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Sec 1.6 Basic Constructions：几何作图与图形构造

Sec 1.6 Basic Constructions：几何作图与图形构造
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2015-09-25 00:40
解析几何变换几何作图
本范例演示了如何使用GeoGebra进行基本几何构造，包括三角形、圆、多边形和角度的绘制。核心数学概念涉及几何作图、坐标几何和变换。作图要点包括使用Segment、Rotate、Angle、Circle、Intersect等GeoGebra命令，以及Point、Vector、Ellipse等对象。适合初中或高中数学学习，用于理解几何构造的基本原理和实际应用。

GeoGebra 命令及参数

  1. Segment(A_1, B_1) → a
  2. Segment(X_1, Y_1) → b
  3. Rotate(C_1, 32*°, B_2) → A_2
  4. Angle(C_1, B_2, A_2) → α
  5. Segment(B_2, A_2) → c
  6. Segment(B_2, C_1) → d
  7. Rotate(C_2, 45*°, B_3) → A_3
  8. Angle(C_2, B_3, A_3) → β
  9. Segment(B_3, A_3) → e
  10. Segment(B_3, C_2) → f
  11. Segment(A_4, B_4) → g
  12. Rotate(D_1, 60*°, A) → D'
  13. Angle(D_1, A, D') → γ
  14. Segment(A, D') → h
  15. Segment(A, D_1) → i
  16. Rotate(Z, 120*°, Y_2) → X_2
  17. Angle(Z, Y_2, X_2) → δ
  18. Segment(X_2, Y_2) → j
  19. Segment(Y_2, Z) → k
  20. Point(g) → E
  21. Circle(A_4, Segment[A_4, E]) → p
  22. Circle(B_4, Segment[A_4, E]) → q
  23. Intersect(p, q, 1) → X
  24. Intersect(p, q, 2) → Y
  25. Segment(Y, X) → l
  26. Intersect(g, l) → C_3
  27. Angle(B_4, C_3, X) → ε
  28. Angle(X, C_3, B_4) → ζ
  29. Segment(S, T) → m
  30. Point(m) → F
  31. Circle(S, Segment[S, F]) → r
  32. Circle(T, Segment[S, F]) → s
  33. Intersect(r, s, 1) → G
  34. Intersect(r, s, 2) → H
  35. Segment(H, G) → n
  36. Intersect(m, n) → I
  37. Point(m) → J
  38. Circle(S, Segment[S, J]) → t
  39. Circle(I, Segment[S, J]) → c_1
  40. Intersect(t, c_1, 1) → K
  41. Intersect(t, c_1, 2) → L
  42. Segment(K, L) → a_1
  43. Intersect(m, a_1) → M
  44. Point(h) → B
  45. Circle(A, Segment[B, A]) → d_1
  46. Intersect(d_1, i, 1) → C
  47. Circle(B, Segment[B, C]) → e_1
  48. Circle(C, Segment[B, C]) → f_1
  49. Intersect(e_1, f_1, 1) → D
  50. Vector(A, N) → u
  51. Angle(C, A, D) → η
  52. Angle(D, A, B) → θ
  53. Point(j) → O
  54. Circle(P, Q) → g_1
  55. Circle(P, R) → h_1
  56. Circle(P, U) → k_1
  57. Circle(P, V) → p_1
  58. Circle(P, W) → q_1
  59. Circle(P, E_1) → r_1
  60. Circle(P, F_1) → s_1
  61. Circle(P, G_1) → t_1
  62. Circle(P, H_1) → c_2
  63. Circle(P, I_1) → d_2
  64. Circle(P, J_1) → e_2
  65. Circle(P, K_1) → f_2
  66. Circle(P, L_1) → g_2
  67. Circle(M_1, N_1) → h_2
  68. Ellipse(O_1, P_1, Q_1) → k_2
  69. Ellipse(R_1, S_1, T_1) → p_2
  70. Ellipse(U_1, V_1, W_1) → q_2
  71. Ellipse(Z_1, R_1, D_2) → r_2