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连接周长

连接周长
几何画板及绘图内容加载中，请稍等……
2018-04-15 19:28
多边形概率统计几何作图滑块动画
①本范例演示如何通过 GeoGebra 构建并分析矩形的周长与分布关系；②涉及核心数学概念包括周长计算、整数的应用、概率分布、除法及对数运算；③作图要点提炼自构造摘要，使用了 Sequence（数列）、Polygon（多边形）、Point（点）、OrthogonalLine（垂线）、Intersect（交点）、Perimeter（周长）、Segment（线段）、Text（文本）等命令与对象；④适合初中及以上数学学习者，用于理解几何图形属性与概率统计的结合应用。

GeoGebra 命令及参数

  1. Sequence(Sequence[Point[{i, j}], i, ((-length)) / 2, length / 2, 1], j, ((-width)) / 2, width / 2, 1) → list1
  2. Polygon(A, B, C, D) → poly1, a, b, c, d
  3. Point(list1) → E
  4. Point(list1) → F
  5. Point(list1) → G
  6. Point(list1) → H
  7. OrthogonalLine(E, d) → e
  8. OrthogonalLine(E, a) → f
  9. OrthogonalLine(F, a) → g
  10. OrthogonalLine(F, b) → h
  11. OrthogonalLine(H, c) → i
  12. OrthogonalLine(H, d) → j
  13. OrthogonalLine(G, c) → k
  14. OrthogonalLine(G, b) → l
  15. Intersect(c, i) → I
  16. Intersect(j, d) → J
  17. Intersect(b, l) → K
  18. Intersect(g, a) → L
  19. Intersect(h, b) → M
  20. Intersect(k, c) → N
  21. Intersect(f, a) → P
  22. Intersect(e, d) → R
  23. Polygon(H, I, R, J, N, G, K, M, F, L, P, E) → poly2, h_1, e_1, r, j_1, i_1, n, g_1, k_1, m, f_1, l_1, p
  24. Perimeter(poly1) → o
  25. Perimeter(poly2) → q
  26. Sequence(Segment[list1(i, 1), list1(i, length + 1)], i, 1, width + 1) → list2
  27. Sequence(Segment[list1(1, i), list1(width + 1, i)], i, 1, length + 1) → list3
  28. Segment((D * (1 - vertMove)) + (I * vertMove), (J * (1 - vertMove)) + (H * vertMove)) → topLeftVert
  29. Segment((C * (1 - horMove)) + (K * horMove), (N * (1 - horMove)) + (G * horMove)) → topRightHor
  30. Segment((C * (1 - vertMove)) + (N * vertMove), (K * (1 - vertMove)) + (G * vertMove)) → topRightVert
  31. Segment((B * (1 - vertMove)) + (L * vertMove), (M * (1 - vertMove)) + (F * vertMove)) → bottomRightVert
  32. Segment((A * (1 - vertMove)) + (P * vertMove), (R * (1 - vertMove)) + (E * vertMove)) → bottomLeftVert
  33. Segment((D * (1 - horMove)) + (J * horMove), (I * (1 - horMove)) + (H * horMove)) → topLeftHor
  34. Segment((A * (1 - horMove)) + (R * horMove), (P * (1 - horMove)) + (E * horMove)) → bottomLeftHor
  35. Segment((B * (1 - horMove)) + (M * horMove), (L * (1 - horMove)) + (F * horMove)) → bottomRightHor
  36. Segment(D, D + (Min[length, perimeterTimer], 0)) → top
  37. Segment(C, C - (0, ((perimeterTimer > length) * Min[width, perimeterTimer - length]))) → right
  38. Segment(B, B - (((perimeterTimer > length + width) * Min[length, perimeterTimer - width - length]), 0)) → bottom
  39. Segment(A, A + (0, ((perimeterTimer > (2 * length) + width) * Min[width, perimeterTimer - (2 * length) - width]))) → left
  40. Text(d, Midpoint[d] + (-1, 0)) → leftWidthText
  41. Text(a, Midpoint[a] + (0, -1)) → bottomLengthText
  42. Text(Distance[R, L], Midpoint[R, L] - (0, 1)) → text1
  43. Text(Distance[P, M], Midpoint[P, M] - (0, 1)) → text2
  44. Text(Distance[I, K], Midpoint[I, K] + (0, 0.5)) → text3
  45. Text(Distance[J, N], Midpoint[J, N] + (0, 0.5)) → text4
  46. Text(topRightHor, Midpoint[topRightHor] + (0, 1 / 2)) → TRHtext
  47. Text(topLeftHor, Midpoint[topLeftHor] + (0, 1 / 2)) → TLHtext
  48. Text(bottomLeftHor, Midpoint[bottomLeftHor] + (0, -1)) → BLHtext
  49. Text(Distance[P, L], Midpoint[P, L] + (0, -1)) → BMHtext
  50. Text(bottomRightHor, Midpoint[bottomRightHor] + (0, -1)) → BRHtext
  51. Text(Distance[R, D], Midpoint[R, D] + (-0.8, 0)) → text8
  52. Text(Distance[J, P], Midpoint[J, P] + (-0.8, 0)) → text6
  53. Text(Distance[J, R], Midpoint[J, R] + (-0.8, 0)) → text9
  54. Text(Distance[I, N], Midpoint[I, N] + (0, 1 / 2)) → topText
  55. Text(c, Midpoint[c] + (0, 1 / 2)) → topLengthText
  56. Text(Distance[K, M], Midpoint[K, M] + (1 / 2, 0)) → text10
  57. Text(Distance[K, B], Midpoint[K, B] + (1 / 2, 0)) → text13
  58. Text(Distance[M, C], Midpoint[M, C] + (1 / 2, 0)) → text14
  59. Text(b, Midpoint[b] + (1 / 2, 0)) → rightWidthText
  60. Text(Distance[N, G], Midpoint[topRightVert] + (1 / 2, 0)) → text11
  61. Text(Distance[I, H], Midpoint[topLeftVert] + (-0.8, 0)) → text5
  62. Text(Distance[F, L], Midpoint[bottomRightVert] + (1 / 2, 0)) → text12
  63. Text(Distance[E, P], Midpoint[bottomLeftVert] + (-0.8, 0)) → text7
  64. Segment(J, J + (Min[Distance[H, J], perimeterTimer], 0)) → p1
  65. Segment(H, H + (0, ((perimeterTimer > Distance[H, J]) * Min[Distance[I, H], perimeterTimer - Distance[H, J]]))) → p2
  66. Segment(I, I + (Min[Distance[I, N], perimeterTimer - p1 - p2], 0)) → p3
  67. Segment(N, N - (0, Min[Distance[G, N], perimeterTimer - p1 - p2 - p3])) → p4
  68. Segment(G, G + (Min[Distance[G, K], perimeterTimer - p1 - p2 - p3 - p4], 0)) → p5
  69. Segment(K, K + (0, (-Min[Distance[M, K], perimeterTimer - p1 - p2 - p3 - p4 - p5]))) → p6
  70. Segment(M, M + ((-Min[Distance[M, F], perimeterTimer - p1 - p2 - p3 - p4 - p5 - p6]), 0)) → p7
  71. Segment(F, F + (0, (-Min[Distance[F, L], perimeterTimer - p1 - p2 - p3 - p4 - p5 - p6 - p7]))) → p8
  72. Segment(L, L + ((-Min[Distance[L, P], perimeterTimer - p1 - p2 - p3 - p4 - p5 - p6 - p7 - p8]), 0)) → p9
  73. Segment(P, P + (0, Min[Distance[P, E], perimeterTimer - p1 - p2 - p3 - p4 - p5 - p6 - p7 - p8 - p9])) → p10
  74. Segment(E, E + ((-Min[Distance[E, R], perimeterTimer - p1 - p2 - p3 - p4 - p5 - p6 - p7 - p8 - p9 - p10]), 0)) → p11
  75. Segment(R, R + (0, Min[Distance[R, J], perimeterTimer - p1 - p2 - p3 - p4 - p5 - p6 - p7 - p8 - p9 - p10 - p11])) → p12
  76. Text(length, Midpoint[A, B] + (0, -1)) → bottomText
  77. Polygon(O, Q, S, T) → q1, o_1, q_1, s_1, t_1

AI 绘图提示语参考

绘制一个由均匀网格点构成的矩形区域，在矩形内部选取四个点，分别向矩形的四条边作垂线，垂线与边相交形成八个交点，将这些交点与四个内部点按顺序连接，构成一个内接于矩形的八边形。矩形和八边形的周长分别标注在图形中。在矩形内部，用线段连接网格点形成水平和垂直的网格线。另外，在矩形的四条边上，用动态线段表示周长遍历的过程，并在矩形内部标注各段长度。
以上提示语为根据原始绘图命令整理而来，仅供参考。