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十三分之四三角形

十三分之四三角形
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2019-08-24 21:21
测试改名0向量几何作图
所属专题 Exploring Feyman's Triangle
①本范例演示了内三角形与外三角形面积比为四比十三的几何构造；②涉及的核心数学概念包括等边三角形、向量、旋转与面积比计算；③作图要点——使用Polygon（多边形）、Midpoint（中点）、Segment（线段）、Ray（射线）、Intersect（交点）、Rotate（旋转）、Point（点）等GeoGebra命令构建图形；④适合高中数学教学，用于理解几何变换与面积比例关系。

GeoGebra 命令及参数

  1. Polygon(A, B, C) → t1, c, a, b
  2. Midpoint(c) → X
  3. Midpoint(a) → Y
  4. Midpoint(b) → Z
  5. Segment(X, B) → f
  6. Segment(B, Y) → g
  7. Segment(Y, C) → h
  8. Segment(C, Z) → i
  9. Segment(Z, A) → j
  10. Segment(A, X) → k
  11. Midpoint(k) → G_1
  12. Midpoint(g) → I
  13. Midpoint(i) → K
  14. Ray(A, I) → l
  15. Ray(C, G_1) → m
  16. Ray(B, K) → n
  17. Intersect(l, m) → D
  18. Intersect(l, n) → E
  19. Intersect(m, n) → F
  20. Polygon(D, E, F) → t2, l_1, h_1, j_1
  21. Segment(B, F) → p
  22. Segment(A, E) → q
  23. Segment(C, D) → r
  24. Midpoint(j_1) → Q
  25. Midpoint(l_1) → G
  26. Midpoint(h_1) → M
  27. Polygon(B, Y, M) → t3, m_1, b_1, y_1
  28. Polygon(C, Q, Z) → t4, z_1, c_1, h_2
  29. Polygon(A, G, X) → t5, x_1, a_1, l_2
  30. Rotate(B, (-α), Y) → B'
  31. Rotate(Y, (-α), Y) → Y'
  32. Rotate(M, (-α), Y) → H'
  33. Polygon(B', Y', H') → t3', m', b', y'
  34. Rotate(C, (-α), Z) → C'
  35. Rotate(Q, (-α), Z) → I'
  36. Rotate(Z, (-α), Z) → Z'
  37. Polygon(C', I', Z') → t4', z', c', h'
  38. Rotate(A, (-α), X) → A'
  39. Rotate(G, (-α), X) → G'
  40. Rotate(X, (-α), X) → X'
  41. Polygon(A', G', X') → t5', x', a', l'
  42. Midpoint(y') → H
  43. Midpoint(z') → J
  44. Midpoint(x') → L
  45. Point(l_1) → N
  46. Segment(N, H) → s
  47. Point(j_1) → P
  48. Segment(E, L) → e
  49. Segment(H, F) → f_1
  50. Segment(J, D) → g_1
  51. Intersect(z', h') → R
  52. Intersect(z', g_1) → O
  53. Point(l') → S
  54. Polygon(G', S, E, N) → q1, g', s_1, e_1, n_1
  55. Intersect(m', y') → T
  56. Point(h_1) → U
  57. Polygon(T, F, U, H') → q3, t_1, f_2, u, i_1
  58. Segment(U, O) → t
  59. Polygon(A, I', Q, D) → q2, a_2, i', q_1, d
  60. Segment(Q, L) → k_1