特殊图形的旋转对称性

特殊图形的旋转对称性
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2015-01-16 19:56
本范例演示特殊图形的旋转对称性,涉及的核心数学概念是旋转对称。通过使用GeoGebra中的Point, Polygon, Centroid, Rotate等命令,可以构造出具有特定旋转对称性的多边形。适合初中及以上学生或教师使用,帮助理解旋转对称的概念。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Point(xAxis) → E
  4. Point(xAxis) → F
  5. Point(xAxis) → M
  6. Point(xAxis) → P
  7. Point(xAxis) → S
  8. Polygon(Z, A_1, 3) → poly1, a, b, c, B_1
  9. Polygon(A, B, C, D) → poly2, a_1, b_1, c_1, d
  10. Polygon(E, F, G, H) → poly3, e, f, g, h
  11. Polygon(I, J, K, L) → poly4, i, j, k, l
  12. Polygon(M, P, O, N) → poly5, m, p, o, n
  13. Polygon(Q, R, S, T) → poly6, q, r, s, t
  14. Polygon(U, V, W) → poly7, w, u, v
  15. Polygon(E_1, F_1, 5) → poly8, l_1, m_1, n_1, p_1, q_1, G_1, H_1, I_1
  16. Polygon(J_1, K_1, 6) → poly9, r_1, O_1, s_1, t_1, a_2, b_2, c_2, L_1, M_1, N_1
  17. Polygon(P_1, Q_1, 8) → poly10, d_2, S_1, T_1, U_1, V_1, W_1, e_2, f_2, g_2, h_2, i_2, j_2, k_2, R_1
  18. Centroid(poly9) → C_1
  19. Centroid(poly8) → D_1
  20. Centroid(poly10) → Z_1
  21. Centroid(poly1) → A_2
  22. Centroid(poly2) → B_2
  23. Centroid(poly3) → C_2
  24. Centroid(poly4) → D_2
  25. Centroid(poly5) → E_2
  26. Centroid(poly7) → F_2
  27. Rotate(A, angle, B_2) → A'
  28. Rotate(B, angle, B_2) → B'
  29. Rotate(C, angle, B_2) → C'
  30. Rotate(D, angle, B_2) → D'
  31. Polygon(A', B', C', D') → poly2', a', b', c', d'
  32. Rotate(E, angle, C_2) → E'
  33. Rotate(F, angle, C_2) → F'
  34. Rotate(G, angle, C_2) → G'
  35. Rotate(H, angle, C_2) → H'
  36. Polygon(E', F', G', H') → poly3', e', f', g', h'
  37. Rotate(I, angle, D_2) → I'
  38. Rotate(J, angle, D_2) → J'
  39. Rotate(K, angle, D_2) → K'
  40. Rotate(L, angle, D_2) → L'
  41. Polygon(I', J', K', L') → poly4', i', j', k', l'
  42. Rotate(M, angle, E_2) → M'
  43. Rotate(P, angle, E_2) → P'
  44. Rotate(O, angle, E_2) → O'
  45. Rotate(N, angle, E_2) → N'
  46. Polygon(M', P', O', N') → poly5', m', p', o', n'
  47. Rotate(U, angle, F_2) → U'
  48. Rotate(V, angle, F_2) → V'
  49. Rotate(W, angle, F_2) → W'
  50. Polygon(U', V', W') → poly7', w', u', v'
  51. Rotate(poly1, angle, A_2) → poly1'
  52. Rotate(poly8, angle, D_1) → poly8'
  53. Rotate(Q, angle, R) → Q'
  54. Rotate(R, angle, R) → R'
  55. Rotate(S, angle, R) → S'
  56. Rotate(T, angle, R) → T'
  57. Polygon(Q', R', S', T') → poly6', q', r', s', t'
  58. Rotate(poly9, angle, C_1) → poly9'
  59. Rotate(poly10, angle, Z_1) → poly10'

AI 绘图提示语参考

绘制一个具有旋转对称性的特殊多边形,首先在x轴上创建点A、B、E、F、M、P、S,然后依次绘制多边形poly1、poly2、poly3、poly4、poly5、poly6,接着绘制多边形poly8、poly9、poly10,并计算它们的质心C1、D1、Z1、A2、B2、C2、D2、E2、F2。最后,围绕点B2、C2、D2、E2、F2旋转多边形,生成新的多边形poly2'、poly3'、poly4'、poly5'、poly6'。
以上提示语为根据原始绘图命令整理而来,仅供参考。