j
  14. OrthogonalLine(T, xAxis) → l
  15. Intersect(j, yAxis) → U
  16. Intersect(l, xAxis) → V
  17. Segment(A, V) → cosinus
  18. Segment(A, U) → sinus
  19. Segment(U, T) → s
  20. Segment(V, T) → t
  21. Segment(C, S) → tangens
  22. Point(yAxis) → D
  23. Point(yAxis) → L
  24. Point(d) → M
  25. Segment(A, J) → m
  26. Intersect(c, m) → O,
  27. OrthogonalLine(O, yAxis) → n
  28. OrthogonalLine(O, xAxis) → p
  29. Intersect(p, xAxis) → P
  30. Intersect(n, yAxis) → Q
  31. Segment(C, J) → q
  32. Segment(A, Q) → r
  33. Segment(A, P) → b_1
  34. Angle(J, A, V) → β
  35. Segment(P, O) → e
  36. Segment(O, Q) → f
  37. Point(xAxis) → W
  38. CircleArc(A, O, C) → g
  39. Segment(T, S) → a
  40. Segment(J, O) → h
  41. Segment(V, Q) → k
  42. Line(C, k) → a_1
  43. Intersect(a_1, yAxis) → F
  44. Line(F, xAxis) → c_1
  45. Line(S, xAxis) → d_1
  46. Point(d_1) → G
  47. Line(G, yAxis) → e_1
  48. Intersect(e_1, c_1) → H
  49. Segment(G, H) → v_{ab}
  50. Segment(G, S) → g_1
  51. Segment(H, F) → h_1
  52. Segment(F, C) → i_1
  53. Polygon(A, B_1, N, U) → p_{ea}, a_2, b_2, E_{a}, u
  54. Polygon(C_1, Z, Q, A) → p_{eb}, c_2, E_{b}, q_1, a_3
  55. Polygon(C, S, D_1, D_2) → p_{ia}, c_3, E_{0a}, d_2, d_3
  56. Polygon(C, F_2, F_1, J) → p_{ib}, c_4, f_2, E_{0b}, j_1