积极 AI Logo 积极 AI

LMOrigami22 腰带立方体

LMOrigami22 腰带立方体
几何画板及绘图内容加载中，请稍等……
2017-05-03 02:25
三角函数立体几何几何作图
这个范例演示了一个由点、多边形和立方体构成的腰带立方体图形。涉及的核心数学概念包括立体几何、对称性和几何作图。作图要点包括使用 GeoGebra 命令如 Point（点）、Intersect（交点）、Polygon（多边形）、OrthogonalLine（垂线）、Mirror（镜像）、Cube（立方体）、Line（直线）、Dilate（缩放）；对象包括 beltwidth（腰带宽度）、C, D, A, B, poly1, a, b, c, d, E, e, F, f, G, H, F', H', poly2, f', f_1, h, h', I, J, g, i, K, K', J', poly3, k, j, j', k', L, l, O, P, Q。适合高中及以上学段学习立体几何和几何作图。

GeoGebra 命令及参数

  1. Point(yAxis) → D
  2. Intersect(xAxis, yAxis) → A
  3. Point(xAxis) → B
  4. Polygon(A, B, C, D) → poly1, a, b, c, d
  5. Point(a) → E
  6. OrthogonalLine(E, a) → e
  7. OrthogonalLine(F, a) → f
  8. Intersect(e, c) → G
  9. Intersect(f, c) → H
  10. Mirror(F, e) → F'
  11. Mirror(H, e) → H'
  12. Polygon(F', F, H, H') → poly2, f', f_1, h, h'
  13. Point(b) → I
  14. OrthogonalLine(I, b) → g
  15. OrthogonalLine(J, b) → i
  16. Intersect(i, f_1) → K
  17. Mirror(K, g) → K'
  18. Mirror(J, g) → J'
  19. Polygon(K, J, J', K') → poly3, k, j, j', k'
  20. Intersect(d, yAxis) → L
  21. Cube(B, C, poly1) → l, O, faceCOSR, faceOPTS, faceQRST, edgeBP, edgeBC, edgeCO, edgeOP, edgeBQ, edgePT, edgeQT, P, edgeQR, edgeCR, edgeRS, edgeOS, edgeST, Q, R, S, T, faceBCOP, faceBPTQ, faceBCRQ
  22. Point(edgeBQ) → U
  23. Point(edgeQT) → W
  24. Point(edgeCR) → Z
  25. Point(edgeST) → B_1
  26. Point(edgePT) → C_1
  27. OrthogonalLine(U, edgeBQ, faceBPTQ) → p
  28. Mirror(U', p) → U''
  29. OrthogonalLine(U', edgeBQ, faceBPTQ) → q
  30. OrthogonalLine(U'', edgeBQ, faceBPTQ) → r
  31. Intersect(q, edgePT) → D_1
  32. Intersect(edgePT, r) → E_1
  33. Polygon(E_1, U'', U', D_1) → poly5, e_1, u'', u', d_1
  34. OrthogonalLine(J', b, faceBCRQ) → s
  35. OrthogonalLine(J, b, faceBCRQ) → t
  36. Intersect(t, edgeQR) → F_1
  37. Intersect(s, edgeQR) → G_1
  38. Polygon(G_1, F_1, J, J') → poly6, g_1, f_2, j_1, j'_1
  39. OrthogonalLine(U', edgeBQ, faceBCRQ) → m
  40. OrthogonalLine(U'', edgeBQ, faceBCRQ) → n
  41. Intersect(m, j'_1) → M
  42. Intersect(n, j'_1) → N
  43. Polygon(U'', N, M, U') → poly4, u''_1, n_1, m_1, u'_1
  44. OrthogonalLine(W, edgeQT, faceQRST) → a_1
  45. Mirror(W', a_1) → W''
  46. OrthogonalLine(W'', edgeQT, faceQRST) → b_1
  47. OrthogonalLine(W', edgeQT, faceQRST) → c_1
  48. Intersect(b_1, edgeRS) → V
  49. Intersect(c_1, edgeRS) → A_1
  50. Polygon(V, A_1, W', W'') → poly7, v, a_2, w', w''
  51. OrthogonalLine(W'', edgeQT, faceBPTQ) → h_1
  52. OrthogonalLine(W', edgeQT, faceBPTQ) → i_1
  53. OrthogonalLine(F, a, faceBPTQ) → k_1
  54. OrthogonalLine(F', a, faceBPTQ) → l_1
  55. Intersect(e_1, l_1) → H_1
  56. Intersect(k_1, e_1) → I_1
  57. Intersect(i_1, u') → J_1
  58. Intersect(h_1, u') → K_1
  59. Polygon(W'', K_1, J_1, W') → poly8, w''_1, k_2, j_2, w'_1
  60. Polygon(F', F, I_1, H_1) → poly9, f'_1, f_3, i_2, h_2
  61. OrthogonalLine(F_1, edgeQR, faceQRST) → p_1
  62. OrthogonalLine(G_1, edgeQR, faceQRST) → q_1
  63. Intersect(p_1, a_2) → L_1
  64. Intersect(q_1, a_2) → M_1
  65. Polygon(M_1, G_1, F_1, L_1) → poly10, m_2, g_2, f_4, l_2
  66. OrthogonalLine(Z, edgeCR, faceCOSR) → r_1
  67. Mirror(Z', r_1) → Z''
  68. OrthogonalLine(Z', edgeCR, faceCOSR) → s_1
  69. OrthogonalLine(Z'', edgeCR, faceCOSR) → t_1
  70. Intersect(s_1, edgeOS) → N_1
  71. Intersect(t_1, edgeOS) → O_1
  72. Polygon(Z'', O_1, N_1, Z') → poly11, z'', o_1, n_2, z'
  73. OrthogonalLine(A_1, edgeRS, faceCOSR) → b_2
  74. OrthogonalLine(V, edgeRS, faceCOSR) → c_2
  75. OrthogonalLine(H, c, faceCOSR) → d_2
  76. OrthogonalLine(H', c, faceCOSR) → e_2
  77. Intersect(t_1, d_2) → P_1
  78. Intersect(t_1, e_2) → Q_1
  79. Intersect(c_2, s_1) → R_1
  80. Intersect(s_1, b_2) → S_1
  81. Polygon(S_1, R_1, V, A_1) → poly12, s_2, r_2, v_1, a_3
  82. Polygon(H, H', Q_1, P_1) → poly13, h_3, h'_1, q_2, p_2
  83. OrthogonalLine(Z', edgeCR, faceBCRQ) → t_2
  84. OrthogonalLine(Z'', edgeCR, faceBCRQ) → b_3
  85. Intersect(t_2, f_2) → T_1
  86. Intersect(b_3, f_2) → U_1
  87. Polygon(U_1, Z'', Z', T_1) → poly14, u_1, z''_1, z'_1, t_3
  88. OrthogonalLine(B_1, edgeST, faceOPTS) → c_3
  89. OrthogonalLine(B_1', edgeST, faceOPTS) → d_3
  90. Mirror(B_1', c_3) → V_1
  91. OrthogonalLine(V_1, edgeST, faceOPTS) → e_3
  92. Intersect(d_3, d) → W_1
  93. Intersect(d, edgeOP) → Z_1
  94. Intersect(e_3, d) → A_2
  95. Polygon(W_1, A_2, V_1, B_1') → poly15, w_1, a_4, v_2, b_1'
  96. OrthogonalLine(O_1, edgeOS, faceOPTS) → g_3
  97. OrthogonalLine(N_1, edgeOS, faceOPTS) → i_3
  98. OrthogonalLine(E_1, edgePT, faceOPTS) → j_3
  99. OrthogonalLine(D_1, edgePT, faceOPTS) → k_3
  100. Intersect(d_3, g_3) → B_2
  101. Intersect(i_3, d_3) → C_2
  102. Intersect(e_3, k_3) → D_2
  103. Intersect(e_3, j_3) → E_2
  104. Polygon(O_1, B_2, C_2, N_1) → poly16, o_2, b_4, c_4, n_3
  105. Polygon(E_1, E_2, D_2, D_1) → poly17, e_4, e_5, d_4, d_5
  106. OrthogonalLine(B_1', edgeST, faceQRST) → l_3
  107. OrthogonalLine(V_1, edgeST, faceQRST) → m_3
  108. Intersect(l_3, w'') → F_2
  109. Intersect(m_3, w'') → G_2
  110. Polygon(B_1', V_1, G_2, F_2) → poly18, b_5, v_3, g_4, f_5
  111. OrthogonalLine(W_1, d, xOyPlane) → p_3
  112. OrthogonalLine(A_2, d, xOyPlane) → q_3
  113. Intersect(p_3, h') → H_2
  114. Intersect(q_3, h') → I_2
  115. Polygon(W_1, H_2, I_2, A_2) → poly19, w_2, h_4, i_4, a_5
  116. Line(A, R) → r_3
  117. Line(T, C) → s_3
  118. Intersect(s_3, r_3) → J_2
  119. Dilate(faceBCOP, cubescale, J_2) → faceBCOP'
  120. Dilate(faceBCRQ, cubescale, J_2) → faceBCRQ'
  121. Dilate(faceBPTQ, cubescale, J_2) → faceBPTQ'
  122. Dilate(faceCOSR, cubescale, J_2) → faceCOSR'
  123. Dilate(faceOPTS, cubescale, J_2) → faceOPTS'
  124. Dilate(faceQRST, cubescale, J_2) → faceQRST'

AI 绘图提示语参考

画一个由点和多边形构成的带状立方体，展示立体几何和对称性。首先绘制一个四边形，然后从其顶点出发，通过正交线和镜像操作创建多个几何形状，包括立方体和多个多边形。最后将这些形状组合起来，形成一个复杂的立体结构，强调几何构造的过程和对称性。
以上提示语为根据原始绘图命令整理而来，仅供参考。