立方体四分之一重叠演示

立方体四分之一重叠演示
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2019-01-22 20:37
①本范例演示立方体四分之一部分的重叠与几何关系;②涉及核心数学概念包括立体几何、线性规划、多边形构造、向量运算及二次方程;③构造要点:使用Intersect(交集)、Point(点)、Polygon(多边形)、Midpoint(中点)、Segment(线段)、Rotate(旋转)、Circle(圆)、Vector(向量)、Translate(平移)、Prism(棱柱)等命令;④适合高中及以上学生及数学爱好者用于理解空间几何与优化问题。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  4. Midpoint(i) → E
  5. Midpoint(h) → F
  6. Midpoint(f) → H
  7. Midpoint(F, H) → I
  8. Midpoint(E, I) → L
  9. Midpoint(F, I) → J
  10. Midpoint(D, I) → B_1
  11. Midpoint(B_1, L) → N_1
  12. Midpoint(N_1, B_1) → A_1
  13. Midpoint(L, N_1) → T
  14. Polygon(T, A_1, 4) → poly5, p_1, q_1, r_1, s_1, C_1, F_1
  15. Midpoint(I, C) → D_1
  16. Midpoint(J, D_1) → P_1
  17. Midpoint(J, P_1) → M
  18. Midpoint(P_1, D_1) → O
  19. Polygon(M, O, 4) → poly4, m, n, p, q, R, S
  20. Segment(F, H) → j
  21. Midpoint(F, J) → N
  22. Rotate(E, (-(90°)), I) → E'
  23. Rotate(B_1, (-(90°)), I) → Z_1
  24. Rotate(L, (-(90°)), I) → L'
  25. Rotate(D, (-(90°)), I) → D'
  26. Rotate(D', (-(90°)), I) → D''
  27. Rotate(E', (-(180°)), I) → E''_1
  28. Rotate(D', (-(180°)), I) → D''_1
  29. Polygon(E, L, R, S, M, J, F, D, T, F_1, C_1, A_1, B_1, I, D_1, O) → poly2, l, l_1, m_1, n_1, t_1, a_1, b_1, d_1, s, t, e, f_1, h_1, i_1, j_1, k_1
  30. Circle(I, r) → c_1
  31. Segment(I, Z_1) → g_1
  32. Intersect(c_1, i_1, 1) → G
  33. Intersect(c_1, j_1, 1) → K
  34. Vector(I, G) → u
  35. Vector(I, K) → v
  36. Rotate(E, 90°, I) → E'_1
  37. Rotate(L, 90°, I) → L'_1
  38. Rotate(T, 90°, I) → T'
  39. Rotate(F_1, 90°, I) → P
  40. Rotate(C_1, 90°, I) → Q
  41. Rotate(A_1, 90°, I) → U
  42. Rotate(B_1, 90°, I) → V
  43. Rotate(I, 90°, I) → I'
  44. Rotate(D_1, 90°, I) → W
  45. Rotate(O, 90°, I) → O'
  46. Rotate(R, 90°, I) → R'
  47. Rotate(S, 90°, I) → S'
  48. Rotate(M, 90°, I) → M'
  49. Rotate(J, 90°, I) → J'
  50. Rotate(F, 90°, I) → F'
  51. Rotate(D, 90°, I) → D'_1
  52. Polygon(E'_1, L'_1, R', S', M', J', F', D'_1, T', P, Q, U, V, I', W, O') → poly2', e'_1, o', r', s', m', j', f', d'_1, l'_1, t', p_2, q_2, u_1, v_1, i', w
  53. Rotate(E, 180°, I) → E'_2
  54. Rotate(L, 180°, I) → L'_2
  55. Rotate(T, 180°, I) → T'_1
  56. Rotate(F_1, 180°, I) → Z
  57. Rotate(C_1, 180°, I) → E_1
  58. Rotate(A_1, 180°, I) → G_1
  59. Rotate(B_1, 180°, I) → H_1
  60. Rotate(I, 180°, I) → I'_1
  61. Rotate(D_1, 180°, I) → I_1
  62. Rotate(O, 180°, I) → O'_1
  63. Rotate(R, 180°, I) → R'_1
  64. Rotate(S, 180°, I) → S'_1
  65. Rotate(M, 180°, I) → M'_1
  66. Rotate(J, 180°, I) → J'_1
  67. Rotate(F, 180°, I) → F'_1
  68. Rotate(D, 180°, I) → D'_2
  69. Polygon(E'_2, L'_2, R'_1, S'_1, M'_1, J'_1, F'_1, D'_2, T'_1, Z, E_1, G_1, H_1, I'_1, I_1, O'_1) → poly2'_1, e'_2, o'_1, r'_1, s'_1, m'_1, j'_1, f'_1, d'_2, l'_2, t'_1, z_1, e_1, g_2, h_2, i'_1, i_2
  70. Rotate(E'_1, 180°, I) → J_1
  71. Rotate(L'_1, 180°, I) → K_1
  72. Rotate(T', 180°, I) → T''
  73. Rotate(P, 180°, I) → P'
  74. Rotate(Q, 180°, I) → Q'
  75. Rotate(U, 180°, I) → U'
  76. Rotate(V, 180°, I) → V'
  77. Rotate(I', 180°, I) → I''
  78. Rotate(W, 180°, I) → W'
  79. Rotate(O', 180°, I) → O''
  80. Rotate(R', 180°, I) → R''
  81. Rotate(S', 180°, I) → S''
  82. Rotate(M', 180°, I) → M''
  83. Rotate(J', 180°, I) → J''
  84. Rotate(F', 180°, I) → F''
  85. Rotate(D'_1, 180°, I) → L_1
  86. Polygon(J_1, K_1, R'', S'', M'', J'', F'', L_1, T'', P', Q', U', V', I'', W', O'') → poly2'', j_2, o'', r'', s'', m'', j'', f'', l_2, k_2, t'', p', q', u', v', i'', w'
  87. Translate(J_1, v) → M_1
  88. Translate(K_1, v) → O_1
  89. Translate(T'', v) → T'''
  90. Translate(P', v) → P''
  91. Translate(Q', v) → Q''
  92. Translate(U', v) → U''
  93. Translate(V', v) → V''
  94. Translate(I'', v) → I'''
  95. Translate(W', v) → W''
  96. Translate(O'', v) → O'''
  97. Translate(R'', v) → R'''
  98. Translate(S'', v) → S'''
  99. Translate(M'', v) → M'''
  100. Translate(J'', v) → J'''
  101. Translate(F'', v) → F'''
  102. Translate(L_1, v) → Q_1
  103. Polygon(M_1, O_1, R''', S''', M''', J''', F''', Q_1, T''', P'', Q'', U'', V'', I''', W'', O''') → poly2''', m_2, o''', r''', s''', m''', j''', f''', q_3, o_1, t''', p'', q'', u'', v'', i''', w''
  104. Translate(E'_2, u) → R_1
  105. Translate(L'_2, u) → S_1
  106. Translate(T'_1, u) → T_1
  107. Translate(Z, u) → Z'
  108. Translate(E_1, u) → U_1
  109. Translate(G_1, u) → V_1
  110. Translate(H_1, u) → W_1
  111. Translate(I'_1, u) → A_2
  112. Translate(I_1, u) → B_2
  113. Translate(O'_1, u) → C_2
  114. Translate(R'_1, u) → D_2
  115. Translate(S'_1, u) → E_2
  116. Translate(M'_1, u) → F_2
  117. Translate(J'_1, u) → G_2
  118. Translate(F'_1, u) → H_2
  119. Translate(D'_2, u) → I_2
  120. Translate(E'_2, Vector[(-u)]) → J_2
  121. Translate(L'_2, Vector[(-u)]) → K_2
  122. Translate(T'_1, Vector[(-u)]) → L_2
  123. Translate(Z, Vector[(-u)]) → Z'_1
  124. Translate(E_1, Vector[(-u)]) → M_2
  125. Translate(G_1, Vector[(-u)]) → N_2
  126. Translate(H_1, Vector[(-u)]) → O_2
  127. Translate(I'_1, Vector[(-u)]) → P_2
  128. Translate(I_1, Vector[(-u)]) → Q_2
  129. Translate(O'_1, Vector[(-u)]) → R_2
  130. Translate(R'_1, Vector[(-u)]) → S_2
  131. Translate(S'_1, Vector[(-u)]) → T_2
  132. Translate(M'_1, Vector[(-u)]) → U_2
  133. Translate(J'_1, Vector[(-u)]) → V_2
  134. Translate(F'_1, Vector[(-u)]) → W_2
  135. Translate(D'_2, Vector[(-u)]) → Z_2
  136. Polygon(J_2, K_2, S_2, T_2, U_2, V_2, W_2, Z_2, L_2, Z'_1, M_2, N_2, O_2, P_2, Q_2, R_2) → poly3, j_3, r_2, s_2, t_2, u_2, v_2, w_2, z_2, k_3, l_3, z'_1, m_3, n_2, o_2, p_3, q_4
  137. Translate(E'_1, Vector[(-v)]) → A_3
  138. Translate(L'_1, Vector[(-v)]) → B_3
  139. Translate(T', Vector[(-v)]) → T''_1
  140. Translate(P, Vector[(-v)]) → P'_1
  141. Translate(Q, Vector[(-v)]) → Q'_1
  142. Translate(U, Vector[(-v)]) → U'_1
  143. Translate(V, Vector[(-v)]) → V'_1
  144. Translate(I', Vector[(-v)]) → I''_1
  145. Translate(W, Vector[(-v)]) → W'_1
  146. Translate(O', Vector[(-v)]) → O''_1
  147. Translate(R', Vector[(-v)]) → R''_1
  148. Translate(S', Vector[(-v)]) → S''_1
  149. Translate(M', Vector[(-v)]) → M''_1
  150. Translate(J', Vector[(-v)]) → J''_1
  151. Translate(F', Vector[(-v)]) → F''_1
  152. Translate(D'_1, Vector[(-v)]) → C_3
  153. Polygon(A_3, B_3, R''_1, S''_1, M''_1, J''_1, F''_1, C_3, T''_1, P'_1, Q'_1, U'_1, V'_1, I''_1, W'_1, O''_1) → poly2''_1, a_3, o''_1, r''_1, s''_1, m''_1, j''_1, f''_1, c_3, b_3, t''_1, p'_1, q'_1, u'_1, v'_1, i''_1, w'_1
  154. Translate(E, u) → E'_3
  155. Translate(L, u) → L'_3
  156. Translate(T, u) → T'_2
  157. Translate(F_1, u) → D_3
  158. Translate(C_1, u) → E_3
  159. Translate(A_1, u) → F_3
  160. Translate(B_1, u) → G_3
  161. Translate(I, u) → I'_2
  162. Translate(D_1, u) → H_3
  163. Translate(O, u) → O'_2
  164. Translate(R, u) → R'_2
  165. Translate(S, u) → S'_2
  166. Translate(M, u) → M'_2
  167. Translate(J, u) → J'_2
  168. Translate(F, u) → F'_2
  169. Translate(D, u) → D'_3
  170. Polygon(E'_3, L'_3, R'_2, S'_2, M'_2, J'_2, F'_2, D'_3, T'_2, D_3, E_3, F_3, G_3, I'_2, H_3, O'_2) → poly2'_2, e'_3, o'_2, r'_2, s'_2, m'_2, j'_2, f'_2, d'_3, l'_3, t'_2, d_3, e_3, f_3, g_3, i'_2, h_3
  171. Prism(poly2''', 8) → a, I_3, R_3, S_3, T_3, U_3, V_3, W_3, Z_3, face1, face3, face4, J_3, face5, face6, face7, face8, face9, face10, face11, face12, face13, face14, K_3, face15, face16, face2, face17, edge1, edge2, edge3, edge4, edge5, edge6, L_3, edge7, edge8, edge9, edge10, edge11, edge12, edge13, edge14, edge15, edge16, M_3, edge17, edge19, edge20, edge21, edge22, edge23, edge24, edge25, edge26, edge27, N_3, edge28, edge29, edge30, edge31, edge32, edge18, O_3, P_3, Q_3
  172. Prism(poly3, 8) → b, A_4, J_4, K_4, L_4, M_4, N_4, O_4, P_4, face18, face20, face21, B_4, face22, face23, face24, face25, face26, face27, face28, face29, face30, face31, C_4, face32, face33, face19, face34, edge33, edge34, edge35, edge36, edge37, edge38, D_4, edge39, edge40, edge41, edge42, edge43, edge44, edge45, edge46, edge47, edge48, E_4, edge49, edge51, edge52, edge53, edge54, edge55, edge56, edge57, edge58, edge59, F_4, edge60, edge61, edge62, edge63, edge64, edge50, G_4, H_4, I_4
  173. Prism(poly2''_1, 8) → c, Q_4, B_5, C_5, D_5, E_5, F_5, G_5, H_5, face35, face37, face38, R_4, face39, face40, face41, face42, face43, face44, face45, face46, face47, face48, S_4, face49, face50, face36, face51, edge65, edge66, edge67, edge68, edge69, edge70, T_4, edge71, edge72, edge73, edge74, edge75, edge76, edge77, edge78, edge79, edge80, U_4, edge81, edge83, edge84, edge85, edge86, edge87, edge88, edge89, edge90, edge91, V_4, edge92, edge93, edge94, edge95, edge96, edge82, W_4, Z_4, A_5
  174. Prism(poly2'_2, 8) → d, I_5, R_5, S_5, T_5, U_5, V_5, W_5, Z_5, face52, face54, face55, J_5, face56, face57, face58, face59, face60, face61, face62, face63, face64, face65, K_5, face66, face67, face53, face68, edge97, edge98, edge99, edge100, edge101, edge102, L_5, edge103, edge104, edge105, edge106, edge107, edge108, edge109, edge110, edge111, edge112, M_5, edge113, edge115, edge116, edge117, edge118, edge119, edge120, edge121, edge122, edge123, N_5, edge124, edge125, edge126, edge127, edge128, edge114, O_5, P_5, Q_5

AI 绘图提示语参考

绘制一个立方体的四分之一部分重叠示例。首先在x轴和y轴的交点创建点A,然后在x轴上创建点B。以A、B为顶点构造一个四边形,接着找到四边形的中点E、F、H、I,并依次构造其他关键点和四边形。通过旋转和中点构造,最终形成一个复杂的重叠图形,包括多个四边形和圆。
以上提示语为根据原始绘图命令整理而来,仅供参考。