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立方体组合4：随机过程与体积演示

立方体组合4：随机过程与体积演示
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2017-10-31 05:48
多边形函数立体几何概率统计几何作图
①本范例通过GeoGebra构建多个立方体（Cube）及其组合，直观展示立体几何中立方体、长方体（Cuboid）的构造与体积关系，并融入随机过程（Stochastic Process）概念，可能用于模拟随机堆叠或体积变化。②核心数学概念包括立方体与长方体的几何性质、体积计算、函数关系以及随机过程的基本思想，涉及点、面、棱的坐标定义与空间关系。③作图要点：从构造摘要可见，使用了Point命令定义点A、B、C等，Cube命令生成立方体，并创建了多个面（如faceABCD、faceADHE等）和棱（如edgeAD、edgeAB等），还定义了辅助点I、J、K、L、M、N及面faceCDJI等，形成组合体；对象包括a、b等变量，可能用于控制尺寸或随机参数。④适合中学高年级或大学低年级学生，用于立体几何教学、体积概念理解，以及结合随机过程的数学建模演示，也可作为GeoGebra动态几何作图的进阶案例。

GeoGebra 命令及参数

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD_1, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  3. Point(Circle[C, Distance[D, C], Segment[D, C]]) → I
  4. Cube(D, C, I) → b, J, faceIJNM, faceKLMN, edgeDJ, edgeCD, edgeCI, edgeIJ, edgeDK, edgeJN, edgeKN, edgeKL, K, edgeCL, edgeLM, edgeIM, edgeMN, L, M, N, faceCDJI, faceDJNK, faceCDKL, faceCIML
  5. Point(Circle[P, Distance[O, P], Segment[O, P]]) → Q
  6. Cube(O, P, Q) → c, R, faceQRVU, faceSTUV, edgeOR, edgeOP, edgePQ, edgeQR, edgeOS, edgeRV, edgeSV, edgeST, S, edgePT, edgeTU, edgeQU, edgeUV_1, T, U, V, faceOPQR, faceORVS, faceOPTS, facePQUT
  7. Point(Circle[U, Distance[V, U], Segment[V, U]]) → W
  8. Cube(V, U, W) → d, Z, face4, face5, edgeVZ, edgeUV, edgeUW, edgeWZ, edge2, edge4, edge6, edge5, A_1, edge1, edge7, edge3, edge8, B_1, C_1, D_1, faceUVZW, face3, face1, face2
  9. Point(Circle[B_1, Distance[A_1, B_1], Segment[A_1, B_1]]) → E_1
  10. Cube(A_1, B_1, E_1) → e, F_1, face10, face11, edge10, edge9, edge12, edge14, edge11, edge16, edge18, edge17, G_1, edge13, edge19, edge15, edge20, H_1, I_1, J_1, face6, face8, face7, face9
  11. Point(Circle[K_1, Distance[Q, K_1], Segment[Q, K_1]]) → L_1
  12. Cube(Q, K_1, L_1) → f, M_1, face16, face17, edge22, edge21, edge24, edge26, edge23, edge28, edge30, edge29, N_1, edge25, edge31, edge27, edge32, O_1, P_1, Q_1, face12, face14, face13, face15
  13. Point(Circle[R_1, Distance[K_1, R_1], Segment[K_1, R_1]]) → S_1
  14. Cube(K_1, R_1, S_1) → g, T_1, face22, face23, edge34, edge33, edge36, edge38, edge35, edge40, edge42, edge41, U_1, edge37, edge43, edge39, edge44, V_1, W_1, Z_1, face18, face20, face19, face21
  15. Point(Circle[V_1, Distance[U_1, V_1], Segment[U_1, V_1]]) → A_2
  16. Cube(U_1, V_1, A_2) → h, B_2, face28, face29, edge46, edge45, edge48, edge50, edge47, edge52, edge54, edge53, C_2, edge49, edge55, edge51, edge56, D_2, E_2, F_2, face24, face26, face25, face27
  17. Point(Circle[H_2, Distance[G_2, H_2], Segment[G_2, H_2]]) → I_2
  18. Cube(G_2, H_2, I_2) → i, J_2, face34, face35, edge58, edge57, edge60, edge62, edge59, edge64, edge66, edge65, K_2, edge61, edge67, edge63, edge68, L_2, M_2, N_2, face30, face32, face31, face33