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动态演示：推特上Ed Southall提出的数学问题

动态演示：推特上Ed Southall提出的数学问题
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2018-11-05 11:51
多边形向量
本范例动态展示了Ed Southall在推特上提出的一个数学问题。它涉及几何图形的构造与变换，包括多边形、向量和变换等核心概念。通过使用GeoGebra命令如Polygon、Midpoint、Line、Circle等，可以直观地理解几何图形的性质和变换规则。适合初中及以上学生或教师使用。

GeoGebra 命令及参数

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Midpoint(B, C) → E
  3. Line(E, xAxis) → j
  4. Circle(E, a / ((2 * sqrt(2)))) → c
  5. Intersect(c, j) → F, G
  6. Mirror(E, F) → E'
  7. Circle(F, E) → d
  8. Circle(E', Distance[E, F] / 2) → e
  9. Intersect(e, j, 1) → H
  10. Circle(H, E') → k
  11. Tangent(k, d) → l, m, n, p
  12. Intersect(-1.2500000000000018x² + y² + 3.775884734705295x - 6.797806385501836y = -8.989895380578599, k) → , , ,
  13. Intersect(m, l) → I
  14. Midpoint(D, C) → J
  15. Midpoint(D, J) → K
  16. Midpoint(J, C) → L
  17. Segment(A, B) → q
  18. Segment(B, C) → r
  19. Segment(A, D) → s
  20. Dilate(H, If[0 < b ≤ 1, 1 - b, 0], E') → H'
  21. Segment(H, H') → t
  22. Midpoint(E', F) → M
  23. Segment(E', M) → f_1
  24. Segment(M, F) → g_1
  25. Segment(F, E) → h_1
  26. Rotate(H, If[1 < b ≤ 2, ((b - 1) * π), π], E') → H'_1
  27. Segment(E', H'_1) → i_1
  28. Rotate(E', If[2 < b ≤ 3, ((b - 2) * π), π], M) → E''
  29. Rotate(H'_1, If[2 < b ≤ 3, ((b - 2) * π), π], M) → N
  30. Segment(E'', N) → j_1
  31. Mirror(E', H) → E''_1
  32. Rotate(H, If[3 < b ≤ 4, ((b - 3) * π / 2), π / 2], H) → H'_2
  33. Rotate(H', If[3 < b ≤ 4, ((b - 3) * π / 2), π / 2], H) → H''
  34. Segment(H'_2, H'') → t'
  35. Dilate(H, If[3 < b ≤ 4, 4 - b, 0], E''_1) → H'_3
  36. Segment(H, H'_3) → k_1
  37. Angle(H'', H, E''_1) → α
  38. Segment(I, C) → l_1
  39. Segment(I, B) → m_1
  40. Dilate(E', If[5 < b ≤ 6, 6 - b, 0], H'') → E''_2
  41. Segment(E', E''_2) → n_1
  42. Dilate(E', If[7 < b ≤ 8, 8 - b, 0], C) → E''_3
  43. Vector(E', E''_3) → u
  44. Translate(E', u) → E''_4
  45. Translate(E''_2, u) → O
  46. Segment(E''_4, O) → p_1
  47. Rotate(E''_4, If[7 < b ≤ 8, ((b - 7) * π / 4), π / 4], E''_4) → P
  48. Rotate(O, If[7 < b ≤ 8, ((b - 7) * π / 4), π / 4], E''_4) → O'
  49. Segment(P, O') → q_1
  50. Angle(B, A, D) → β
  51. Angle(A, D, C) → γ
  52. Angle(C, B, A) → δ
  53. Rotate(P, If[8 < b ≤ 9, ((-(b - 8)) * π), (-π)], L) → P'
  54. Rotate(O', If[8 < b ≤ 9, ((-(b - 8)) * π), (-π)], L) → O''
  55. Segment(P', O'') → r_1
  56. Segment(D, A) → s_1
  57. Rotate(P', If[9 < b ≤ 10, ((-(b - 9)) * π), (-π)], J) → P''
  58. Rotate(O'', If[9 < b ≤ 10, ((-(b - 9)) * π), (-π)], J) → O'''
  59. Segment(P'', O''') → t_1
  60. Rotate(P'', If[10 < b ≤ 11, ((-(b - 10)) * π), (-π)], K) → P'''
  61. Rotate(O''', If[10 < b ≤ 11, ((-(b - 10)) * π), (-π)], K) → Q
  62. Segment(P''', Q) → a_1
  63. Segment(A, B) → b_1