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宇宙之谜

宇宙之谜
几何画板及绘图内容加载中，请稍等……
2016-10-04 17:22
三角函数解析几何立体几何
所属专题 3D printing in the school can be cool
这个范例通过几何图形展示了宇宙学中的神秘现象。它涉及椭圆、正方形、直方图和二次函数等核心数学概念。通过使用GeoGebra命令如Point、Intersect、OrthogonalPlane等，构建了一个复杂的几何模型。适合高中及以上学生或教师使用，用于教学或探索数学与宇宙学的联系。

GeoGebra 命令及参数

  1. Point(yAxis) → A
  2. Intersect(xAxis, zAxis) → O
  3. OrthogonalPlane(O, zAxis) → a
  4. Sphere(O, A) → b
  5. Intersect(xAxis, b) → B', B
  6. Intersect(zAxis, b) → C, C'
  7. Octahedron(A, B, C) → c, D, faceCEF, faceDEF, edgeAC, edgeAB, edgeBC, edgeAF, edgeCF, edgeAD, edgeDF, edgeBD, E, edgeBE, edgeDE, edgeCE, edgeEF, F, faceABC, faceACF, faceADF, faceABD, faceBDE, faceBCE
  8. Centroid(faceABC) → G
  9. Sphere(O, G) → d
  10. Line(O, C) → f
  11. Line(O, A) → g
  12. Sphere(O, A) → h
  13. IntersectPath(a, h) → k
  14. IntersectPath(a, d) → p
  15. Point(f) → H
  16. Plane(H, a) → l
  17. PointIn(l) → I
  18. Rotate(I, 72°, H, l) → I'
  19. Angle(I, H, I', l) → α
  20. Sphere(I, I') → m
  21. Intersect(f, m) → J, K
  22. Icosahedron(I, J, I') → n, L, faceII'J, faceII'N, faceINP, faceILP, faceIJL, faceJLQ, faceJMQ, faceI'JM, faceI'MR, faceI'NR, M, faceMQT, faceMRT, faceRTU, faceNRU, faceQST, faceSTU, facePSU, faceNPU, faceLQS, faceLPS, N, edgeII', edgeIJ, edgeI'J, edgeIN, edgeI'N, edgeIP, edgeNP, edgeIL, edgeLP, edgeJL, P, edgeJQ, edgeLQ, edgeJM, edgeMQ, edgeI'M, edgeI'R, edgeMR, edgeNR, edgeMT, edgeQT, Q, edgeRT, edgeRU, edgeTU, edgeNU, edgeST, edgeQS, edgeSU, edgePU, edgePS, edgeLS, R, S, T, U
  23. Midpoint(J, U) → V
  24. Plane(V, l) → o
  25. Centroid(faceIJL) → I_1
  26. Sphere(V, I_1) → u
  27. Line(V, g) → q
  28. Intersect(q, u) → W, Z
  29. Line(A, Z) → r
  30. Intersect(f, r) → A_1
  31. Line(A_1, I) → s
  32. Line(A_1, I') → t
  33. Sphere(A_1, Distance[A_1, I] / ratioico) → w
  34. Intersect(s, w) → B_1, C_1
  35. Intersect(t, w) → D_1, E_1
  36. Sphere(A_1, Distance[A_1, J] / ratioico) → a_1
  37. Intersect(f, a_1) → F_1, G_1
  38. Icosahedron(E_1, C_1, G_1) → b_1, H_1, face1, face6, face8, face7, face2, face4, face5, face3, face9, face10, J_1, face13, face14, face19, face16, face18, face20, face17, face15, face12, face11, K_1, edge6, edge1, edge2, edge8, edge11, edge9, edge19, edge7, edge13, edge3, L_1, edge5, edge14, edge4, edge16, edge10, edge12, edge17, edge20, edge18, edge25, M_1, edge26, edge27, edge30, edge21, edge28, edge24, edge29, edge23, edge22, edge15, N_1, O_1, P_1, Q_1
  39. IntersectPath(a, b_1) → poly1, R_1, C_2, f_1, g_1, h_1, i_1, j_1, k_1, l_1, m_1, n_1, S_1, p_1, T_1, U_1, V_1, W_1, Z_1, A_2, B_2
  40. Sphere(O, L_1) → d_1
  41. IntersectPath(a, d_1) → e_1
  42. Intersect(g, e_1) → D_2, E_2
  43. PointIn(l) → F_2
  44. Rotate(F_2, 72°, H, l) → G_2
  45. Angle(F_2, H, G_2, l) → β
  46. Dodecahedron(F_2, G_2, l) → q_1, H_2, Q_2, R_2, S_2, T_2, U_2, V_2, W_2, Z_2, A_3, face21, I_2, face23, face22, face24, face25, face26, face30, face31, face27, face28, face29, J_2, face32, edge32, edge31, edge34, edge36, edge38, edge33, edge40, edge48, edge50, K_2, edge49, edge41, edge35, edge42, edge43, edge37, edge44, edge45, edge39, edge46, L_2, edge47, edge54, edge60, edge55, edge57, edge51, edge56, edge52, edge58, edge53, M_2, edge59, N_2, O_2, P_2
  47. Intersect(f, face32) → B_3
  48. Midpoint(B_3, H) → C_3
  49. Plane(C_3, l) → r_1
  50. Sphere(C_3, B_3) → s_1
  51. Line(C_3, g) → f_2
  52. Intersect(f_2, s_1) → D_3, E_3
  53. Line(D_2, E_3) → g_2
  54. Intersect(f, g_2) → F_3
  55. Plane(O_1, a) → u_1
  56. Line(F_3, F_2) → h_2
  57. Line(F_3, G_2) → i_2
  58. Intersect(h_2, u_1) → G_3
  59. Intersect(i_2, u_1) → H_3
  60. Dodecahedron(G_3, H_3, u_1) → v_1, I_3, R_3, S_3, T_3, U_3, V_3, W_3, Z_3, A_4, B_4, face33, J_3, face35, face34, face36, face37, face38, face42, face43, face39, face40, face41, K_3, face44, edge62, edge61, edge64, edge66, edge68, edge63, edge70, edge78, edge80, L_3, edge79, edge71, edge65, edge72, edge73, edge67, edge74, edge75, edge69, edge76, M_3, edge77, edge84, edge90, edge85, edge87, edge81, edge86, edge82, edge88, edge83, N_3, edge89, O_3, P_3, Q_3
  61. Sphere(O, L_3) → a_2
  62. PointIn(l) → C_4
  63. Rotate(C_4, 120°, H, l) → D_4
  64. Angle(C_4, H, D_4, l) → γ
  65. Polygon(C_4, D_4, 3, l) → poly2, j_2, k_2, l_2, E_4
  66. Point(Circle[Midpoint[C_4, D_4], (Distance[C_4, D_4] * sqrt(3) / 2), Segment[C_4, D_4]]) → F_4
  67. Tetrahedron(C_4, D_4, F_4) → c_2, G_4, edge96, edge95, face45, face47, face46, face48, edge92, edge91, edge94, edge93
  68. Centroid(face46) → H_4
  69. Centroid(face47) → I_4
  70. Segment(I_4, H) → m_2
  71. Midpoint(I_4, H) → J_4
  72. Midpoint(H, H_4) → K_4
  73. Segment(H, H_4) → n_2
  74. OrthogonalPlane(J_4, m_2) → d_2
  75. OrthogonalPlane(K_4, n_2) → e_2
  76. IntersectPath(e_2, d_2) → p_2
  77. Intersect(f, p_2) → L_4
  78. Sphere(L_4, H) → o_2
  79. Plane(L_4, l) → q_2
  80. Line(L_4, g) → r_2
  81. Intersect(g, a_2) → M_4, N_4
  82. Intersect(r_2, o_2) → O_4, P_4
  83. Line(P_4, N_4) → t_2
  84. Intersect(f, t_2) → Q_4
  85. Line(Q_4, C_4) → f_3
  86. Line(Q_4, D_4) → g_3
  87. Line(Q_4, F_4) → h_3
  88. Intersect(f, a_2) → R_4, S_4
  89. Plane(S_4, a) → u_2
  90. Intersect(f_3, u_2) → T_4
  91. Intersect(t_2, u_2) → U_4
  92. Intersect(h_3, u_2) → V_4
  93. Intersect(g_3, u_2) → W_4
  94. Point(Circle[Midpoint[W_4, V_4], (Distance[W_4, V_4] * sqrt(3) / 2), Segment[W_4, V_4]]) → Z_4
  95. Tetrahedron(W_4, V_4, Z_4) → v_2, A_5, edge102, edge99, face49, face52, face50, face51, edge100, edge97, edge98, edge101
  96. Sphere(O, A_5) → a_3
  97. Intersect(f, a_3) → B_5, C_5
  98. Intersect(xAxis, a_3) → D_5, E_5
  99. Intersect(yAxis, a_3) → F_5, G_5
  100. Plane(A_5, a) → b_3
  101. Plane(C_5, a) → c_3
  102. OrthogonalPlane(E_5, xAxis) → d_3
  103. OrthogonalPlane(D_5, xAxis) → e_3
  104. OrthogonalPlane(G_5, g) → i_3
  105. OrthogonalPlane(F_5, g) → j_3
  106. IntersectPath(b_3, j_3) → k_3
  107. IntersectPath(d_3, b_3) → l_3
  108. IntersectPath(i_3, b_3) → m_3
  109. IntersectPath(e_3, b_3) → n_3
  110. Intersect(l_3, m_3) → H_5
  111. Intersect(k_3, l_3) → I_5
  112. Intersect(m_3, n_3) → J_5
  113. OrthogonalLine(J_5, c_3) → p_3
  114. OrthogonalLine(H_5, c_3) → q_3
  115. Intersect(p_3, c_3) → K_5
  116. Intersect(q_3, c_3) → L_5
  117. Point(Circle[K_5, Distance[L_5, K_5], Segment[L_5, K_5]]) → M_5
  118. Cube(L_5, K_5, M_5) → o_3, N_5, face57, face58, edge106, edge103, edge104, edge108, edge107, edge110, edge112, edge111, O_5, edge105, edge113, edge109, edge114, P_5, Q_5, R_5, face53, face56, face54, face55
  119. Sphere(O, P_5) → s_3
  120. Intersect(f, s_3) → T_5, U_5
  121. IntersectPath(a, s_3) → c_4
  122. Segment(T_5, U_5) → f_4
  123. Sphere(U_5, ((w_3 * f_4)) / 5) → a_4
  124. Intersect(f, a_4) → S_5, W_5
  125. Plane(S_5, a) → v
  126. IntersectPath(v, s_3) → t_1
  127. IntersectPath(v, o_3) → poly3, V_5, Z_5, A_6, B_6, s_2, g_4, h_4, i_4
  128. IntersectPath(v, a_3) → d_4
  129. IntersectPath(v, v_2) → poly4, C_6, D_6, E_6, j_4, k_4, l_4
  130. IntersectPath(v, a_2) → e_4
  131. IntersectPath(v, v_1) → poly5, F_6, O_6, m_4, n_4, p_4, q_4, r_4, s_4, t_4, b_4, f_5, G_6, g_5, H_6, I_6, J_6, K_6, L_6, M_6, N_6
  132. IntersectPath(v, d_1) → c_5
  133. IntersectPath(v, b_1) → poly6, P_6, A_7, h_5, i_5, j_5, k_5, l_5, m_5, n_5, p_5, q_5, Q_6, r_5, R_6, S_6, T_6, U_6, V_6, W_6, Z_6
  134. IntersectPath(v, h) → d_5
  135. IntersectPath(v, c) → poly7, B_7, C_7, D_7, E_7, s_5, t_5, a_5, b_5
  136. IntersectPath(v, d) → e_5

AI 绘图提示语参考

这是一个基于几何形状的复杂模型，展示宇宙学中的神秘现象。模型包含中心点O、垂直平面a、球体b、椭球体c等关键对象。通过相交、球体构造和椭球体生成等步骤，这些对象相互关联，形成一个多面体结构。构造顺序从确定中心点开始，依次构建平面、球体和椭球体，最终形成复杂的几何图形，适合用于教学和探索数学与宇宙的连接。
以上提示语为根据原始绘图命令整理而来，仅供参考。