Minecraft球体

Minecraft球体
几何画板及绘图内容加载中,请稍等……
2014-09-14 10:12
①这个范例演示了如何在三维空间中构建一个球体,并展示其基本属性;②涉及的核心数学概念包括立体几何、三维图形的构造、坐标几何等;③作图要点——从下方『构造摘要』提炼用到了哪些 GeoGebra 命令/对象:Intersect(交集)、Circle(圆)、Polygon(多边形)、Point(点)、Mirror(镜像);④适合的学段或用途:高中数学立体几何教学、几何作图练习、三维图形可视化。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 7) → c
  3. Circle(A, 9.8) → d
  4. Circle(A, 11.9) → e
  5. Circle(A, 13.6) → f
  6. Circle(A, 15) → g
  7. Circle(A, 16.2) → h
  8. Circle(A, 17.3) → k
  9. Circle(A, 18.3) → p
  10. Circle(A, 19.2) → q
  11. Circle(A, 20) → r
  12. Circle(A, 20.7) → s
  13. Circle(A, 21.4) → t
  14. Polygon(C, D, E, F) → poly1, c_1, d_1, e_1, f_1
  15. Point(c) → P
  16. Point(c) → A_1
  17. Intersect(c, yAxis, 1) → F_1
  18. Point(c) → K_1
  19. Point(c) → T_1
  20. Intersect(c, yAxis, 2) → B_2
  21. Point(c) → F_2
  22. Intersect(c, xAxis, 1) → K_2
  23. Point(c) → P_2
  24. Point(c) → U_2
  25. Point(c) → Z_2
  26. Polygon(B_2, C_2, K_2, L_2, M_2, N_2, O_2, P_2, Q_2, R_2, S_2, T_2, L, U_2, V_2, W_2, Z_2, A_3, K_1, B_3, C_3, D_3, E_3, D_2, F_3, G_3, H_3, I_3, J_3, K_3, L_3, M_3, N_3, E_2, F_2, G_2, H_2, I_2, J_2) → poly2, b_2, j_2, k_2, l_2, m_2, n_2, o_2, p_2, q_2, r_2, s_2, c_2, t_2, u_2, v_2, w_2, z_2, a_3, k_1, b_3, c_3, d_3, l, e_3, f_3, g_3, h_3, i_3, j_3, k_3, l_3, m_3, n_3, d_2, e_2, f_2, g_2, h_2, i_2
  27. Point(yAxis) → O_3
  28. Intersect(c, e_2, 1) → S_3
  29. Intersect(c, i_3, 1) → T_3
  30. Polygon(R_3, S_3, T_3, U_3, V_3, W_3, P_3, Q_3) → poly3, r_3, s_3, t_3, u_3, v_3, w_3, p_3, q_3
  31. Intersect(c, a_3, 1) → Z_3
  32. Polygon(T_3, Z_3, A_4, B_4, C_4, D_4, E_4, F_4) → poly4, t_1, z_3, a_4, b_4, c_4, d_4, e_4, f_4
  33. Intersect(c, o_2, 1) → G_4
  34. Polygon(Z_3, G_4, H_4, I_4, J_4, K_4, L_4, M_4) → poly5, z_1, g_4, h_4, i_4, j_4, k_4, l_4, m_4
  35. Polygon(G_4, S_3, N_4, O_4, P_4, Q_4, R_4, S_4) → poly6, g_1, s_1, n_4, o_4, p_4, q_4, r_4, s_4
  36. Point(r_3) → T_4
  37. Point(s_1) → B_5
  38. Polygon(T_4, U_4, V_4, W_4, Z_4, A_5, B_5, S_3) → poly7, t_4, u_4, v_4, w_4, z_4, a_5, b_5, s_5
  39. Point(s_4) → C_5
  40. Point(d) → F_5
  41. Point(g_4) → I_5
  42. Polygon(C_5, D_5, E_5, F_5, G_5, H_5, I_5, G_4) → poly8, c_5, d_5, e_5, f_5, g_5, h_5, i_5, g_6
  43. Point(d) → M_5
  44. Point(d) → O_5
  45. Point(m_4) → P_5
  46. Polygon(Z_3, J_5, K_5, L_5, M_5, N_5, O_5, P_5) → poly9, z_5, j_5, k_5, l_5, m_5, n_5, o_5, p_5
  47. Point(t_3) → Q_5
  48. Point(d) → V_5
  49. Polygon(Q_5, T_3, R_5, S_5, T_5, U_5, V_5) → poly10, q_5, t_5, r_5, s_6, t_6, u_5, v_5
  50. Point(yAxis) → W_5
  51. Point(e) → I_6
  52. Point(yAxis) → J_6
  53. Polygon(W_5, Z_5, I_6, J_6, A_6, B_6, C_6, D_6, E_6, F_6, G_6, H_6) → poly11, w_5, h_6, i_6, j_6, z_6, a_6, b_6, c_6, d_6, e_6, f_6, g_7
  54. Mirror(W_5, a) → K_6
  55. Mirror(Z_5, a) → L_6
  56. Mirror(A_6, a) → M_6
  57. Mirror(B_6, a) → N_6
  58. Mirror(C_6, a) → O_6
  59. Mirror(D_6, a) → P_6
  60. Mirror(E_6, a) → Q_6
  61. Mirror(F_6, a) → R_6
  62. Mirror(G_6, a) → S_6
  63. Mirror(H_6, a) → T_6
  64. Mirror(I_6, a) → U_6
  65. Mirror(J_6, a) → V_6
  66. Polygon(K_6, L_6, U_6, V_6, M_6, N_6, O_6, P_6, Q_6, R_6, S_6, T_6) → poly11', k_6, t_7, u_6, v_6, l_6, m_6, n_6, o_6, p_6, q_6, r_6, s_7
  67. Mirror(W_5, yAxis) → W_6
  68. Mirror(Z_5, yAxis) → Z_6
  69. Mirror(A_6, yAxis) → A_7
  70. Mirror(B_6, yAxis) → B_7
  71. Mirror(C_6, yAxis) → C_7
  72. Mirror(D_6, yAxis) → D_7
  73. Mirror(E_6, yAxis) → E_7
  74. Mirror(F_6, yAxis) → F_7
  75. Mirror(G_6, yAxis) → G_7
  76. Mirror(H_6, yAxis) → H_7
  77. Mirror(I_6, yAxis) → I_7
  78. Mirror(J_6, yAxis) → J_7
  79. Polygon(W_6, Z_6, I_7, J_7, A_7, B_7, C_7, D_7, E_7, F_7, G_7, H_7) → poly11'_1, w_6, h_7, i_7, j_7, z_7, a_7, b_7, c_7, d_7, e_7, f_7, g_8
  80. Mirror(K_6, yAxis) → K_7
  81. Mirror(L_6, yAxis) → L_7
  82. Mirror(M_6, yAxis) → M_7
  83. Mirror(N_6, yAxis) → N_7
  84. Mirror(O_6, yAxis) → O_7
  85. Mirror(P_6, yAxis) → P_7
  86. Mirror(Q_6, yAxis) → Q_7
  87. Mirror(R_6, yAxis) → R_7
  88. Mirror(S_6, yAxis) → S_7
  89. Mirror(T_6, yAxis) → T_7
  90. Mirror(U_6, yAxis) → U_7
  91. Mirror(V_6, yAxis) → V_7
  92. Polygon(K_7, L_7, U_7, V_7, M_7, N_7, O_7, P_7, Q_7, R_7, S_7, T_7) → poly11'', k_7, t_8, u_7, v_7, l_7, m_7, n_7, o_7, p_7, q_7, r_7, s_8
  93. Intersect(e, a, 1) → W_7
  94. Polygon(W_7, Z_7, A_8, B_8, C_8, D_8, E_8, U_7, T_7, F_8) → poly12, w_7, f_8, z_8, a_8, b_8, c_8, d_8, e_8, u_1, t_9
  95. Mirror(W_7, a) → G_8
  96. Mirror(Z_7, a) → H_8
  97. Mirror(A_8, a) → I_8
  98. Mirror(B_8, a) → J_8
  99. Mirror(C_8, a) → K_8
  100. Mirror(D_8, a) → L_8
  101. Mirror(E_8, a) → M_8
  102. Mirror(U_7, a) → N_8
  103. Mirror(T_7, a) → O_8
  104. Mirror(F_8, a) → P_8
  105. Polygon(G_8, H_8, I_8, J_8, K_8, L_8, M_8, N_8, O_8, P_8) → poly12', g_9, p_8, h_8, i_8, j_8, k_8, l_8, m_8, n_8, o_8
  106. Mirror(J_8, yAxis) → Q_8
  107. Mirror(G_8, yAxis) → R_8
  108. Mirror(H_8, yAxis) → S_8
  109. Mirror(I_8, yAxis) → T_8
  110. Mirror(J_8, yAxis) → U_8
  111. Mirror(K_8, yAxis) → V_8
  112. Mirror(L_8, yAxis) → W_8
  113. Mirror(M_8, yAxis) → Z_8
  114. Mirror(N_8, yAxis) → A_9
  115. Mirror(O_8, yAxis) → B_9
  116. Mirror(P_8, yAxis) → C_9
  117. Polygon(R_8, S_8, T_8, U_8, V_8, W_8, Z_8, A_9, B_9, C_9) → poly12'', r_8, c_9, s_9, t_{10}, u_8, v_8, w_8, z_9, a_9, b_9
  118. Mirror(R_8, a) → D_9
  119. Mirror(S_8, a) → E_9
  120. Mirror(T_8, a) → F_9
  121. Mirror(U_8, a) → G_9
  122. Mirror(V_8, a) → H_9
  123. Mirror(W_8, a) → I_9
  124. Mirror(Z_8, a) → J_9
  125. Mirror(A_9, a) → K_9
  126. Mirror(B_9, a) → L_9
  127. Mirror(C_9, a) → M_9
  128. Polygon(D_9, E_9, F_9, G_9, H_9, I_9, J_9, K_9, L_9, M_9) → poly12''', d_9, m_9, e_9, f_9, g_{10}, h_9, i_9, j_9, k_9, l_9
  129. Point(yAxis) → N_9
  130. Point(f) → Q_9
  131. Point(f) → V_9
  132. Point(f) → D_{10}
  133. Polygon(W_5, N_9, W_9, Z_9, A_{10}, B_{10}, C_{10}, D_{10}, E_{10}, F_{10}, G_{10}, H_{10}, O_9, I_{10}, J_{10}, K_{10}, L_{10}, M_{10}, P_9, Q_9, R_9, S_9, T_9, U_9, V_9) → poly13, w_1, v_9, w_9, z_{10}, a_{10}, b_{10}, c_{10}, d_{10}, e_{10}, f_{10}, g_{11}, n_9, h_{10}, i_{10}, j_{10}, k_{10}, l_{10}, m_{10}, o_9, p_9, q_9, r_9, s_{10}, t_{11}, u_9
  134. Mirror(W_5, a) → N_{10}
  135. Mirror(N_9, a) → O_{10}
  136. Mirror(O_9, a) → P_{10}
  137. Mirror(P_9, a) → Q_{10}
  138. Mirror(Q_9, a) → R_{10}
  139. Mirror(R_9, a) → S_{10}
  140. Mirror(S_9, a) → T_{10}
  141. Mirror(T_9, a) → U_{10}
  142. Mirror(U_9, a) → V_{10}
  143. Mirror(V_9, a) → W_{10}
  144. Mirror(W_9, a) → Z_{10}
  145. Mirror(Z_9, a) → A_{11}
  146. Mirror(A_{10}, a) → B_{11}
  147. Mirror(B_{10}, a) → C_{11}
  148. Mirror(C_{10}, a) → D_{11}
  149. Mirror(D_{10}, a) → E_{11}
  150. Mirror(E_{10}, a) → F_{11}
  151. Mirror(F_{10}, a) → G_{11}
  152. Mirror(G_{10}, a) → H_{11}
  153. Mirror(H_{10}, a) → I_{11}
  154. Mirror(I_{10}, a) → J_{11}
  155. Mirror(J_{10}, a) → K_{11}
  156. Mirror(K_{10}, a) → L_{11}
  157. Mirror(L_{10}, a) → M_{11}
  158. Mirror(M_{10}, a) → N_{11}
  159. Polygon(N_{10}, O_{10}, Z_{10}, A_{11}, B_{11}, C_{11}, D_{11}, E_{11}, F_{11}, G_{11}, H_{11}, I_{11}, P_{10}, J_{11}, K_{11}, L_{11}, M_{11}, N_{11}, Q_{10}, R_{10}, S_{10}, T_{10}, U_{10}, V_{10}, W_{10}) → poly13', n_{10}, w_{10}, z_{11}, a_{11}, b_{11}, c_{11}, d_{11}, e_{11}, f_{11}, g_{12}, h_{11}, o_{10}, i_{11}, j_{11}, k_{11}, l_{11}, m_{11}, n_{11}, p_{10}, q_{10}, r_{10}, s_{11}, t_{12}, u_{10}, v_{10}
  160. Mirror(N_{10}, yAxis) → O_{11}
  161. Mirror(O_{10}, yAxis) → P_{11}
  162. Mirror(P_{10}, yAxis) → Q_{11}
  163. Mirror(Q_{10}, yAxis) → R_{11}
  164. Mirror(R_{10}, yAxis) → S_{11}
  165. Mirror(S_{10}, yAxis) → T_{11}
  166. Mirror(T_{10}, yAxis) → U_{11}
  167. Mirror(U_{10}, yAxis) → V_{11}
  168. Mirror(V_{10}, yAxis) → W_{11}
  169. Mirror(W_{10}, yAxis) → Z_{11}
  170. Mirror(Z_{10}, yAxis) → A_{12}
  171. Mirror(A_{11}, yAxis) → B_{12}
  172. Mirror(B_{11}, yAxis) → C_{12}
  173. Mirror(C_{11}, yAxis) → D_{12}
  174. Mirror(D_{11}, yAxis) → E_{12}
  175. Mirror(E_{11}, yAxis) → F_{12}
  176. Mirror(F_{11}, yAxis) → G_{12}
  177. Mirror(G_{11}, yAxis) → H_{12}
  178. Mirror(H_{11}, yAxis) → I_{12}
  179. Mirror(I_{11}, yAxis) → J_{12}
  180. Mirror(J_{11}, yAxis) → K_{12}
  181. Mirror(K_{11}, yAxis) → L_{12}
  182. Mirror(L_{11}, yAxis) → M_{12}
  183. Mirror(M_{11}, yAxis) → N_{12}
  184. Mirror(N_{11}, yAxis) → O_{12}
  185. Polygon(O_{11}, P_{11}, A_{12}, B_{12}, C_{12}, D_{12}, E_{12}, F_{12}, G_{12}, H_{12}, I_{12}, J_{12}, Q_{11}, K_{12}, L_{12}, M_{12}, N_{12}, O_{12}, R_{11}, S_{11}, T_{11}, U_{11}, V_{11}, W_{11}, Z_{11}) → poly13'', o_{11}, z_{12}, a_{12}, b_{12}, c_{12}, d_{12}, e_{12}, f_{12}, g_{13}, h_{12}, i_{12}, p_{11}, j_{12}, k_{12}, l_{12}, m_{12}, n_{12}, o_{12}, q_{11}, r_{11}, s_{12}, t_{13}, u_{11}, v_{11}, w_{11}
  186. Mirror(O_{11}, a) → P_{12}
  187. Mirror(P_{11}, a) → Q_{12}
  188. Mirror(Q_{11}, a) → R_{12}
  189. Mirror(R_{11}, a) → S_{12}
  190. Mirror(S_{11}, a) → T_{12}
  191. Mirror(T_{11}, a) → U_{12}
  192. Mirror(U_{11}, a) → V_{12}
  193. Mirror(V_{11}, a) → W_{12}
  194. Mirror(W_{11}, a) → Z_{12}
  195. Mirror(Z_{11}, a) → A_{13}
  196. Mirror(A_{12}, a) → B_{13}
  197. Mirror(B_{12}, a) → C_{13}
  198. Mirror(C_{12}, a) → D_{13}
  199. Mirror(D_{12}, a) → E_{13}
  200. Mirror(E_{12}, a) → F_{13}
  201. Mirror(F_{12}, a) → G_{13}
  202. Mirror(G_{12}, a) → H_{13}
  203. Mirror(H_{12}, a) → I_{13}
  204. Mirror(I_{12}, a) → J_{13}
  205. Mirror(J_{12}, a) → K_{13}
  206. Mirror(K_{12}, a) → L_{13}
  207. Mirror(L_{12}, a) → M_{13}
  208. Mirror(M_{12}, a) → N_{13}
  209. Mirror(N_{12}, a) → O_{13}
  210. Mirror(O_{12}, a) → P_{13}
  211. Polygon(P_{12}, Q_{12}, B_{13}, C_{13}, D_{13}, E_{13}, F_{13}, G_{13}, H_{13}, I_{13}, J_{13}, K_{13}, R_{12}, L_{13}, M_{13}, N_{13}, O_{13}, P_{13}, S_{12}, T_{12}, U_{12}, V_{12}, W_{12}, Z_{12}, A_{13}) → poly13''', p_{12}, a_{13}, b_{13}, c_{13}, d_{13}, e_{13}, f_{13}, g_{14}, h_{13}, i_{13}, j_{13}, q_{12}, k_{13}, l_{13}, m_{13}, n_{13}, o_{13}, p_{13}, r_{12}, s_{13}, t_{14}, u_{12}, v_{12}, w_{12}, z_{13}

AI 绘图提示语参考

在三维空间中绘制一个球体,从中心点出发绘制多个不同半径的圆形,然后通过这些圆形的交点构建多个多边形,形成球体的表面网格,展示球体的基本几何特性和坐标几何关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。