旋转对称性演示 by juliacyng

旋转对称性演示 by juliacyng
几何画板及绘图内容加载中,请稍等……
2014-03-17 12:03
①本范例演示图形绕中心点旋转一定角度后与原图重合的现象;②涉及核心数学概念为旋转对称性、角度、几何变换;③作图要点:使用 GeoGebra 命令 Circle(画圆)、Point(创建点)、Angle(设置角度)、Rotate(旋转对象)等构建图形;④适合初中及以上学生学习几何变换与对称性知识,也可用于数学演示。

GeoGebra 命令及参数

  1. Circle(O, A) → c
  2. Point(c) → B
  3. Angle(A, O, B) → α
  4. Rotate(pic1, α, O) → pic1'
  5. Circle(D, C) → d
  6. Point(d) → E
  7. Angle(C, D, E) → β
  8. Rotate(pic2, β, D) → pic2'
  9. Circle(G, F) → e
  10. Point(e) → H
  11. Angle(F, G, H) → γ
  12. Rotate(pic15, γ, G) → pic15'
  13. Circle(I, J) → f
  14. Point(f) → K
  15. Angle(J, I, K) → δ
  16. Rotate(pic9, δ, I) → pic9'
  17. Circle(L, M) → g
  18. Point(g) → N
  19. Angle(M, L, N) → ε
  20. Rotate(pic18, ε, L) → pic18'
  21. Circle(P, Q) → h
  22. Point(h) → R
  23. Angle(Q, P, R) → ζ
  24. Rotate(pic5, ζ, P) → pic5'
  25. Circle(S, T) → k
  26. Point(k) → U
  27. Angle(T, S, U) → η
  28. Rotate(pic6, η, S) → pic6'
  29. Circle(V, W) → p
  30. Point(p) → Z
  31. Angle(W, V, Z) → θ
  32. Rotate(pic11, θ, V) → pic11'
  33. Circle(A_1, B_1) → q
  34. Point(q) → C_1
  35. Angle(B_1, A_1, C_1) → ι
  36. Rotate(pic13, ι, A_1) → pic13'
  37. Circle(D_1, E_1) → r
  38. Point(r) → F_1
  39. Angle(E_1, D_1, F_1) → κ
  40. Rotate(pic10, κ, D_1) → pic10'
  41. Circle(G_1, H_1) → s
  42. Point(s) → I_1
  43. Angle(H_1, G_1, I_1) → λ
  44. Rotate(pic7, λ, G_1) → pic7'
  45. Circle(J_1, K_1) → t
  46. Point(t) → L_1
  47. Angle(K_1, J_1, L_1) → μ
  48. Rotate(pic17, μ, J_1) → pic17'
  49. Circle(M_1, N_1) → c_1
  50. Point(c_1) → O_1
  51. Angle(N_1, M_1, O_1) → ν
  52. Rotate(pic8, ν, M_1) → pic8'
  53. Circle(P_1, Q_1) → d_1
  54. Point(d_1) → R_1
  55. Angle(Q_1, P_1, R_1) → ξ
  56. Rotate(pic16, ξ, P_1) → pic16'
  57. Circle(S_1, T_1) → e_1
  58. Point(e_1) → U_1
  59. Angle(T_1, S_1, U_1) → ο
  60. Rotate(pic14, Angle[T_1, S_1, U_1], S_1) → pic14'
  61. Circle(V_1, W_1) → f_1
  62. Point(f_1) → Z_1
  63. Rotate(pic4, Angle[W_1, V_1, Z_1], V_1) → pic4'
  64. Circle(A_2, B_2) → g_1
  65. Point(g_1) → C_2
  66. Rotate(pic3, Angle[B_2, A_2, C_2], A_2) → pic3'
  67. Circle(D_2, E_2) → h_1
  68. Point(h_1) → F_2
  69. Rotate(pic12, Angle[E_2, D_2, F_2], D_2) → pic12'

AI 绘图提示语参考

绘制一个中心对称图形,围绕一个点旋转。首先画一个圆,然后在圆上取一个点,测量该点与圆心的夹角。接着,以圆心为中心,将圆旋转该角度。重复此过程,每次旋转不同的角度,直到形成一个具有多个旋转对称性的图形。
以上提示语为根据原始绘图命令整理而来,仅供参考。