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立方体构造演示 by cicilia intan

立方体构造演示 by cicilia intan
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2016-12-20 02:50
解析几何立体几何几何作图
①本范例演示了如何使用 GeoGebra 构造一个立方体及其各个面、边和顶点；②涉及的核心数学概念包括立体几何、点、线、面关系、坐标几何；③作图要点——从下方『构造摘要』提炼用到了 Intersect（相交）、Point（点）、Cube（立方体）等 GeoGebra 命令/对象；④适合高中及以上学生学习和理解立体几何图形的构成与性质。

GeoGebra 命令及参数

  1. Intersect(xAxis, zAxis) → A
  2. Point(xAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD_1, edgeAE, edgeDH, edgeEH, edgeEF_1, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Point(xAxis) → I
  6. Point(Circle[I, Distance[B, I], Segment[B, I]]) → J
  7. Cube(B, I, J) → b, K, faceJKON, faceLMNO, edgeBK, edgeBI, edgeIJ, edgeJK, edgeBL, edgeKO, edgeLO, edgeLM, L, edgeIM, edgeMN, edgeJN, edgeNO, M, N, O, faceBIJK, faceBKOL, faceBIML, faceIJNM
  8. Point(Circle[C, Distance[D, C], Segment[D, C]]) → P
  9. Cube(D, C, P) → c, Q, facePQUT, faceRSTU, edgeDQ, edgeCD, edgeCP, edgePQ, edgeDR, edgeQU, edgeRU, edgeRS, R, edgeCS, edgeST, edgePT, edgeTU, S, T, U, faceCDQP, faceDQUR, faceCDRS, faceCPTS
  10. Point(Circle[J, Distance[C, J], Segment[C, J]]) → V
  11. Cube(C, J, V) → d, W, face4, face5, edgeCW, edgeCJ, edgeJV, edgeVW, edgeCZ, edge3, edge5, edge4, Z, edge1, edge6, edge2, edge7, A_1, B_1, C_1, faceCJVW, face2, face1, face3
  12. Point(Circle[F, Distance[E, F], Segment[E, F]]) → D_1
  13. Cube(E, F, D_1) → e, E_1, face10, face11, edge8, edgeEF, edge10, edge12, edge9, edge14, edge16, edge15, F_1, edge11, edge17, edge13, edge18, G_1, H_1, I_1, face6, face8, face7, face9
  14. Point(Circle[M, Distance[F, M], Segment[F, M]]) → J_1
  15. Cube(F, M, J_1) → f, K_1, face16, face17, edge19, edgeFM, edge21, edge23, edge20, edge25, edge27, edge26, L_1, edge22, edge28, edge24, edge29, M_1, N_1, O_1, face12, face14, face13, face15
  16. Point(Circle[D_1, Distance[H, D_1], Segment[H, D_1]]) → P_1
  17. Cube(H, D_1, P_1) → g, Q_1, face22, face23, edge31, edge30, edge33, edge35, edge32, edge37, edge39, edge38, R_1, edge34, edge40, edge36, edge41, S_1, T_1, U_1, face18, face20, face19, face21
  18. Point(Circle[J_1, Distance[D_1, J_1], Segment[D_1, J_1]]) → V_1
  19. Cube(D_1, J_1, V_1) → h, W_1, face28, face29, edge43, edge42, edge45, edge47, edge44, edge49, edge51, edge50, Z_1, edge46, edge52, edge48, edge53, A_2, B_2, C_2, face24, face26, face25, face27
  20. Point(Circle[V, Distance[I, V], Segment[I, V]]) → D_2
  21. Cube(I, V, D_2) → i, E_2, face34, face35, edge54, edgeIV, edge56, edge58, edge55, edge60, edge62, edge61, F_2, edge57, edge63, edge59, edge64, G_2, H_2, I_2, face30, face32, face31, face33

AI 绘图提示语参考

在三维空间中，从坐标原点出发，沿x轴取一系列点，并以每个点为基准，利用相邻点构造正方形，进而生成多个立方体。这些立方体沿x轴方向依次排列，彼此共享边或顶点，形成一条连续的立方体链。每个立方体都清晰展示其六个面、十二条棱和八个顶点，整体呈现为立体几何的构造演示，强调点、线、面之间的空间关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。