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立方体构造与属性演示

立方体构造与属性演示
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2017-10-31 05:42
向量立体几何几何作图
①本范例通过 GeoGebra 构造了一个立方体，并展示了其顶点、棱、面等几何元素；②涉及的核心数学概念包括立体几何、空间几何关系、几何作图；③作图要点提炼自构造摘要，使用了 Point（点）、Cube（立方体）、edge（棱）、face（面）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，也可用于相关课题的辅助教学演示。

GeoGebra 命令及参数

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. Point(Circle[V, Distance[U, V], Segment[U, V]]) → W
  3. Point(Circle[F_1, Distance[E_1, F_1], Segment[E_1, F_1]]) → G_1
  4. Point(Circle[N_1, Distance[M_1, N_1], Segment[M_1, N_1]]) → O_1
  5. Point(Circle[E, Distance[D, E], Segment[D, E]]) → F
  6. Cube(D, E, F) → a, G, faceFGKJ, faceHIJK, edgeDG, edgeDE, edgeEF, edgeFG, edgeDH, edgeGK, edgeHK, edgeHI, H, edgeEI, edgeIJ, edgeFJ, edgeJK, I, J, K, faceDEFG, faceDGKH, faceDEIH, faceEFJI
  7. Point(Circle[M, Distance[L, M], Segment[L, M]]) → N
  8. Cube(L, M, N) → b, O, faceNOSR, facePQRS, edgeLO, edgeLM, edgeMN, edgeNO, edgeLP, edgeOS, edgePS, edgePQ, P, edgeMQ, edgeQR, edgeNR, edgeRS, Q, R, S, faceLMNO, faceLOSP, faceLMQP, faceMNRQ
  9. Point(Circle[Z, Distance[T, Z], Segment[T, Z]]) → A_1
  10. Cube(T, Z, A_1) → c, B_1, face5, face6, edge1, edgeTZ, edge3, edge5, edge2, edge7, edge9, edge8, C_1, edge4, edge10, edge6, edge11, D_1, H_1, I_1, face1, face3, face2, face4
  11. Point(Circle[D_1, Distance[C_1, D_1], Segment[C_1, D_1]]) → J_1
  12. Cube(C_1, D_1, J_1) → d, K_1, face11, face12, edge13, edge12, edge15, edge17, edge14, edge19, edge21, edge20, L_1, edge16, edge22, edge18, edge23, P_1, Q_1, R_1, face7, face9, face8, face10
  13. Point(Circle[P_1, Distance[L_1, P_1], Segment[L_1, P_1]]) → S_1
  14. Cube(L_1, P_1, S_1) → e, T_1, face17, face18, edge25, edge24, edge27, edge29, edge26, edge31, edge33, edge32, U_1, edge28, edge34, edge30, edge35, V_1, W_1, Z_1, face13, face15, face14, face16
  15. Point(Circle[T, Distance[A_2, T], Segment[A_2, T]]) → B_2
  16. Cube(A_2, T, B_2) → f, C_2, face23, face24, edge39, edge36, edge37, edge41, edge40, edge43, edge45, edge44, D_2, edge38, edge46, edge42, edge47, E_2, F_2, G_2, face19, face22, face20, face21
  17. Point(edgeDG) → I_2
  18. Point(Circle[I_2, Distance[H_2, I_2], Segment[H_2, I_2]]) → J_2
  19. Cube(H_2, I_2, J_2) → g, K_2, face29, face30, edge49, edge48, edge51, edge53, edge50, edge55, edge57, edge56, L_2, edge52, edge58, edge54, edge59, M_2, N_2, O_2, face25, face27, face26, face28