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代数谜题：发展

代数谜题：发展
几何画板及绘图内容加载中，请稍等……
2019-12-29 16:21
函数三角函数解析几何几何作图
所属专题 Algebraic puzzles for binomial formula
①本范例演示了代数谜题的图形化解法，通过动态图形展示方程的解；②涉及核心数学概念包括代数、期望值、圆锥曲线、分段函数、特殊点和对数；③作图要点：使用Line, Point, Segment, Vector, Translate, Sequence, Polygon, Midpoint等GeoGebra命令构建图形；④适合高中及以上数学学习者，用于理解代数与几何的结合应用。

GeoGebra 命令及参数

  1. Line(A, xAxis) → a
  2. Point(a) → F
  3. Segment(A, F) → c
  4. Point(c) → C
  5. Point(c) → B
  6. Line(A, yAxis) → b
  7. Point(b) → G
  8. Segment(A, G) → d
  9. Point(d) → E
  10. Point(d) → D
  11. Vector(H, V) → v
  12. Translate(I, Vector[(Animation * v)]) → I'
  13. Segment(A, D) → f
  14. Segment(A, B) → e
  15. Sequence(A + (i, 0), i, 0, e, e / e1) → liste1
  16. Sequence(D + (i, 0), i, 0, e, e / e1) → liste2
  17. Sequence(A - (0, i), i, 0, f, f / f1) → liste4
  18. Sequence(Segment[Element[liste1, i], Element[liste2, i]], i, 1, Length[liste1]) → liste3
  19. Sequence(B - (0, i), i, 0, f, f / f1) → liste5
  20. Sequence(Segment[Element[liste4, i], Element[liste5, i]], i, 1, Length[liste5]) → liste6
  21. Polygon(A, B, H, D) → poly1, a_1, b_1, h, d_1
  22. Segment(B, C) → g
  23. Sequence(B + (i, (0 * i)), i, 0, g, g / g1) → liste7
  24. Sequence(H + (i, (0 * i)), i, 0, g, g / g1) → liste8
  25. Sequence(Segment[Element[liste7, i], Element[liste8, i]], i, 1, Length[liste7]) → liste9
  26. Sequence(C - (0, i), i, 0, f, f / f1) → liste10
  27. Sequence(Segment[Element[liste10, i], Element[liste5, i]], i, 1, Length[liste5]) → liste11
  28. Polygon(B, C, I, H) → poly2, i, j, k, l
  29. Segment(D, E) → m
  30. Sequence(D - (0, i), i, 0, m, m / m1) → liste12
  31. Sequence(H - (0, i), i, 0, m, m / m1) → liste13
  32. Sequence(Segment[Element[liste12, i], Element[liste13, i]], i, 1, Length[liste12]) → liste14
  33. Sequence(E + (i, 0), i, 0, e, e / e1) → liste15
  34. Sequence(Segment[Element[liste15, i], Element[liste2, i]], i, 1, Length[liste1]) → liste16
  35. Polygon(D, H, J, E) → poly3, d_2, h_1, j_1, e_1
  36. Polygon(H, I, K, J) → poly4, h_2, i_1, k_1, j_2
  37. Sequence(J + (i, (0 * i)), i, 0, g, g / g1) → liste17
  38. Sequence(Segment[Element[liste17, i], Element[liste8, i]], i, 1, Length[liste7]) → liste18
  39. Sequence(I - (0, i), i, 0, m, m / m1) → liste19
  40. Sequence(Segment[Element[liste19, i], Element[liste13, i]], i, 1, Length[liste12]) → liste20
  41. Midpoint(A, B) → L
  42. Midpoint(B, C) → M
  43. Midpoint(A, D) → N
  44. Midpoint(D, E) → O
  45. Midpoint(B, D) → P
  46. Midpoint(I, J) → Q
  47. Midpoint(I, B) → R
  48. Midpoint(J, D) → S
  49. Vector(D, T) → u
  50. Translate(A, Vector[(Animation * u)]) → A'
  51. Translate(B, Vector[(Animation * u)]) → B'
  52. Translate(H, Vector[(Animation * u)]) → H'
  53. Translate(D, Vector[(Animation * u)]) → D'
  54. Polygon(A', B', H', D') → poly1', a', b', h', d'
  55. Vector(E, I') → w
  56. Translate(B, Vector[(Animation * v)]) → B'_1
  57. Translate(C, Vector[(Animation * v)]) → C'
  58. Translate(H, Vector[(Animation * v)]) → H'_1
  59. Polygon(B'_1, C', I', H'_1) → poly2', b'_1, c', i', h'_1
  60. Translate(D, Vector[(Animation * w)]) → D'_1
  61. Translate(H, Vector[(Animation * w)]) → H'_2
  62. Translate(J, Vector[(Animation * w)]) → J'
  63. Translate(E, Vector[(Animation * w)]) → E'
  64. Polygon(D'_1, H'_2, J', E') → poly3', d'_1, h'_2, j', e'
  65. Vector(H, W) → z
  66. Translate(H, Vector[(Animation * z)]) → H'_3
  67. Translate(I, Vector[(Animation * z)]) → I'_1
  68. Translate(K, Vector[(Animation * z)]) → K'
  69. Translate(J, Vector[(Animation * z)]) → J'_1
  70. Polygon(H'_3, I'_1, K', J'_1) → poly4', h'_3, i'_1, k', j'_1
  71. Midpoint(B', T) → Z
  72. Midpoint(D'_1, I') → C_1
  73. Segment(C', D'_1) → p
  74. Segment(D'_1, I') → q
  75. Midpoint(I'_1, J'_1) → A_1
  76. Midpoint(C', V) → B_1
  77. Midpoint(H'_2, I') → D_1
  78. Vector(B_1, I') → r
  79. Vector(D_1, I') → s