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立方体构造与表面演示

立方体构造与表面演示
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2017-10-31 05:45
多边形立体几何几何作图
①本范例通过动态演示立方体的构造过程及其表面展开，直观展示三维几何图形的生成与分解；②涉及的核心数学概念包括立体几何、多边形表面、向量运算与空间坐标；③作图要点提炼自构造摘要，主要运用了Point（点）、Cube（立方体）、face（面）、edge（边）等GeoGebra命令与对象，实现了立方体及其表面的精确构建与交互；④适合高中及以上学段学生及数学爱好者学习立体几何构造、空间想象与几何作图技巧。

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_1, edgeDK, edgeJN, edgeKN, edgeKL, K, edgeCL, edgeLM, edgeIM, edgeMN, L, M, N, faceCDJI, faceDJNK, faceCDKL, faceCIML
  5. Point(Circle[I, Distance[J, I], Segment[J, I]]) → O
  6. Cube(J, I, O) → c, P, faceOPTS, faceQRST, edgeJP, edgeIJ, edgeIO, edgeOP_1, edgeJQ, edgePT, edgeQT, edgeQR, Q, edgeIR, edgeRS, edgeOS, edgeST, R, S, T, faceIJPO, faceJPTQ, faceIJQR, faceIOSR
  7. Point(Circle[O, Distance[P, O], Segment[P, O]]) → U
  8. Cube(P, O, U) → d, V, face3, face4, edgePV, edgeOP, edgeOU, edgeUV, edgePW, edge2, edge3, edgeWZ, W, edgeOZ, edge4, edge1, edge5, Z, A_1, B_1, faceOPVU, face2, faceOPWZ, face1
  9. Point(Circle[D_1, Distance[C_1, D_1], Segment[C_1, D_1]]) → E_1
  10. Cube(C_1, D_1, E_1) → e, F_1, face9, face10, edge7, edge6, edge9, edge11, edge8, edge13, edge15, edge14, G_1, edge10, edge16, edge12, edge17, H_1, I_1, J_1, face5, face7, face6, face8
  11. Point(Circle[E_1, Distance[K_1, E_1], Segment[K_1, E_1]]) → L_1
  12. Cube(K_1, E_1, L_1) → f, M_1, face15, face16, edge21, edge18, edge19, edge23, edge22, edge25, edge27, edge26, N_1, edge20, edge28, edge24, edge29, O_1, P_1, Q_1, face11, face14, face12, face13
  13. Point(Circle[G_1, Distance[P_1, G_1], Segment[P_1, G_1]]) → R_1
  14. Cube(P_1, G_1, R_1) → g, S_1, face21, face22, edge33, edge30, edge31, edge35, edge34, edge37, edge39, edge38, T_1, edge32, edge40, edge36, edge41, U_1, V_1, W_1, face17, face20, face18, face19
  15. Point(Circle[J_1, Distance[O_1, J_1], Segment[O_1, J_1]]) → Z_1
  16. Cube(O_1, J_1, Z_1) → h, A_2, face27, face28, edge45, edge42, edge43, edge47, edge46, edge49, edge51, edge50, B_2, edge44, edge52, edge48, edge53, C_2, D_2, E_2, face23, face26, face24, face25
  17. Point(Circle[Z, Distance[R, Z], Segment[R, Z]]) → F_2
  18. Cube(R, Z, F_2) → i, G_2, face33, face34, edge54, edgeRZ, edge56, edge58, edge55, edge60, edge62, edge61, H_2, edge57, edge63, edge59, edge64, I_2, J_2, K_2, face29, face31, face30, face32
  19. Point(Circle[C_2, Distance[B_2, C_2], Segment[B_2, C_2]]) → L_2
  20. Cube(B_2, C_2, L_2) → j, M_2, face39, face40, edge66, edge65, edge68, edge70, edge67, edge72, edge74, edge73, N_2, edge69, edge75, edge71, edge76, O_2, P_2, Q_2, face35, face37, face36, face38