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i几何维度演示

i几何维度演示
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2016-01-13 13:29
圆向量复数几何作图
①本范例演示复数单位i在复平面上的几何表示及其与单位圆的关系；②涉及核心数学概念包括复数、单位圆、向量、几何变换；③作图要点：使用了Vector、Point、Line、Segment、Distance、Circle、Mirror、Polygon、Factors、ReducedRowEchelonForm、Angle、CircleArc、Intersect等GeoGebra命令与对象；④适合高中及以上数学学习者，用于理解复数几何意义和操作。

GeoGebra 命令及参数

  1. Vector((0, 0), (1, 0)) → u
  2. Vector((0, -0.007890188248790508), (a^(0.5), a^(0.5))) → d
  3. Vector((0, 0), ((-a^(0.5)), (-a^(0.5)))) → e
  4. Vector((0, 0), (a^(0.5), (-a^(0.5)))) → f
  5. Vector((0, 0), ((-a^(0.5)), a^(0.5))) → g
  6. Point(b) → C
  7. Point(v) → D
  8. Point(w) → E
  9. Point(c) → F
  10. Point(d) → G
  11. Point(e) → H
  12. Point(g) → I
  13. Point(f) → J
  14. Point(f) → K
  15. Line(G, w) → h
  16. Point(v) → L
  17. Vector((0, 0), (a^(0.5), 0)) → i
  18. Point(i) → M
  19. Segment(M, G) → j
  20. Segment(D, E) → k
  21. Segment(E, C) → l
  22. Segment(C, F) → m
  23. Segment(F, D) → n
  24. Segment(G, I) → p
  25. Segment(I, H) → q
  26. Segment(H, J) → r
  27. Segment(J, M) → s
  28. Point(k) → A
  29. Distance(K, A) → distanceKA
  30. Distance(G, K) → distanceGK
  31. Point(v) → B
  32. Distance(B, A) → distanceBA
  33. Segment(B, A) → t_x
  34. Circle(K, H) → c_1
  35. Circle(K, C) → d_1
  36. Segment(I, J) → a_1
  37. Mirror(e, a_1) → e'
  38. Mirror(M, p) → M'
  39. Mirror(G, p) → G'
  40. Segment(M', G') → j'
  41. Distance(M, M') → distanceMM'
  42. Polygon(K, E, A) → poly1, a_2, k_1, e_2
  43. Point(d_1) → N
  44. Point(d_1) → O
  45. Segment(N, O) → b_1
  46. Factors(o) → matrix1
  47. ReducedRowEchelonForm(matrix1) → matrix2
  48. Segment(E, M') → h_1
  49. Point(Circle[E, 1.16]) → P
  50. Segment(E, P) → g_1
  51. Point(Circle[P, 1.16]) → Q
  52. Segment(P, Q) → i_1
  53. Point(Circle[E, 1.64]) → R
  54. Segment(E, R) → j_1
  55. Angle(M', E, R) → α
  56. Point(Circle[M', 1.16]) → S
  57. Segment(M', S) → l_1
  58. Point(Circle[E, 1.16]) → T
  59. Segment(E, T) → m_1
  60. CircleArc(K, I, H) → p_1
  61. CircleArc(K, H, G) → e_1
  62. CircleArc(K, E, I) → q_1
  63. Intersect(j', h_1) → V
  64. Point(Circle[M, 1.64]) → W
  65. Segment(M, W) → r_1
  66. Point(Circle[W, 1.16]) → Z
  67. Segment(W, Z) → s_1
  68. Point(Circle[Z, 1.16]) → A_1
  69. Segment(Z, A_1) → t_1