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泰勒斯与金字塔

泰勒斯与金字塔
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2020-02-25 03:07
三角函数解析几何立体几何几何作图
①本范例演示了泰勒斯利用几何方法测量金字塔高度的现象；②涉及的核心数学概念包括几何作图、相似三角形、向量与坐标几何；③作图要点——从下方『构造摘要』提炼用到了 Line, Point, Segment, Vector, OrthogonalLine, Rotate, Angle, Intersect, Ray, Translate, Midpoint, Polygon, Circle 等GeoGebra命令/对象；④适合高中及以上学段学习几何证明与实际应用。

GeoGebra 命令及参数

  1. Line(A, B) → a
  2. Point(a) → C
  3. Point(a) → D
  4. Segment(C, D) → b
  5. Point(b) → F
  6. Vector(F1, I1) → v
  7. Point(b) → E
  8. OrthogonalLine(E, a) → c
  9. Point(c) → G
  10. OrthogonalLine(F, a) → d
  11. Segment(E, G) → haut
  12. Point(d) → H
  13. Segment(F, H) → persona
  14. Line(H, a) → e
  15. Line(G, a) → f
  16. Point(e) → I
  17. Point(f) → J
  18. Rotate(I, α, H) → K
  19. Angle(I, H, K) → β
  20. Rotate(J, α, G) → L
  21. Angle(J, G, L) → γ
  22. Line(G, L) → g
  23. Line(H, K) → h
  24. Point(haut) → M
  25. Point(haut) → N
  26. Point(haut) → O
  27. Point(haut) → P
  28. Line(M, g) → i
  29. Line(N, i) → j
  30. Line(O, j) → k
  31. Line(P, k) → l
  32. Line(B, haut) → m
  33. Intersect(g, a) → U
  34. Intersect(h, a) → V
  35. Ray(V, H) → s
  36. Ray(U, G) → t
  37. Segment(E, U) → a1
  38. Segment(F, V) → b1
  39. Vector(F1, C1) → u
  40. Translate(E, u) → E1
  41. Translate(G, u) → D1
  42. Translate(H, v) → H1
  43. Translate(F, v) → G1
  44. Angle(F, V, H) → δ
  45. Angle(E, U, G) → ε
  46. Midpoint(b1) → J1
  47. Midpoint(a1) → K1
  48. Midpoint(persona) → L1
  49. Midpoint(haut) → M1
  50. Line(R, s) → p
  51. Line(Q, s) → q
  52. Intersect(a, p) → S
  53. Intersect(q, a) → T
  54. Line(N1, t) → r
  55. Intersect(r, a) → O1
  56. Segment(Q, T) → c1
  57. Segment(R, S) → d1
  58. Segment(N1, O1) → e1
  59. Intersect(a, xAxis) → P1
  60. Line(G, a) → f1
  61. Point(f1) → Q1
  62. Point(a) → A1
  63. Point(a) → B1
  64. Polygon(A1, B1, S1, T1) → poly1, a1_1, b1_1, s1, t1
  65. Circle(D, 4) → k1
  66. Intersect(k1, a1_1) → W1, Z1
  67. Polygon(G, Z1, W1) → poly2, w1, g_1, z1
  68. Segment(W1, U) → h1
  69. Polygon(G, W1, Z1) → poly3, z1_1, g_2, w1_1
  70. Point(t) → U1
  71. Segment(W1, D) → g1
  72. Point(a1_1) → A_1
  73. Midpoint(D_1, C_1) → E_1
  74. Vector(E_1, C_1) → z
  75. Vector(E_1, D_1) → u_1
  76. Segment(D_1, C_1) → a_1
  77. Segment(U, D_1) → b_1
  78. Segment(W1, F_1) → c_1
  79. Segment(D, C_1) → d_1