旋转图案

旋转图案
几何画板及绘图内容加载中,请稍等……
2017-11-03 22:28
①本范例演示了通过旋转和几何构造创建的复杂图案;②涉及的核心数学概念包括旋转、多边形构造、函数图像、立体几何;③作图要点使用了GeoGebra的Polygon(多边形)、Midpoint(中点)、Semicircle(半圆)、Sequence(数列)等命令和对象;④适合高中数学教学和几何作图学习。

GeoGebra 命令及参数

  1. Polygon(A, B, 5) → poly1, f, g, h, i, j, C, D, E
  2. Midpoint(E, A) → F
  3. Midpoint(A, B) → G
  4. Midpoint(B, C) → H
  5. Midpoint(C, D) → I
  6. Midpoint(D, E) → J
  7. Semicircle(J, I) → c
  8. Semicircle(I, H) → d
  9. Semicircle(H, G) → e
  10. Semicircle(G, F) → k
  11. Semicircle(F, J) → p
  12. Semicircle(J, F) → q
  13. Semicircle(F, G) → r
  14. Semicircle(G, H) → s
  15. Semicircle(H, I) → t
  16. Semicircle(I, J) → c_1
  17. Polygon(A, B, 3) → poly2, l, m, n, K
  18. Polygon(B, C, 3) → poly3, a, b, f_1, L
  19. Polygon(C, D, 3) → poly4, g_1, h_1, i_1, M
  20. Polygon(D, E, 3) → poly5, j_1, k_1, l_1, N
  21. Polygon(E, A, 3) → poly6, m_1, n_1, p_1, O
  22. Polygon(M, N, 5) → poly7, q_1, r_1, s_1, t_1, a_1, P, Q, R
  23. Semicircle(F, A) → d_1
  24. Semicircle(B, H) → e_1
  25. Semicircle(H, C) → c_2
  26. Semicircle(C, I) → d_2
  27. Semicircle(I, D) → e_2
  28. Semicircle(D, J) → f_2
  29. Semicircle(J, E) → g_2
  30. Semicircle(E, F) → h_2
  31. Semicircle(A, G) → k_2
  32. Semicircle(G, B) → p_2
  33. Sequence(Rotate[c, ((i * 2) * π / w), S], i, 1, w) → L_1
  34. Sequence(Rotate[c_1, ((i * 2) * π / w), S], i, 1, w) → L_2
  35. Sequence(Rotate[c_2, ((i * 2) * π / w), S], i, 1, w) → L_3
  36. Sequence(Rotate[d_2, ((i * 2) * π / w), S], i, 1, w) → L_4
  37. Sequence(Rotate[d_1, ((i * 2) * π / w), S], i, 1, w) → L_5
  38. Sequence(Rotate[d, ((i * 2) * π / w), S], i, 1, w) → L_6
  39. Sequence(Rotate[e, ((i * 2) * π / w), S], i, 1, w) → L_7
  40. Sequence(Rotate[e_1, ((i * 2) * π / w), S], i, 1, w) → L_8
  41. Sequence(Rotate[e_2, ((i * 2) * π / w), S], i, 1, w) → L_9
  42. Sequence(Rotate[f_2, ((i * 2) * π / w), S], i, 1, w) → L_{10}
  43. Sequence(Rotate[g_2, ((i * 2) * π / w), S], i, 1, w) → L_{11}
  44. Sequence(Rotate[h_2, ((i * 2) * π / w), S], i, 1, w) → L_{12}
  45. Sequence(Rotate[k_2, ((i * 2) * π / w), S], i, 1, w) → L_{13}
  46. Sequence(Rotate[p_2, ((i * 2) * π / w), S], i, 1, w) → L_{14}
  47. Sequence(Rotate[p, ((i * 2) * π / w), S], i, 1, w) → L_{15}
  48. Sequence(Rotate[k, ((i * 2) * π / w), S], i, 1, w) → L_{16}
  49. Sequence(Rotate[q, ((i * 2) * π / w), S], i, 1, w) → L_{17}
  50. Sequence(Rotate[r, ((i * 2) * π / w), S], i, 1, w) → L_{18}
  51. Sequence(Rotate[s, ((i * 2) * π / w), S], i, 1, w) → L_{19}
  52. Sequence(Rotate[t, ((i * 2) * π / w), S], i, 1, w) → L_{20}
  53. Sequence(Rotate[poly7, ((i * 2) * π / w), S], i, 1, w) → L_{21}

AI 绘图提示语参考

绘制一个由五个点A、B、C、D、E构成的正五边形,然后依次找到每两点的中点,连接这些中点形成新的正五边形。接着,以每个中点为圆心,以中点到原五边形顶点的距离为半径,画出一系列半圆。最后,围绕每个半圆旋转这些半圆,形成复杂的旋转图案。
以上提示语为根据原始绘图命令整理而来,仅供参考。